Pulsed power

PULSED POWER PULSED POWER Gennady A. Mesyats Institute of High Current Electronics, Tomsk, and Institute of Electroph...

Author: Gennady A. Mesyats

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PULSED POWER

PULSED POWER

Gennady A. Mesyats Institute of High Current Electronics, Tomsk, and Institute of Electrophysics, Ekaterinburg Russian Academy of Sciences, Russia

Springer

Library of Congress Cataloging-in-Publication Data Mesiats, G. A. (Gennadii Andreevich) Pulsed power/by Gennady A. Mesyats. p. cm. Includes bibliographical references and index. ISBN 0-306-48653-9 (hardback) - ISBN 0-306-48654-7 (eBook) 1. Pulsed power systems. I. Title. TK2986.M47 2004 621.381534—dc22 2004051665 ISBN: 0-306-48653-9 (hardback) ISBN: 0-306-48654-7 (eBook) Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 10 9 8 7 6 5 4 3 2 springer.com

(SPI)

Contents

Preface PART 1.

xiii PULSED SYSTEMS: DESIGN PRINCIPLES

1

Chapter 1. LUMPED PARAMETER PULSE SYSTEMS 1. Principal schemes for pulse generation 2. Voltage multiplication and transformation References

3 3 6 12

Chapter 2. PULSE GENERATION USING LONG LINES 1. Generation of nanosecond pulses 2. Voltage multipUcation in line-based generators 3. Pulse systems with segmented and nonuniform lines References

13 13 19 22 25

PART 2.

PHYSICS OF PULSED ELECTRICAL DISCHARGES

Chapter 3. THE VACUUM DISCHARGE 1. General considerations 2. Vacuum breakdown 2.1 The electrode surface 2.2 Vacuum breakdown criteria 3. The ecton and its nature 4. The vacuum spark

27 29 29 30 30 32 36 40

vi

CONTENTS 5. The surface discharge in vacuum References

Chapter 4. THE PULSED DISCHARGE IN GAS 1. Elementary processes in gas-discharge plasmas 2. Types of discharge 2.1 The Townsend discharge. Paschen' s law 2.2 The streamer discharge 2.3 The multiavalanche pulsed discharge 2.4 Single-electron-initiated discharges 3. The spark current and the gap voltage drop 4. The discharge in gas with direct injection of electrons 4.1 Principal equations 4.2 The discharge column 4.3 Constriction of volume discharges 5. Recovery of the electric strength of a spark gap References

47 53 55 55 61 61 64 66 70 72 77 77 80 84 86 89

Chapter 5. ELECTRICAL DISCHARGES IN LIQUIDS 1. Background 2. The pulsed electric strength of liquid dielectrics 3. The electrical discharge in water 4. The role ofthe electrode surface 5. The role of the state of the liquid References

91 91 93 95 98 102 105

PART 3.

107

PROPERTIES OF COAXIAL LINES

Chapter 6. SOLID-INSULATED COAXL\L LINES 1. Principal characteristics 2. Pulse distortion 3. Nonuniformities 4. Pulsed electric strength of solid insulators References

109 109 111 115 118 122

Chapter 7. LIQUID-INSULATED LINES 1. General considerations 2. Types of liquid-insulated line 3. Physical properties of Hquid-insulated lines 4. Flashover of base insulators References

123 123 125 127 128 132

CONTENTS

vii

Chapter 8. VACUUM LINES WITH MAGNETIC SELF-INSULATION 1. Physics of magnetic insulation 2. The quasistationary mode 3. The wave mode 4. Plasmas and ions in a line References

133 13 3 136 140 146 148

PART 4.

151

SPARK GAP SWITCHES

Chapter 9. HIGH-PRESSURE GAS GAPS 1. Characteristics of switches 2. Two-electrode spark gaps 3. Three-electrode spark gaps 4. Trigatrons 5. Spark gaps triggered by external radiation 5.1 Ultraviolet triggering 5.2 Laser triggering 5.3 Electron-beam triggering 6. Sequence multielectrode spark gap switches 6.1 Principle of operation 6.2 Sequence microgap switches 6.3 Spark gaps for parallel connection of capacitors 6.4 Megavolt sequence spark gaps References

153 15 3 156 158 161 166 166 168 169 173 173 175 177 180 182

Chapter 10. LOW-PRESSURE SPARK GAPS 1. Vacuum spark gaps 2. Pulsed hydrogen thyratrons 3. Pseudospark gaps References

185 185 188 195 199

Chapter 11. SOLID-STATE AND LIQUID SPARK GAPS 1. Spark gaps with breakdown in solid dielectric 2. Spark gaps with breakdown over the surface of solid dielectric 3. Liquid switches References

201 201 203 206 211

viii PART 5.

CONTENTS GENERATORS WITH PLASMA CLOSING SWITCHES

213

Chapter 12. GENERATORS WITH GAS-DISCHARGE SWITCHES 1. Design principles of the generators 2. Generators with an energy storage line 3. Spark peakers References

215 215 217 222 228

Chapter 13. MARX GENERATORS 1. Nanosecond Marx generators 2. Charging of a capacitive energy store from a Marx generator 3. Types ofmicrosecond Marx generator 4. Multisection Marx generators 5. High-power nanosecond pulse devices with Marx generators References

229 229 233 235 239 244 248

Chapter 14. PULSE TRANSFORMERS 1. Introduction 2. Generators with Tesla transformers. Autotransformers 3. Line pulse transformers 4. Transformers using long lines References

251 251 252 259 265 267

PART 6.

GENERATORS WITH PLASMA OPENING SWITCHES

269

Chapter 15. PULSE GENERATORS WITH ELECTRICALLY EXPLODED CONDUCTORS 1. Introduction 2. Choice of conductors for current interruption 3. The MHD method in designing circuits with EEC switches 4. The similarity method in studying generators with EEC switches 5. Description of pulse devices with EEC switches References

278 281 287

Chapter 16. PULSE GENERATORS WITH PLASMA OPENING SWITCHES 1. Generators with nanosecond plasma opening switches 2. Generators with microsecond POS's 3. Nanosecond megajoule pulse generators with MPOS's

289 289 293 298

271 271 273 276

CONTENTS

ix

4. Other types of generator with MPOS's References Chapter 17. ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES 1. Introduction 2. Triggering of an injection thyratron 3. The current cutoff mode References PART 7.

PULSE POWER GENERATORS WITH SOLID-STATE SWITCHES

303 305

307 307 308 316 321

323

Chapter 18. SEMICONDUCTOR CLOSING SWITCHES 1. Microsecond thyristors 2. Nanosecond thyristors 3. Picosecond thyristors 4. Laser-activated thyristors References

325 325 329 333 335 338

Chapter 19. SEMICONDUCTOR OPENING SWITCHES 1. General considerations 2. Operation of SOS diodes 3. SOS-diode-based nanosecond pulse devices References

339 339 343 350 353

Chapter 20. PULSE POWER GENERATORS IN CIRCUITS WITH MAGNETIC ELEMENTS 1. Properties of magnetic elements in pulsed fields 2. Generation ofnanosecond high-power pulses 3. Magnetic generators using SOS diodes References

355 355 360 364 371

Chapter 21. LONG LINES WITH NONLE^JEAR PARAMETERS 1. Introduction 2. Formation of electromagnetic shock waves due to induction drag 375 3. The dissipative mechanism of the formation of electromagnetic shock waves 4. Designsof lines with electromagnetic Shockwaves 5. Generation ofnanosecond high-power pulses with the use of electromagnetic shock waves References

373 373

378 383 385 387

X PART 8.

CONTENTS ELECTRON DIODES AND ELECTRON-DIODEBASED ACCELERATORS

389

Chapter 22. LARGE-CROSS-SECTION ELECTRON BEAMS 1. Introduction 2. The cathodes of LCSB diodes 2.1 Multipoint cathodes 2.2 Liquid-metal cathodes 3. Metal-dielectric cathodes 3.1 Explosive electron emission from a triple junction 3.2 Metal-dielectric cathode designs 4. Physical processes in LCSB diodes 4.1 Nanosecond beams 4.2 Large-cross-section beams of microsecond and longer duration 5. Designs of LCSB accelerators References

405 407 410

Chapter 23. ANNULAR ELECTRON BEAMS 1. Principle of operation of diodes 2. Device of electron guns for MICD's 3. The cathode plasma in a magnetic 4. Formation of electron beams References

413 413 416 419 425 431

field

Chapter 24. DENSE ELECTRON BEAMS AND THEIR FOCUSING 1. The diode operation 2. Diodes with plane-parallel electrodes 3. Blade-cathode diodes 4. Focusing of electron beams References PART 9.

HIGH-POWER PULSE SOURCES OF ELECTROMAGNETIC RADIATION

Chapter 25. HIGH-POWER X-RAY PULSES 1. Historical background 2. On the physics of x rays 3. Characteristics of x-ray pulses 4. High-power pulsed x-ray generators 4.1 X-ray tubes 4.2 Compact pulsed x-ray apparatus

391 391 392 3 92 394 396 396 399 402 402

433 433 435 440 446 453

455 457 457 459 464 469 469 473

CONTENTS 5. Superpower pulsed x-ray generators 6. Long-wave x-ray generators References

xi 477 484 488

Chapter 26. HIGH-POWER PULSED GAS LASERS 1. Principles of operation 1.1 General information L2 Typesof gas lasers 2. Methods of pumping 2.1 General considerations 2.2 Electric-discharge lasers 2.3 Electron-beam pumping 2.4 Electroionization lasers 3. Design and operation of pulsed CO2 lasers 4. Design and operation of high-power excimer lasers References

491 491 491 494 498 498 500 503 507 508 514 518

Chapter 27. GENERATION OF HIGH-POWER PULSED MICROWAVES 1. General information 2. Effects underlying relativistic microwave electronics 3. The carcinotron 4. Vircators 5. High-power microwave pulse generators 6. Carcinotron-based radars References

521 521 523 527 534 537 542 544

Chapter 28. GENERATION OF ULTRAWIDEBAND RADIATION PULSES 1. General remarks 2. UWB antennas 3. Design of high-power UWB generators References

549 549 552 556 563

Index

565

Preface

This monograph is devoted to pulsed power technology and high-power electronics - a new rapidly evolving field of research and development. Here, we deal with pulse power systems with tremendous parameters: powers up to 10^"^ W, voltages up to 10^-10^ V, and currents as high as 10^ A and even higher. Recall that all world's power plants together produce a power of the order of 10^^ W, i.e., one terawatt. The duration of pulses generated by pulse power systems is generally no more than 10"^ s. Thus, this is nanosecond high-power pulse technology. Depending on the purposes, pulse power devices may operate either in the single-pulse or in repetitively pulsed mode. It is clear that the highest parameters of pulses are achieved in the single-pulse mode. Pulse repetition rates of up to 10"^ are currently attainable at pulse parameters considerably lower than those mentioned above. Pulsed power is not an alternative to traditional ac or dc power engineering. It is intended to solve other problems and deals with essentially different loads. Evolution of this "exotic" power engineering called for the creation of analogs to all devices used in conventional power engineering, such as pulse generators, switches, transformers, power transmission lines, systems for changing pulse waveforms, etc. The main peculiarity of pulsed power technology is that all system components must operate on the nanosecond time scale. The frequency spectrum of nanosecond pulses extends up to superhigh frequencies; therefore, the equipment designed to produce and transfer such pulses should have a wide bandwidth and, at the same time, be capable to hold off high voltages. The short times inherent in the operation of active components of pulsed power systems are attained by taking advantage of a variety of physical phenomena such as electrical

xiv

PREFACE

discharges in gases, vacuum, and liquid and solid dielectrics; rapid remagnetization of ferromagnetics; fast processes in semiconductors; plasma instabilities; transient processes in nonlinear lines, etc. It should be noted that the mechanisms of the processes occurring in the mentioned active components are identical over wide ranges of pulse parameters, and therefore the author of this book has been able to construct a rather consistent ideology of pulsed power for the range lO^-lO^"* W. Which are loads in pulsed power technology, viz., its applications? Chronologically, a first application was the study of the development of discharges in solid, liquid, and gaseous dielectrics exposed to strong electric fields. Another field of use to be mentioned is high-speed photography where high-voltage pulses of nanosecond duration have been used, initially with optical gates and then with electron-optical image converters, in studying fast processes in plasmas of exploded conductors, various types of electrical discharge, etc. In radiolocation, short pulses have long been employed for high-precision ranging. Production of short x-ray flashes has made it possible to obtain a series of fundamental resuhs in ballistics and explosion physics. Nanosecond high-voltage pulse technology has played a key role in developing spark and streamer chambers, which are now the most-used instruments in nuclear physics. There are many other fields of application of pulsed power technology among which quantum electronics deserves mention. The progress in nanosecond pulsed power in the 1960s~ 1970s gave rise to a breakthrough in laser physics and engineering: first high-power pulse solid-state lasers were developed along with a variety of high-power gas lasers which cover the wave spectrum from ultraviolet to infi'ared. However, a fiill-scale revolution in pulsed power technology occurred in the mid 1960s once nanosecond high-power pulse accelerators had been created independently in the United States and in the Soviet Union. Of crucial importance was the discovery made by the author of this monograph and his co-workers who revealed that the electron emission taking place in the diodes of accelerators of this type is an essentially new phenomenon unknown to physicists until that time (it was believed to be field emission). This phenomenon was given the name explosive electron emission. The creation of accelerators of this type and the use of high-power electron beams for various purposes permitted speaking of high-power pulse electronics. As demonstrated below, pulsed power technology and highpower electronics are intimately related; this is why the author has decided to combine them in one monograph. High-power pulse electronics involves, first, the studies of explosive electron emission and electron beams at currents of up to 10^ A; second, the studies of high-power ion beams which are produced fi-om the plasma

PREFACE

XV

generated due to the interaction of a high-power electron beam with an anode; third, production of various types of high-power pulsed electromagnetic radiation such as x rays, laser beams, and microwaves, and, finally, the creation of nanosecond pulsed electron accelerators capable of producing pulse powers of up to 10^ W and electron energies of 10^-10^ eV and operating repetitively at pulse repetition rates of 10^-10^ Hz. They serve the same functions as conventional stationary accelerators, being used in medicine and food production, for sterilization and purification of air and water of harmful impurities, as units of medical x-ray apparatus, for modification of properties of various materials, etc. At the same time, they are smaller than conventional accelerators, compare with them in lifetime, and are not too expensive. The monograph consists of 28 chapters subdivided into 9 parts. The first part describes the simplest schemes of pulse generation using lumped- and distributed-constant circuits. The consideration of these circuits implies that they operate with perfect switches. The second part is devoted to the physics of pulsed electrical discharges in vacuum, gases, and liquid dielectrics. A knowledge of the properties of electrical discharges in vacuum helps the designer, on the one hand, to understand how to design the insulation in diodes of pulsed electron accelerators and, on the other hand, to choose a proper design for vacuum switches and understand the mechanism of their operation. Moreover, since the initial phase of a vacuum discharge is explosive electron emission, to gain a more penetrating insight into this phenomenon is to better understand the phenomenon of vacuum discharge. The study of pulsed discharges in gases provides data necessary to design gas-discharge switches and gas lasers, while information on the properties of electrical discharges in liquid dielectrics is helpful to the designers of liquid-insulated switches and coaxial lines. The properties of coaxial lines with solid, liquid, and vacuum insulation are discussed in Part III. Coaxial lines are generally used for energy storage in high-power pulse generators and for transmission of pulsed energy. For vacuum lines, the mode of their operation under the conditions of magnetic self-insulation is considered, such that the self magnetic field of the current carried by the line is strong enough to return explosive emission electrons back to the cathode thereby impeding the development of a vacuum discharge in the line. Part IV covers various types of spark gap switch, such as high-pressure and low-pressure spark gaps and switches with discharges in solid and liquid dielectrics. High-pressure spark gaps are in most common use; therefore, they are described in great detail. In particular, much attention is given to

xvi

PREFACE

sequence multielectrode spark gaps which are candidates for switching very high pulsed powers. All high-power pulse generators considered in this monograph depend for their operation on two principles. The first principle implies accumulation of energy in a capacitive energy store (capacitor or pulseforming line) which operates through a switch into a load. The relevant devices are referred to as generators with closing switches. The second principle consists in storing energy in an inductor, and an electric pulse is generated as the current flowing in the circuit containing the storage inductor is interrupted with the help of an opening switch. Therefore, Part V concentrates on the principles of operation and design of high-power pulse generators with plasma closing switches, viz., the spark gaps considered in Part IV. These are generators with discharging capacitors and energy storage lines, Marx generators, and generators with capacitive stores charged from various transformers and pulsed voltage multiplication devices. The six part deals with high-power pulse generators with plasma current interrupters, such as generators with electrically exploded conductors, plasma opening switches, and gas-discharge switches triggered with the help of injection thyratrons. Part VII describes semiconductor and magnetic switches and the nanosecond high-power pulse generators using these switches. The operation of semiconductor closing switches - microsecond, nanosecond, and picosecond thyristors - is discussed in detail. Of particular interest are semiconductor opening switches, so-called SOS diodes, which operate at voltages of up to 1 MV, diode current densities of up to 10"* A/cm^, and pulse repetition rates over 10^ Hz. Magnetic switches make it possible to compress energy in a pulse, i.e., to considerably increase the pulse power and decrease the pulse duration. Hybridization of SOS diodes and magnetic compressors gave rise in fact to a new field in pulsed power technology. This part terminates with a description of long lines with nonlinear line parameters in which, under certain conditions associated with the occurrence of electromagnetic shock waves, pulse rise times shorter than 1 ns can be attained. In Part VIII, diodes are considered that produce high-power electron beams of various types, such as large-cross-section, annular, and dense and focused beams. The first-type beams are used for pumping das lasers and in technologies, beams of the second type for the production of microwaves, and the third-type beams for heating plasmas and investigating their properties. The final, ninth part of the monograph is the largest one and contains four chapters. It is devoted to high-power pulsed electromagnetic radiation sources such as x-ray generators, gas lasers, microwave oscillators, and

PREFACE

xvii

sources of ultrawideband radiation. It should be stressed that all these unique systems became feasible only due to the advances in pulsed power technology and high-power electronics. They are capable of producing pulse powers which are many orders of magnitude greater that those attainable with earlier devices. A considerable body of the results presented in this monograph were obtained by the author and his co-workers at Tomsk Polytechnic University and at two institutes of the Russian Academy of Sciences that were established and long headed by the author: the Institute of High Current Electronics (Tomsk) and Institute of Electrophysics (Ekaterinburg). These results were published in author's numerous articles, theses, and patents and reviewed in a number of monographs the first of which goes back to 1963. Also used are the most important results obtained at other laboratories of the United States, Russia, Great Britain, and Germany. It should be noted that the most powerful pulse generators have been developed and built in the United States. The monograph has the feature that special attention is paid to the pioneering works that were responsible for the development of new fields in pulsed power technology and high-power electronics. However, the author is not sure that his choice was correct in all cases because a great deal of work in this field was security-guarded for years both in Russia and abroad. Therefore, he presents his apologies to the reader for possible incorrect citing of priority publications. In conclusion, I would like to thank my colleagues who helped me in writing this book, in particular, V. D. Korolev and V. I. Koshelev who in fact co-authored Chapters 8 and 28, respectively. Helpful suggestions made by E. N. Abdullin, S. A. Barengolts, S. A. Darznek, Yu. D. Korolev, S. D. Korovin, B. M. Koval'chuk, D. I. Proskurovsky, N. A. Ratakhin, S. N. Rukin, V. G. Shpak, V. F. Tarasenko, and M. I. Yalandin in discussing particular topics of this work are also acknowledged. Thanks also go to V. D. Novikov for his advice in the course of preparation of the manuscript. Much work on typing the manuscript and preparing its camera-ready version was done by my assistants of many years Irina Kaminetskaya, Lena Uimanova, and Larisa Fridman, and it is a pleasure to gratefully acknowledge their contribution. Finally, my most sincere appreciation is extended to Tatiana Cherkashina who had the courage to translate this giant and multitopical book into English. G. A. Mesyats

PULSED POWER

PART 1. PULSED SYSTEMS: DESIGN PRINCIPLES

Chapter 1 LUMPED PARAMETER PULSE SYSTEMS

1.

PRINCIPAL SCHEMES FOR PULSE GENERATION

There are two essentially different schemes for pulse generation (Fig. 1.1) with the storage of electrical energy either in a capacitor or in an inductor. In the first case (see Fig. 1.1, a), a pulse is produced when a capacitor C, previously charged to a voltage Vo, discharges into a load of resistance 7?ioad- The energy stored in the capacitor is CVQ/2. In this case, the circuit carries a displacement current dV / =C ^ , (1.1) at where V(t) is the voltage across the capacitor during its discharge. In the second case (see Fig. 1.1, 6), a pulse is generated upon breakage of a circuit in which an inductor L carries an initial current /o. The inductor stores an energy L/Q/2, and a self-inductance emf, which is given by 8=- ! ^ , (1.2) at where I{t) is the current during the pulse formation, appears across the inductor. Let us consider these schemes in more detail.

Chapter 1 {a)

^ (10^-10^)>/L//C/, where / is the LC-circuit number.

^load

Figure 1.3. Voltage multiplication circuit with 2^ efficiency

As the switch Si operates, the capacitor Co, charged to a voltage Fo, discharges into the capacitor C\. Neglecting the resistive losses in this LC circuit, in view of condition (1.11), we obtain the time-varying voltage across the capacitor Ci: Fi«Fo l~cos

r ^^[UQ

(1.12)

From (1.12) we have that at t = ti= TCÂQ the maximum voltage Fimax is equal to 2Fo. If the switch ^2 closes at the time tu then, in virtue of condition (1.11), C\ discharges into C2 much faster than into Co. In t = t2 = n^^LiCi, the voltage across C2 becomes Vims^^^W^, Thus, as each next-in-tum switch Si closes, the maximum voltage across C/ becomes almost twice that across C/-i. Eventually, the maximum voltage across Civ will be F^«2^Fo.

(1.13)

The actual voltage Vj^ will be lower than that given by formula (1.13) because of certain (not infinitely large) capacitance ratios Co/Ci, C1/C2, ..., CN-\/CN, resistive losses in the LC circuits, and partial recharging of the capacitors. Fitch and Howell (1964) described an LC generator in which the capacitors are switched in series upon reversal of polarity of the voltage across the even stages in oscillatory LC circuits. The circuit diagram of this generator is given in Fig. 1.4. Initially, the capacitors are charged from a dc voltage source, as in an MG circuit. At / = 0, as the switches close, the even capacitors start discharging through the inductors L. In a time x = n^fZc, the voltage across the capacitors reverses sign, and the output voltage of the

Chapter 1

8

generator becomes Fout = NV^^, where N is the number of stages. In no-load operation, the output voltage varies by the law ôut(0 = A^f'o(l-e«^coso)0,

(1.14)

where co^ = \ILC, a = RI2L , and R is the resistance (in ohms) of the LC circuit. From (1.14) it can be seen that here, in contrast to an MG, the voltage rise time is determined by the inductance of an inductor specially connected in the circuit, and decreasing L may decrease the voltage multiplication factor because of the increase in parameter a.

Figure 1.4. An LC generator with reversal of voltage polarity

This scheme has the advantage over the Marx one that the number of switches is halved. However, the switches must be operated as simultaneously as possible by using special trigger circuits. Another advantage is that the resistances and inductances of the switches have no effect on the circuit output impedance if the LC generator picks up the load through an additional fast switch. Pulse transformers with lumped parameters, because of their poor frequency characteristics, cannot be employed directly in nanosecond pulse power technology. However, as well as MG's, they are widely used as charging devices for pulse-forming lines. They generally operate on the microsecond time scale. The choice of this time scale is dictated by two factors. On the one hand, in order that the insulation of the components of pulse generators be reliable, it is necessary that the charging pulses be as short as possible. On the other hand, the charging pulse should be long enough so that all transient processes in the pulse-forming line have time to be completed and the switch connecting the line to the load operate reliably

LUMPED PARAMETER PULSE SYSTEMS at a desired time. In this respect, the microsecond time scale is optimal. For this purpose, Tesla transformers, line transformers, conventional pulse transformers, and autotransformers are used. Transformers are more compact and reliable than MG's and they can be repetitively operated. A Tesla transformer contains two inductively coupled oscillatory LC circuits (Fig. 1.5). As the switch S closes, free oscillations appear in the Lid circuit and are transferred to the L2C2 circuit. For the capacitance C2, the capacitance of the pulse-forming line of the accelerator is generally used. In order that the energy transfer from the first to the second LC circuit be as complete as possible, it is necessary that the oscillation frequencies in these circuits be equal: fi =

1 27X-y/ZiCi

/2=-

1

(1.15)

2TiyjL2C_

Analyzing the transient processes in these circuits with no account of losses, we get for the voltage across the capacitor C2 V2=-

(1.16)

(COS(0IT-COSC02T),

where x = tf-slLiQ is the dimensionless time; coi = 1/Vl + k and CO2 = are the dimensionless cyclic frequencies; k = M/->/A^2 ; ^ i s the coefficient of mutual inductance between the circuits, and t is the time. From (1.16) it follows that the voltage V2 is beating. (a) I

(b)

s 00,0

S

Is,

^

C2±Z

N^C2d=:

Figure 1.5. The original {a) and equivalent {b) circuits of a Tesla transformer

The highest possible value of the voltage V2 across the capacitor C2 is given by ^2max

= F;

(1.17)

If we choose C\ = n^Ci, then the voltage will be multiplied by a factor of n. For a pulse system to operate efficiently, it is important that V2 reach a

Chapter 1

10

maximum during the first half-period of beats. In this case, the electric strength of the insulation will be higher. From (1.16) it follows that Viit) reaches a maximum during the first half-period at some fixed k determined from the condition CO2 + coi _ Vl + A: + \l\-k ©2 -c5i yjx + k -yjl-k= n.

(1.18)

where n is an odd integer. From (1.18) we obtain that the optimal k values are given by ko =2n(n^ +1)"^ For instance, for « = 1, 3, and 5 we have ^0= 1, 0.6, and 0.385, respectively. Figure 1.5, Z? presents the equivalent circuit of a Tesla transformer. Here, Lsi and Ls2 are the effective stray inductances of the first and the second LC circuit, respectively, and L^ is the magnetizing inductance. Widely used in pulsed power technology are line pulse transformers (LPT's) (Mesyats, 1979). An LPT consists ofN single-turn transformers with a common secondary winding. The secondary winding is a metal rod on which toroidal inductors carrying primary windings are put. Figure 1.6, a gives the equivalent circuit of an LPT. The circuit transformation is performed by reducing the primary winding to the secondary one. The primary windings of the inductors are connected in series. This is true since the current in each circuit element and the voltage across the element are invariable in amplitude, waveform, and duration. The inductance Li includes the capacitor, spark gap, and lead inductances and the stray inductance of the primary winding of the inductor; L^^ is the stray inductance of the rod, and Lioad is the inductance of the load. Experience of operating systems of this type shows that generally we have for the secondary winding capacitance Cs2Zo Zo ^load

Figure 2.1, Circuit diagram of a pulse generator with an open energy storage line

The value of V is found from the boundary condition at the load end of the line (x = I), which is given by Ohm's law. As at x = / the voltage across the line and the current in the line coincide with the voltage across the load, Fioad, and the current in the load, /load, then Fioad = ^loadîoad • Substituting expressions (2.2) into this expression, we obtain F o + F = -i?iload

whence, putting R\oad = ZQ, we find Zo Moad + Zo

V = Vo-

EL 2

(2.3)

In view of relation (2.3), we have r. Vn Vio^=Vo + V = ^

(2.4)

The voltage and current that are expressed by relations (2.2) will also appear with time in other cross sections of the line as the first backward voltage wave and the related current wave will propagate along the line. At a time t = l/v= Tl, where v is the wave propagation velocity and T is the time per unit length for which the wave is delayed in the line, the V and / waves arrive at the open end of the line and then are reflected from this end. As a result, the V and / waves start propagating from the open end of the line toward the load. If we assume for the charging resistance R » Zo, then the coefficient of reflection of the voltage wave will be equal to unity, and, therefore, F = ~Fo/2 and I=-VQ/2ZO. At the instant the / and V waves

PULSE GENERATION USING LONG LINES

15

reach the load end, the voltage and current will be zero in all cross sections of the line, and the discharging process in the line will be completed. It should be borne in mind that as the forward waves arrive at the load end, reflected waves do not appear since i?ioad = ô and so the coefficient of reflection is zero. Therefore, the amplitudes of the current and voltage pulses will be determined by formulas (2.1). In operator form, the input resistance of such a line is given by (Lewis and Wells, 1954) Zinput=ZoCth/7r/,

(2.5)

where/? is the parameter in the Laplace transform. The pulse duration t^ is twice the time it takes a wave to travel through the line: ,,=2/r=2( = ^ , V

(2.6)

C

where 8 and |i are the relative permittivity and permeability, respectively, and c is the velocity of light. An open line segment (with a charging resistance R » Zo) can be considered as a capacitive energy store with a total capacitance C = /Co, where Co is the line capacitance per unit length. When the line is charged from a source of voltage Fo through a resistor i?, it stores an electric field energy ICOVQ/2, AS the switch (Fig. 2.1) operates to connect the line to a load of resistance i?ioad = Zo, the energy stored in the capacitor is completely released in the load in time ^p, and thus we have

K%

-LA.

Zo

4

\—lT-

iu

-Yl

Co

\JL()CQ -

2 \|A)

_ VQ'ICO

(2.7)

2

If the load resistance is not matched to the wave impedance of the line (^load i" ZQ), a stepped pulse with a step length tp rather than a single pulse will appear across the load (Fig. 2.2). The waveform of the pulse across the load will vary depending on whether /?ioad is greater or lower than the wave impedance. For 7?ioad < ZQ the pulse steps periodically change sign (Fig. 2.2, a), while for iJioad > ZQ they are of the same sign. In the general case, the voltage of the kth step is given by rr

rr

^load

R\o?id - ZQ

^load + ZQ V ^load -^ZQ J

A:=l,2,3, ...

(2.8)

16

Chapter 2 id)

Vk\

3|

x-^

4j

tlu

ib)

yk\

t/try

Figure 2.2. Waveform of the pulse across the load for /?ioad < ô (^) and /?ioad » ô (b)

For A: = 1 and i?ioad = ZQ, the value of Vk = Fo/2 equals the pulse amplitude. The admissible ratio R\oad^Zo is generally determined by the relative height of the second pulse. If, for instance, it is prescribed that the height of the second pulse should make no more than 5% of the amplitude of the main pulse, ^load/ô should be 0.9 or 1.1; that is, the load resistance should lie in the range 0.9Zo^0.

•0

: -^load

'Vo

B

t=Ot=x — •

FT t

'^ a

(b)

"

1 if )ao 1

U^ô- •Vo

1

f t

1 ^

1f t ,

1

^load

,J

f=0/=T (C)

O-Uoô Vo

lô~l

TT t t J_J.

:^load

Figure 2.6. Circuit diagram of a pulse generator based on series-connected strip lines with several switches (a) and with a single switch (Z), c)

Figure 2.6, a shows three strip pulse-forming lines of this type and a load cormected in series (Fitch and Howell, 1964). Initially, the switches are open and the lines are charged to a voltage FQ. There is no voltage across the load. As the switches close simultaneously, after a time equal to the time it takes a wave to travel through the line, if the switches are perfect, the output voltage ofn series-connected lines is determined by the formula

20

Chapter 2

The output resistance of a generator with strip lines is given by 311 na ôut = nZo = ^ ,

(2.13)

and the pulse duration by r p = ^ , (2.14) c where a is the strip separation and b and / are the strip width and length, respectively. The operation of the generator shown in Fig. 2.6, a calls for a great number of switching units, which sometimes can be replaced by a single switch. For doing this, a decoupling resistor should be involved in the generator circuit to prevent the lines from discharging through the common conductor formed by the plates of the nearby lines. Two circuit designs of the strip-line generator, considered by Fitch and Howell (1964), are presented in Fig. 2.6, b, c. In this type of generator, the wave impedance of the passive lines formed by the plates of the main lines serves as a decoupling impedance Zdecoup. The latter is chosen from the condition Zdecoup ^ Zo, which corresponds to ao» a, where ao is the strip separation in the decoupling line. As the switch closes, the active lines completely discharge, while the passive lines discharge only partially. It can readily be seen from Fig. 2.6, b that as the voltage wave propagating in a passive line toward the load arrives at the line end, the wave amplitude is ^

IVQZO Z H- 2Zdecoup

^ IVpa ^Vpa Zi, Z3 > Z2, ..., Z„ > Z„î, we have for the amplitude of the output pulse V^=2-Vo^^

^

Z2+Z1 Z,+Zo

^!^^.

(2.20)

Z' + Z,

If, for example, Zj = 2Zy_i (7 = 1, 2, ..., «), then V,=^

^5o^^—Fo.

(2.21)

For n = 5 and the end of the last line open, the transformation coefficient is VJVQ =6.31. If the delay time per unit length, T, is the same for all line segments and the input pulse duration tp < khT, where /sh is the length of the shortest line segment, a transformed pulse with numerous additional pulses caused by reflections of the input pulse from both ends of each segment will appear across the load. This method is used for pulse transformation if the additional pulses can be shunted or if it is necessary to have short-rise-time pulses with the top flattened at a certain distance from the beginning of the pulse leading edge, while the rest of the pulse waveform is of no significance. Such pulses are required, for instance, in studying the processes responsible for the delay of some phenomena caused by the action of a high voltage. The use of this pulse transformation method is substantially limited

24

Chapter 2

due to the processes that occur at the line segment joints and increase the pulse rise time. At the joints, line segments with different geometric dimensions are connected, and this is the same as if some shunting capacitors were connected at these places. An original voltage multiplication scheme based on a cumulative discharge of a charged segmented line was proposed by Smith (1962). The line consists of several (« in the general case) segments with the same delays, but with different wave impedances. The proportion between the wave impedances of the segments is optimized so that the energy stored in each previous segment is completely transferred to the next one within the doubled time it takes a pulse to travel through this section. To eliminate the joint effects, lines with variable wave impedances are used where the capacitance and inductance per unit length vary with line length. The general theory of nonuniform long lines is presented by Litvinenko and Soshnikov (1962). The most widely used lines are exponential ones whose inductance, capacitance, and wave impedance vary along the line as A)x -

LQO^^^

\

Cox -

CQQQ ^^

;

ZQX

- J~pr~^^^' Vôo

(2.22)

where K is a positive or negative constant. If a rectangular pulse is applied to such a line, its amplitude will increase and the transformation coefficient will vary with distance x from the beginning of the line as «=e''''^=J^.

(2.23)

At the same time, the decrement of the amplitude of a unit voltage pulse within the pulse duration t^ is given by (Lewis and Wells, 1954) A=^ ^ .

(2.24)

Nonuniform lines can also be used as pulse-forming units in pulse generators. For instance, it was proposed (Litvinenko and Soshnikov, 1962) to connect a capacitor in series with a parabolic line (Fig. 2.8). The wave resistance of a parabolic line varies by the law

f

xV

Zo(x) = Zoo 1 - -

,

(2.25)

PULSE GENERATION USING LONG LINES

25

where a is a parameter which characterizes the degree of uniformity of the line. The input impedance of such a Hne with its one end open is written in operator form as

Zi„=Zoocth/7/r^-^, p

(2.26)

a

where/? is the parameter in the Laplace transform and / the length of the line.

Figure 2.8. Diagram of a circuit with a parabolic line and a capacitor, designed to produce rectangular pulses

The first term of this formula, according to (2.5), represents the input impedance of an open uniform line with a load whose resistance is equal to the wave impedance Zoo. If we introduce a capacitor of capacitance C = a/vZoQ, the line impedance in operator form will be Z=

vZi00

(2.27)

ap Hence, the net impedance of the line and capacitor and Zin will be equal to the input impedance of a uniform line open at one end. Therefore, if we assume that /?ioad = Zoo, then, as for an open uniform line with tp = 21/v and Ka = Fo/2, a rectangular pulse will be formed across the load. REFERENCES Fitch, R. A. and Howell, V. T. S., 1964, Novel Principle of Transient High Voltage Generation, Proc./££. 111:849-855. Lewis, I., 1955, Some Transmission Devices for Use with Millimicrosecond Pulses, Electr. Eng. 27:332. Lewis, L A. D. and Wells, F. H., 1954, Millimicrosecond Pulse Techniques. Pergamon Press, London.

26

Chapter 2

Litvinenko, O. N. and Soshnikov, V. I., 1962, Design of Pulse-Forming Lines (in Russian). Gostekhizdat, Kiev. Mesyats, G. A., Nasibov, A. S., and Kremnev, V. V., 1970, Formation of Nanosecond HighVoltage Pulses (in Russian). Energia, Moscow. Smith, I. D., 1982, A Novel Voltage Multiplication Scheme Using Transmission Lines. In Proc. IEEE Conf XVPower Modulation Symp., New York, pp. 223-226. Vvedensky, Yu. V., 1959, A Thyratron Generator of Nanosecond Pulses with a Universal Input,/zv. Vyssh. Uchebn. Zaved.,Fiz. 2:249-251.

PART 2. PHYSICS OF PULSED ELECTRICAL DISCHARGES

Chapter 3 THE VACUUM DISCHARGE

1.

GENERAL CONSIDERATIONS

A vacuum discharge, as any type of discharge, goes through three phases: breakdown, a spark, and an arc. Breakdown involves some phenomena, which eventually destroy the electrical insulation of a vacuum gap. For a vacuum discharge, these are the phenomena resulting in the concentration of energy in a cathode microvolume to a density sufficient for the material confined in this microvolume to explode. A spark is a combination of selfsustaining phenomena responsible for the current rise in a vacuum gap, namely, the processes occurring during explosive electron emission (EEE). An arc is the terminating phase of a vacuum discharge that features a comparatively low fall voltage and a steady current, which is determined by the circuit parameters and by the voltage applied to the gap. Of greatest interest for pulsed power technology are the first two phases: the breakdown and the spark. The study of breakdown is of importance to find ways for improving the electrical insulation of pulse generators, accelerators of electrons and ions, microwave devices, pulsed x-ray generators, etc. The creation of compact and reliable pulsed power systems is impossible without a knowledge of the mechanism of vacuum breakdown. As for vacuum sparks, they occur during the operation of the diodes of electron accelerators, in x-ray tubes, and in vacuum switches and peakers. A fundamental process in a spark is the formation of ectons, portions of electrons produced by cathode microexplosions, which are responsible for explosive electron emission. To ensure normal operation of diodes, switches, and peakers, it is necessary to control the vacuum spark parameters such as the current, its rise rate and density, the current distribution over the cathode

30

Chapter 3

and anode surfaces, etc. Vacuum breakdown and the initial phase of a spark also take place in magnetically insulated vacuum coaxial transmission lines, which are used to transfer nanosecond high-power pulses. Of great interest is the discharge over the surface of a dielectric in vacuum. The presence of a dielectric in a vacuum gap substantially complicates the pattern of the discharge. In this case, the contact between the dielectric and the cathode becomes important where metal-dielectricvacuum triple junctions play the key role. At these junctions, the initiation of explosive electron emission occurs much easier. The discharge pattern is also complicated by the secondary electron emission from the dielectric, by the charging of the dielectric surface, and by the gas desorption from this surface.

2.

VACUUM BREAKDOWN

2.1

The electrode surface

To achieve the greatest possible electric strength for a vacuum insulation, it is necessary that the surfaces of the electrodes, especially the cathode surface, be clean and smooth. However, it is impossible to make a surface perfectly clean and smooth for many reasons associated with the treatment of the electrodes at the stage of their preparation, the methods used for electrode conditioning, the conditions under which they are operated, the degree of vacuum, etc. As a result, the electrode surface is characterized by a peculiar kind of microstructure and chemical composition. Figure 3.1 gives some examples of the imperfection of the surface structure. This imperfection may involve microprotrusions, dielectric inclusions, oxide and other inorganic dielectric films, adsorbed gas layers, grain boundaries emerged at the surface, micro particles, oil vapor cracking products, edges of craters formed upon breakdowns, pores and cracks, and the like. All these surface flaws may become emission centers, which participate in primary or secondary processes leading to vacuum breakdown (Mesyats and Proskurovsky, 1989). An important role in a vacuum breakdown is played by the field emission (FE) from cathode microprotrusions. The essence of this phenomenon is the tunneling of electrons through the potential barrier at a metal-vacuum interface in a strong electric field. Thefiindamentalrelation of the FE theory, which is called the Fowler-Nordheim formula (Elinson and Vasiliev, 1958), establishes a relationship between emission current density j and electric field E at the metal surface:

THE VACUUM DISCHARGE y = 1.55-10-*

6.85-10>^'2

£2

t\y)^>

31 ^{y)

exp

(3.1)

Here, j is the FE current density (A/cm^), £ is the electric field (V/cm), cp is the work function for the metal (eV), and t{y) and 6(y) are functions of the quantity jv = 3.62-10"^£''-^9 '. For practical calculations, it is generally assumed that tîy)^\.\;

e(>')«0.95-1.03>'2

From formula (3.1) it follows that the plot of the dependence (lgj)/E^ = /(VE) is a straight line. This, however, is the case for the FE current densities j < 10* A/cm^. For higher current densities, the function j (E) is almost independent of work function cp. A reason for this is the influence of the electronic space charge that exists near an emitter (Barbour etal., 1953). In this case, the dependence 7(£) is described by the ChildLangmuir law 4 J=-SoJ-E'''yEri'".. 9'

(3.2)

where So is the dielectric constant; e and m are the electron charge and mass; JE is a factor, determined by the emitter shape and size, whose value is of the order of unity, and r^ is the radius of the emission area. (b)

Figure 3.1. Various types of emission centers leading to vacuum breakdown: microprotrusions (a), dielectric inclusions (b), oxide and other inorganic dielectric films (c), adsorbed gas layer (d), grain boundaries emerged on the surface (e), micro particles (/), products of oil vapor cracking (g), edges of craters produced by breakdowns (h), and pores and cracks (/)

32

Chapter 3

A vacuum breakdown is initiated in the main by the FE current from microprotrusions present on the cathode surface. The electric field at the tips of microprotrusions is enhanced many times compared to the average field; therefore, the notion of the factor of electric field enhancement (3^ is introduced. This factor is defined as the ratio of the actual electric field at the protrusion tip to the average macroscopic field E^v = VId, where V is the voltage across the gap and d is the electrode separation. Relationships between the factor (i^ and the irregularity parameters were found for simple protrusion geometries (Latham, 1995). For the practically usefial range of p^ values, one can use simple approximate relations between p£ and hir, where h and r are the microprotrusion height and tip radius, respectively. For instance, for an ellipsoid with (3^ = 7-100 we have P£= — + 1, (3.3) r where a is of the order of unity; for a cyUnder with a spherical tip and P£= 10-1000 p £ = - + 2, (3.4) r and for a cone with a spherical tip, cone angle 0 = 5-10°, and p£ = 20-3000 p £ = A + 5. 2r

2.2

(3.5)

Vacuum breakdown criteria

The breakdown criteria are of importance in characterizing the phenomenon of vacuum breakdown. We now consider the main criteria associated with pulsed and dc voltages. In a study of the pulsed breakdown of a vacuum gap with a point tungsten cathode whose tip radius and cone angle were known (Mesyats and Proskurovsky, 1989) it was established that the time delay to breakdown, t^, and the density of the FE current from the point tip are related as (Fig. 3.2) j^t^ =consti.

(3.6)

It can be seen that, in accordance with formula (3.6), on the double logarithmic scale, all experimental points fall well on a straight line with the slope equal to 2. It follows that the product of the squared current density by the time delay to the explosion of a field emitter is an almost constant quantity over wide limits of t^ andy.

THE VACUUM DISCHARGE

33 j [A/cm^] 10«

1 A9

10^

1

10^ 10^ -

1

10^ 10^ 105 -

^v

10^ 103 -

\

^"""^-V^

102 101 : J

0.5

0.7

\

\

0.9

1.1

L_

1.3

\

1

1.5

1.6

EQ'XO-^ [V/cm]

Figure 3.2. Explosion delay time as a function of electric field (I) and current density (2) for a tungsten field emitter

From this plot we find that j^td = 4-10^ A^-s/cm"^. Also given in Fig. 3.2 is the dependence of the explosion delay time U on the electric field at the emitter tip, EQ, for the same experimental points. As the electric field EQ is increased from 7-10^ to 1.3-10^ V/cm, the critical current density increases fi-om 4.5-10^ to 2.2-10^ A/cm^, which in turn causes the time delay to the point explosion to decrease from 4-10"^ to MO"^ s. This suggests a very strong dependence of the breakdown delay time on the electric field at the point tip. Formula (3.6) is also valid for plane-parallel electrodes having microprotrusions on the surface. Thus, the criterion for a pulsed breakdown to occur in a vacuum gap between a point cathode and a plane anode is relation (3.6). On the other hand, from the studies of electrically exploded conductors it is well known that

i:/*=*-

(3.7)

where t^ is the explosion delay time, the quantity h is called the specific action for the explosion, and j is the current density in the conductor. The quantity h is determined by the metal type and only weakly depends on current density. Therefore, this quantity can be considered invariable for a given metal over a certain range of current densities. The electrical explosion of metals is discussed in details in Chapter 15 and by Mesyats (2000), Burtsev et al (1990), and Chace and Moore (1959, 1962). Thus, the data presented in this chapter provide strong grounds to believe that for a point cathode the breakdown phase ends with the electrical explosion of the point

Chapter 3

34

tip. After that, the spark phase begins which is associated with explosive electron emission. The values of h for several metals are given in Table 3.1 (Mesyats, 2000). Tables.]. Metal h

Cu 4.1

Al 1.8

Au 1.8

Ni 1.9

Ag 2.8

Fe 1.4

Alpert et al. (1964) investigated the breakdown of vacuum gaps of spacing 10""^-1 cm at a dc voltage. They established that for metals, such as Al, Cu, Au, Pt, Mo, W, and other, the breakdown electric field is independent of gap spacing. For instance, for tungsten it is (6.5 ±1)40^ V/cm (Fig. 3.3). In accordance with formula (3.1) for the FE current, this fact can be interpreted so that breakdown occurs as the FE current density reaches a certain value, i.e., y = const2.

(3.8)

Relations (3.7) and (3.8) are criteria, respectively, for pulsed and dc breakdown of vacuum gaps. They in fact imply that a vacuum breakdown occurs as a result of the electrical explosion of a cathode microprotrusion where the energy density reaches high values due to the heating of the microprotrusion by the FE current. 10«

r_

- , n D

0 / ^ O r t / ^

A

rSi,r£ip tllO^ \ 1

1 a 1 1-4

10^

10

2 o 1

10-

3 L 1

1

10-2 10d [mm]

1

1

10 10^^ p/^ cm-^s"^ (Mesyats, 2000).

Z)2=ll

Figure 3.11. Photographs of the cathode and anode plasma luminosity (3 ns exposure time) for ); 22 ns, 150 A (c), and 34 ns, 230 A {d) (arc phase)

Now the question arises of why the current density is enhanced. Immediately in the microexplosion zone, the ion current density is not over -'10^ A/cm^. For a liquid-metal jet to explode within 10"^ s it is necessary to have a current density of 10^ A/cm^, i.e., Py should be > 10^. For a jet having the shape of a cone, Py « 2/0, where 6 is the cone angle. For the cathode spot of a copper-cathode arc, we have 9 « 0.5 (Mesyats, 2000) and, hence, P^ « 4; that is, the factor of current density enhancement is too small. For a

46

Chapter 3

cylindrical jet, we have py « 2h/r, where h and r are the jet height and radius, respectively. The quantity p, coincides in value with the electric field enhancement factor P^, which, for a pulse duration of 5-50 ns, is not over 10-20 (Mesyats and Proskurovsky, 1989). It follows that py > 10^ cannot be achieved for a conical or cylindrical jet. A much higher degree of current density enhancement is attained with a sphere attached to the apex of a cone. This is the case where a droplet breaks off a liquid-metal jet. As this takes place (Fig. 3.12), the current density in the droplet-cone bridge increases by a factor Py = 4r//r^, where r^ is the radius of the droplet and r is the radius of the bridge. The process of breakout of the droplet will last a time of the order of ^ = r^/vd, where v^ is the velocity of motion of the droplet. Since v^^^ 10"^ cm/s, the breakout time will be '-10"^ s. For the bridge to explode within the time /, the current density should be ^l/2

(3.27)

Droplet

Cathode

Figure 3.12. Sketch of a liquid-metal jet at which an ecton is formed, r^ is the radius of the molten metal zone, r^ is the length for which the ecton zone is heated; p^ is the plasma pressure on the liquid metal; p^ is the plasma pressure at the instant the ecton ceases to operate, and / is the current

Proceeding from the fact that during the spark phase of a discharge the current from the cathode occurs in the form of individual portions of electrons (ectons), we estimate the number of ectons and the rate at which they come in the gap. In the foregoing, we supposed that every ecton cycle is

THE VACUUM DISCHARGE

47

accompanied by one liquid-metal droplet leaving the cathode. This takes place when the rates of current rise are not very high: dlldt < 10^ A/s. In this case, the charge of the ecton electrons will be q^ ^l/Yd, where Yd is the number of droplets per unit charge. The total number of ectons formed during the spark phase is determined by the relation No= — \'Îdt = y,\'Îdt,

(3.28)

where 4 is the duration of the spark phase. If the evolution of the spark current is approximated by a linear function, the total charge built up during the spark phase is given by ^s=iU,

(3.29)

where /a is the peak current, which corresponds to the purrent of the vacuum arc. Since 4 ^ div, then N,=^

=l^^,

(3.30)

For /a = 100 A, J = 1 cm. Yd = 2-10^ C'^ (for copper) (Mesyats and Proskurovsky, 1989), and t;« 2-10^ cm/s, relation (3.30) gives the number of ectons generated during the spark phase of a vacuum discharge Aô« 10^. There is another, highly efficient, way of initiating secondary ectons where the cathode plasma affects the cathode surface cpntaining dielectric films and inclusions. The ion current of the plasma charges the dielectric, the latter is broken down, and the plasma resulting fi'om this event promotes the formation of a new ecton. The electron beam that is formed at the cathode due to EEE is then accelerated and, arriving at the anode, heats the latter. This heating results in the formation of anode plasma, liquid metal, and metal vapors, which generally appear with some delay relative to the appearance of the cathode plasma. The velocity of the cathode plasma may reach 10^ cm/s (Mesyats and Proskurovsky, 1989).

5.

THE SURFACE DISCHARGE IN VACUUM

A knowledge of the mechanism of a discharge over a dielectric surface in vacuum is of great importance since dielectrics are widely used in highvoltage vacuum devices. A major application of this type of discharge is associated with electrical insulators. A spark over a dielectric in vacuum may serve as a source of ultraviolet radiation, which can be utilized, in

48

Chapter 3

particular, for pumping gas lasers and in pulsed switching devices. For instance, spark gaps with this type of discharge are convenient for peaking pulses; they are also used as triggers in triggered vacuum switches. Of particular importance is the use of surface vacuum sparks in metal-dielectric cathodes for the production of high-power electron and ion beams. In this section, we shall focus attention on pulsed discharges (in accordance with the scope of this monograph). This type of discharge is sometimes referred to as the sliding discharge or flashover. Comparing the phenomenology of a sliding discharge with that of a discharge between metal electrodes in vacuum, one can see that a dielectric introduced in a vacuum gap reduces abruptly the electric strength of the gap. Here we are up against a number of phenomena that do not occur in a vacuum gap. Among them are the enhancement of the electric field at the cathode due to the presence of metal-dielectric microgaps, the charging of the dielectric surface by electron bombardment, and the appeaiance of a gas medium in the discharge gap as a result of the gas desorption from the insulator and its destruction. The presence of a dielectric in a vacuum gap results in an enhancement of the electric field in the region of the cathode-dielectric contact due to the existence of microgaps. Kofoid (1960) investigated the processes occurring at a metal-dielectric contact on application of an electric field. The electrode and the insulator were immersed in a magnetic field normal to the electric field to remove electrons from the discharge gap. These electrons were "dumped" onto grounded plates coated with a phosphor. The voltage between the electrodes at which the phosphor starts to fluoresce is a criterion for evaluating the intensity of the contact phenomena. The electron yield from the contact increases with dielectric permittivity. This has the result that the pulsed voltage at which a luminosity appears at the cathode decreases almost sevenfold as the dielectric permittivity 8 is increased from 6.6 (steatite) to 1800 (barium titanate). An increase in electric field in the contact region resulting from the plane-to-point change in cathode geometry also increases the electron current. A change of the cathode material has a slight effect on the electron yield from the contact. The electric field at the cathode-dielectric contact is enhanced because the surfaces of both the dielectric and the cathode are not perfectly smooth. They touch one another only by their protrusions (Fig. 3.13). To roughly estimate the electric field at the contact, one may idealize the contact geometry. Let us denote the averaged microgap width by A and the dielectric thickness by d and assume that the gap length is much less than its width so that the field in the gap could be considered uniform except for the edges. The field strength in the gap Ec can be found as that in a gap connected in series with a dielectric:

THE VACUUM DISCHARGE E.=-

49

1+-

(3.31)

8A

Based on formula (3.31), two conclusions can be made. First, if J/sA 10-15 eV), the electron levels are excited in the main. Ionization events are always accompanied by excitation events; the excited molecules are even greater in numbers than the ions. This is of great importance for a spark breakdown, since there is a high probability that some excited molecules and atoms will emit photons. Photons participate in the generation of the initial electrons that give rise to avalanche ionization. When electron energies are some tens of electron-volts, the inelastic energy losses are much greater than elastic. In this case, elastic collisions are of minor importance compared to inelastic ones, and electrons are scattered in elastic collisions predominantly in the forward direction. Under these conditions, an electron will be gradually accelerated notwithstanding inelastic losses. This is called the electron runaway effect. In nitrogen this effect takes place for Elp > 365 V/(cm-Torr). In a dense gas, an electron can be accelerated to energies over 1 keV. Electrons not only are bom due to the ionization of atoms and molecules, but also annihilate when they recombine with ions or attach to gas molecules. In the course of the recombination of electrons with positive ions, if it is not

60

Chapter 4

complicated by other simultaneous processes such as ionization, the electron density of a neutral plasma with rie = rit decreases with time by the law ^ = -P«2, „ , = — ^ , «o.=«e(0), (4.12) at 1 + pnoJ where P is the coefficient of electron-ion recombination. Electron attachment is one of the most important processes of electron annihilation in electronegative gases. In cold air in the absence of an electric field, electrons attach to oxygen molecules in triple collisions: e+ 02+M-^02+M,

M = 02,N2,H20.

(4.13)

In an electric field, where electrons acquire several electron-volts of energy, reactions of dissociative attachment proceed which call for, in contrast to reactions (4.13), an energy to be expended for the decay of molecules: e + 0 2 + 3 . 6 e V - ^ 0 + 0-.

(4.14)

At low humidity, the electron attachment to oxygen plays the major part. The cross section for reaction (4.14) increases with gas temperature, and the threshold energy for this reaction is lower than 3.6 eV. This is because vibrationally excited molecules are involved in the reaction and their energy also goes for the decay of molecules. As with ionization, electron attachment in a dc field occurs on the background of their drift. The attachment coefficient r|, which is similar to the ionization coefficient a, defines the number of attachment events experienced by an electron as it moves for 1 cm along the field. The similarity law that is valid for ionization processes is also valid for dissociative attachment: r|/« = A^ln). The electron multiplication in an avalanche is described by the equation dnjdx = (a - v^rie and is determined by the effective coefficient a^^ = a - r|. For air, the ionization frequency and the ionization coefficient a more strongly depend on EIn than the attachment fi'equency and attachment coefficient r|, since ionization demands an energy several times greater than that needed for dissociative attachment. Therefore, the curves aln and r[/n in Fig. 4.1, b intersect (Bazelyan and Raizer, 1997). According to the calculations based on the kinetic equation for air, they intersect at £'/p«41 V/(cm-Torr). For lower values of Elp we have a > r|, and the electron avalanche fails to develop. For another technologically important gas, SF6 (elegas), the curves of a and r| intersect at Elp « 117.5 V/(cm-Torr). Correspondingly, the threshold for breakdown is high, and this, along with other acceptable properties of SFe, is the reason for its use as a high-strength gas insulator and as a fill gas in nanosecond spark gaps.

THE PULSED DISCHARGE IN GAS

2.

TYPES OF DISCHARGE

2.1

The Townsend discharge. Paschen's law

61

Let us consider discharges of different types, proceeding from the proportion between the gap spacing d and the critical length of electron avalanche, Xcr, at which the discharge of a single avalanche substantially distorts the electric field applied to the gap. Three types of discharge are distinguished: Townsend, streamer, and avalanche discharges. The distinguishing feature of a Townsend discharge is that the space charge of a single avalanche does not distort the electric field in the gap since Xcr > d, where Xcr is the critical length of the avalanche at which the field of the ion space charge is equal to the external field. For this case, we have {[nNecj)la> d, where A^^cr is the number of electrons in the avalanche at jc = Xcr. If Xcr < d, the dominant role in the development of the discharge is played by the primary avalanche, which changes into a streamer and then into a discharge channel (streamer discharge). For a streamer discharge to exist, it is also necessary that the avalanche emit a sufficient number of photons or runaway electrons capable of ionizing gas molecules near the avalanche head. The photons are emitted by excited gas molecules, whose average lifetime êxc is generally 10"^-10"^ s. Therefore, if the time it takes an avalanche to develop to its critical size, /„, is shorter than ^xc, the development of a streamer from the primary avalanche will be hindered. The criterion for a streamer discharge to exist is (In Aêcr)/^^ ^ d- Finally, there is a type of discharge for which Xcr

(4-15)

where d is the gap spacing; IQ is the electron current from the cathode, produced by some external source, y is the number of secondary electrons per positive ion produced at the cathode, and e is the natural logarithm base. For the secondary electron emission initiated by photons incident on the cathode, we obtain an expression similar to (4.15) (Loeb, 1939). Therefore, it is conventional to characterize various types of secondary emission by a unified coefficient y, which is determined by the cathode material and surface condition and by the gas type and pressure. According to the Townsend theory, the condition under which the denominator in expression (4.15) becomes zero is the criterion for discharge initiation. Since y «: 1, (4.15) takes the form ye^«l.

(4.16)

If ye^ < 1, the discharge is non-self-sustained. In this case, the discharge current / will cease if the initial current h is decreased to zero. If ye""^« 1, the number of ions generated by one avalanche resulting from a single initiating electron, e""^, is such that one secondary electron may appear owing to which the discharge will further develop. Thus, the discharge will be selfsustained. In terms of the Townsend mechanism, condition (4.16) is a criterion for discharge initiation. Increasing the electric field in a gas gap eventually results in ye""^ > 1. In this case, the ionization will be cumulative in character because of the generation of successive avalanches, and the discharge formative time will increase with ye^"^. Condition (4.16) makes it possible to determine the breakdown voltage of a discharge gap if the relations alp = F\{Elp) and y = FiiElp) are known. Assume that y = const and the dependence of alp on Elp is expressed by formula (4.10). In this case, for the dc breakdown voltage, in view of y «: 1, we get V,^=

M . \nApd-\-\n\ny

The function V^cipd) has a minimum at

(4.17)


63 (4.18)

(/'^)min=—In-.

A Y

For the minimum value of Fdc we then have ''^dcmin ""

(4.19)

. *^

A

y

Formula (4.17) is a representation of the similarity law since F^c =f(pd). The dependence of y on E/p in (4.17) can be neglected because y is under a double logarithm. This dependence is pronounced only in the region of the Fdc minimum, since in formulas (4.18) and (4.19) y is under a single logarithm. The quantity y is a generalized characteristic of the secondaryemission properties of a cathode surface; therefore, it can be said that the properties of a cathode show up only in the region adjacent to the minimum of the function Vddpd). This type of the relationship F^c = f{pd) had been found experimentally before the appearance of the Townsend theory. This relationship is called the Paschen law that reads: if for a uniform field the product of discharge gap spacing by gas pressure remains constant, the breakdown voltage is a constant as well. Paschen's curves for several gases are given in Fig. 4.2. If the initial phase of a discharge is due to a great number of successive electron avalanches with the number of electrons in each Ne < Necr, this mechanism results in spatial passage of the current during the discharge formation phase. In particular, a glow discharge forms at low gas pressures. 10^

10^ t

10^ y^

1 Q 2

I

10-^

1

I I ij-iiil

I

10-3

I I I Itill

I

I I I 11 111

I

IQ-2 10-1 pd [cm-atm]

I I ! iiiil

IQO

Figure 4.2. Breakdown voltage versus/?J for different gases

64

Chapter 4 1000

J =60,H%

800

lyÔ 25 20 115

700

/

X

z

h

r ^

600 ^

Ômm

y

^^ /

^ 10 mm

500

^ 400

5 mm

300 200 100 0

A/ ^ v^''

3 mm

1 mm 8 12 p j [cmatm]

16

20

Figure 4.3. The right branch of the function Fdc = fipd) for elegas, plotted for different electrode separations

As shown by Meek and Craggs (1953), the similarity law for V(pd) can be violated. This takes place for the points on Paschen's curves that correspond to high electric fields [(0.3-0.5)-10^ V/cm]. For instance, this refers to the left branch of Paschen's curve corresponding to low pressures (near vacuum). This violation is due to the field emission (FE) current from cathode microprotrusions at the tips of which the electric field is enhanced many times. The FE electrons ionize the gas, and the resulting ions move toward the cathode. As this takes place, the FE is enhanced by the ion space charge and thus the FE current density further increases. Eventually, this leads to explosive electron emission and the formation of ectons and a cathode spot, as this occurs in a vacuum discharge. Paschen's curve also has deviations in its right branch corresponding to high pressures. This is associated with the electric field enhancement at the cathode microprotrusions resulting in a field emission current and in a violation of the similarity law (Meek and Craggs, 1953). Figure 4.3 presents V^c as a function of pd for elegas (SF6) in a uniform field at different gap spacings (d= 1-60 mm) (Bortnik, 1988).

2.2

The streamer discharge

The principal difference between the streamer and Townsend discharge mechanisms lies in the fact that the space charge of an avalanche can transform the avalanche into a plasma streamer. The electrons in the avalanche


65

not only produce impact ionization, but also excite the gas molecules and atoms. The excited molecules or atoms, as they go to the normal state, emit photons that ionize the gas, generating photoelectrons. The electron avalanche arriving at the anode leaves at its surface positive ions whose charge creates an additional field E\ The photoelectrons appearing near the anode move toward the positive space charge region in the field E + E, where E is the field due to the applied voltage V. If E reaches a value of the order of E, the photoelectrons, while moving toward the positive space charge region, have time to initiate new avalanches. These avalanches neutralize the ion charge at the anode thus creating conducting plasma. The new positive ions resulting from the action of photoelectron avalanches behave as described above, and a plasma column, called a positive streamer, rapidly propagates toward the cathode. Raether (1964) and Meek and Craggs (1953) have formulated a condition for the formation of a streamer: E = kE, where A: is a number of the order of unity. During the formation and propagation of a streamer, the contribution to the generation of daughter avalanches is not only from photons, but also from runaway electrons, which appear in the primary avalanche plasma at rather high Elp. When the number of electrons in the avalanche reaches Necr'> the avalanche space charge becomes high enough for its internal electric field to be comparable to the (counterdirected) external field. As this takes place, the field inside the avalanche appears to be enhanced. The velocity of propagation of a streamer is generally an order of magnitude greater than that of an avalanche. Therefore, it can roughly be assumed that the discharge formative time is ^^ÎnJV^

(4.20)

As established in numerous experiments, A^cr « 10^ for many gases imder nearly atmospheric pressures (Raether, 1964); hence, InA/^cr® 20. Formula (4.20) for atmospheric pressure air and £" = 50 and 80 kV/cm yields t^ = 10"^ and 240"^ s, respectively. From formula (4.20) it follows that for the discharge formative time t^ a similarity law is valid: pU =fiE/p). Figure 4.4 shows this relationship for a number of gases, obtained by Felsenthal and Proud (1965). The decisive role in the Townsend-to-streamer discharge transition is played by the overvoltage factor Kover- Allen and Phillips (1963) have shown that there exists a curve that divides the manifold of the values of the product of air pressure and gap spacing,/?(i, and coefficient Kover into two regions (Fig. 4.5). If the discharge conditions correspond to the region above this curve, the discharge occurs by the streamer mechanism; otherwise the Townsend mechanism comes into effect.

Chapter 4

66 W

B

103

^^^1^

t'o^ •0"Ar -He 10' 10-

1

10-

1

1

10-7 10-^ ptd [Torr-s]

1

10-

Figure 4.4. The similarity law for the breakdown formative time plotted for different gases

250

850

1450 2050 pd [Torrcm]

2650

Figure 4.5. The curve separating the regions corresponding to the streamer and the Townsend mechanism of a discharge in air

The electron density in a streamer channel, vie, approximately equals their density in an avalanche with a critical number of carriers: 3iV., Anr'^

(4.21)

Measurements for various gases give the avalanche radius r = 0.01-0.1 cm. Assuming that iVecr= 10^, we obtain n = 10^^-10^^ cm"^ This means that even for r = 0.1 cm and n=W^ cm"-^, the resistance of the streamer channel under typical experimental conditions is over some tens of kiloohms. We take into account that the wave impedance of the coaxial cables by which a voltage pulse arrives at the discharge gap is Zo » 50-75 Q. This implies that the decrease in gap voltage will be due the increase in channel conductivity in the subsequent phases of the discharge. This problem will be discussed in detail below. It should be noted that there exists two types of streamer: cathode-directed and anode-directed. The streamer considered above is anode-directed since the avalanche reaches its critical size inside the gap {Xcv < d) and, therefore, the streamer grows toward the anode. However, if the gap overvoltage is not too large, such that jCcr « d, the space charge field in the region adjacent to the anode will be high; then the streamer will grow toward the cathode. This will be a cathode-directed streamer.

2.3

The multiavalanche pulsed discharge

For highly overvolted gas gaps, the discharge formative time t^ lies in the range of nanosecond and subnanosecond times. In this range, a pulsed discharge has the feature that the spark development time is comparable to


67

the time of growth of avalanches to their critical sizes and the time of de-excitation of excited molecules. This affects the spatial structure of the discharge, the statistical delay time, the duration of the process, etc. This type of discharge, which takes place at overvoltages Kover ^ 1.5, is used in the switches and peakers of nanosecond high-power pulse generators. The criterion for such a discharge to be initiated is Xcr 10^^ cm"^ and p = 760 Torr. If the channel conductivity a is a constant and the magnetic pressure is low compared to the gas-kinetic pressure, the relationship between discharge current and spark resistance has the form (Braginsky, 1958)

Rs-d[ll

-1

P^^dt] .

(4.28)

In a streamer breakdown, the channel diameter is an order of magnitude greater than that in breakdowns of overvolted gaps and in single-electroninitiated discharges. Therefore, an increase in density even to « « 10^^ cm"^ results in an insignificant decrease in voltage at short-circuit currents of several hundreds of amperes (ThoU et al, 1970; Koppitz, 1967). Here, the switching characteristic is described in terms of the hydrodynamic model of an expanding channel. In this case, not only the calculated and measured switching times coincide, but also the measured channel expansion velocity coincides with that calculated from the power delivered to the channel (Koppitz, 1967). For very high short-circuit currents in the discharge circuit (/> 10 kA), the conditions in the discharge channel by the onset of voltage drop are such that the conductivity of the channel increases in the main due to its hydrodynamic expansion. Therefore, the model of an expanding channel is generally used to calculate the switching characteristics of nanosecond high-current switches (Mesyats, 1974). In the above models, the physical limitations are very stringent and, actually, the description of the process takes into account only one factor, which is dominant under given conditions (e.g., hydrodynamic expansion). Such a situation is possible in model tests with a specially created single channel (Tholl et al, 1970; Koppitz, 1967) rather than under the operating conditions of a spark gap over a wide range of currents. Measurements of switching characteristics in combination with observations of the dynamics of channel development by the laser shadow and interferometric methods with nanosecond time resolution (Korolev and Mesyats, 1998) show that the conductivity increases due to several factors, which can hardly be considered independently. To calculate the rise time of a pulse generated in a circuit with a spark gap, the switching characteristic is sometimes represented as an exponential function:


11

where the value of QQ is to be found from experiment or from well-known models of a spark. For instance, the model of Rompe and Weizel gives ô=0.038ap

Ê^ .P)

where E is the electric field at which breakdown occurs.

4.

THE DISCHARGE IN GAS WITH DIRECT INJECTION OF ELECTRONS

4.1

Principal equations

As shown above, free electrons present in a gas-discharge gap radically alter the physics of the discharge phenomena. The simplest way of producing free electrons in a gap is to initiate electron emission from the cathode due to the photoelectric effect, to illuminate the gap with ultraviolet radiation to cause photoionization, or to locally heat the cathode surface with a laser beam to cause thermoelectron emission. Mesyats et al (1972a) proposed to inject electrons produced by an electron accelerator directly into the gas gap. The electron beam should pass through a thin metal foil cathode. In preliminary experiments (Kovarchuk et al, 1970), these authors were able to produce a discharge in nitrogen at a pressure of 15 atm, and this was a volume discharge having no channel. Various modes of such a discharge have been used for pumping high-power gas lasers, in nanosecond highpower gas switches, in pulsed power plasmatrons, etc. The first comprehensive study of this type of discharge was carried out by Koval'chuk et al (1971). The charge voltage of the energy-storage line reached 1000 kV, the maximum energy of the electron beam downstream of the foil was 200 keV, the beam current was varied from a few amperes to a kiloampere, and the beam current duration was about 10"^ s (Fig. 4.11, a). The discharge processes depend substantially on whether the voltage across the gas gap, F, is higher or lower than the dc breakdown voltage Fdc. If V< Fdc, the discharge current in the gap is close in waveform to the beam current and increases linearly with the latter. As this takes place, if the electron supply into the gap is terminated, the discharge current ceases. In this case, the mode of a non-self-sustained discharge is realized, and the discharge operates throughout the volume into which electrons are injected (Fig. 4.11, 6).

78

Chapter 4

Figure 4.11. Typical current waveforms for injected electrons {a\ a non-self-sustained discharge {b\ a spark discharge (c), and an avalanche discharge {d)

If the voltage is increased to about the dc breakdown voltage, the nonself-sustained volume discharge will change into a channel discharge and the current will abruptly increase (Fig. 4.11, c). For V> V^c (pulsed discharge) (Fig. 4.11, d), a spatial glow was observed during 10"^ s in a discharge in nitrogen at a pressure of -3 atm. In this case, the discharge operated due to avalanche multiplication of electrons as a multielectron-initiated pulsed discharge. The transition into a channel phase may occur in both selfsustained and non-self-sustained discharges. A discharge in gas operating under the conditions of intense ionization of the gas by an injected electron beam differs from a discharge operating at lowintensity ionization by the mechanism of conduction, which resembles that realized in a glow discharge. At high ionization rates (over 10^^ cm"^-s"0 and high pressures (10"*-10^ Pa), the electric field is enhanced in a narrow nearelectrode region, remaining practically constant in the discharge column (Fig. 4.12). In this case, the fall potentials in the near-cathode and near-anode regions are generally low compared to the total voltage applied to the gap. Thus, the gap conductance is governed by the discharge column, and, since the use of an electron beam ensures high ionization rates, high discharge current densities are realized. First pulsed discharge experiments were carried out with electron beams of duration 10"^ s and shorter (Koval'chuk et al, 1970; 1971; Marcus, 1972). A discharge sustained by an electron beam of duration 10"^ s was realized by Fenstemacher et al (1972).


E-beam

»

]///

II

Vi\1 \

79

_

y1/

_ \

k 1*0

EK

£o

t

H 'A

d

.

Figure 4.12. Sketch of the field distribution between the electrodes

If we restrict ourselves to the consideration of only the volume discharge phase and do not consider the problems of discharge stability, the principal processes occurring in the discharge can be described by the continuity equations and Poisson's equation for the electric field. For the onedimensional case, we have dng

SjneVe) = av, dx

drij

SjniVi) _

aVene-^ngrti+Y,

••aVg

8t 8E^ dx

dx =

-e{ni-n,')eo;

(4.29) (4.30) (4.31)

Ve = \XeE;

(4.32)

v , = iiiE.

(4.33)

These equations should be complemented with initial and boundary conditions:

«,(0,0v.(0,0 = Y«/(0,0v/(0,0;

(4.34) (4.35)

fÊ(x)dx = Vo.

(4.36)

In Eqs. (4.29)-(4.36), «/ and rie are the ion and the electron density, respectively; v^, v/, lo.^, and \ii are the respective drift velocities and mobilities of electrons and ions; E is the electric field; VQ is the potential difference between the electrodes; d is the gap spacing; \\f is the rate of ionization of the

80

Chapter 4

gas by the beam electrons; q is the rate of thermalization of fast electrons; Y is the coefficient of secondary electron emission from the cathode; a and p are the impact ionization and recombination coefficients, respectively; So is the dielectric constant, and e is the electron charge. For rigorous account of the electron impact ionization of gas, one should complement Eqs. (4.29)-(4.36) with the kinetic equation, which describes the transfer of fast electrons in matter, and consider self-consistently two subsystems: the electrons and ions of the gas discharge, on the one hand, and the beam electrons, on the other hand. The self-consistency implies that the quantities v|/ and q depend on the fast electron flux, which is affected, in turn, by the field E, and, hence, by the quantity rti-ng. However, in this case, the problem becomes much more complicated and its solution looses in clearness. Therefore, we assume that v|/ and q are determined by the beam electrons and by the external field E. The ratios q/\\f and g/^, where 8 is the average energy going for the formation of one electron-ion pair and ^ is the average energy of the beam electrons, are of the same order of magnitude. The function \\f(x) is determined from the relation

^^ = AP(xl,

(4.37)

ee where y'b is the current density of the injected electron beam and D(x) is the distribution of the energy lost per electron along the gap. The distribution D{x) depends on the initial energy of the beam electrons and on the electric field in the gap. We assume that the ionization in the gap is uniform throughout the gap. Qualitatively, the field distribution between the electrodes is the same as that in the case of weak ionization (see Fig. 4.12). In region // of the discharge column, the field is constant, the space charges of electrons and ions neutralize one another, and the ionization is balanced by volume recombination. In the cathode (I) and anode (III) regions, the electric field is stronger than in the column due to the prevalence of the space charge of ions and electrons, respectively. We shall not consider in detail the phenomena taking place in regions / and ///, since the most important phenomena occur in region //, that is, in the discharge column.

4.2

The discharge column

Let us first consider the case of uniform ionization of the gap. If there is no thermalization of electrons (q = 0) and the ionization is uniform, the electric field in the discharge column, i.e., in a region away from both the cathode and the anode, will be invariable and equal to EQ. In this case, for


81

practically important pressures and electrode separations, relations ^0 ^ l^c + Â; d»lc+lAy where VQ is the total voltage across the gap, are generally fulfilled. It follows that the conductance of a gas-discharge gap is mainly the conductance of the plasma column where rij =ne=n. The above considerations substantially simplify the determination of the discharge current-voltage characteristic, since in Eqs. (4.29) and (4.30) we may put d(nv)/dx = 0 for both ions and electrons and define the electric field in the column as Eo=(Vo-Vc-V/^)/d^Vo/d, Then, for a non-self-sustained discharge (a = 0) we readily obtain n(t) =

vP/

*—^ 1 + exp ;-2(v|/py/2^] •

(4.38)

From (4.38) it can be seen that in classifying discharges it is convenient to compare the discharge operative time and the duration of the fast electron beam current, /b- If ^b 10"^ Q~^-m"^ exposed to voltage for t > 10"^ s, the electrothermal ("bubble") discharge mechanism is realized. In the region of the transition from the ionization to the electrothermal breakdown mechanism, the gas formation due to electrolysis (electrochemical discharge) is substantial. If the electrothermal or electrochemical mechanism of a discharge in water in a uniform field is realized, the discharge is initiated at that electrode where the gas generation is more intense (Ushakov, 1975). In this case, the delay in the appearance of luminosity is largely determined by the formation of a gas bubble (or film) on the electrode and its growth to some critical size (Alfimove/a/.,1970). In the range of microsecond pulse durations, the discharge occurs as a leader process developing in two stages (Ushakov, 1975). The first stage is the growth of constricted channels of diameter (1-5)40"^ m, called primary channels, from the electrode into the gap with a velocity of 10^-10^ m/s. For an electrode potential of 10^ V, the electric field at the head of a primary channel reaches 10^^ V/m. The development of a primary channel from the positive or negative electrode is due to self-ionization or impact ionization in the liquid, respectively. At the stage of nucleation of a primary channel, the electric field necessary for the development of ionization in the liquid (about 10^^ V/m) is created at electrode microprotrusions. Primary channels consist of weakly ionized plasma and have high resistance. The longitudinal gradients of potential in a primary channel are (1.5--2)-10^ V/m. As the temperature at the base of a primary channel reaches its critical value, the second stage begins; namely, the ionization wave starts propagating through the ionization channel and the latter transforms into a highly conducting channel. The pressure in the channel increases to several thousands of atmospheres, the channel expands, with a velocity of (1-5)-10^ m/s, to (5-10)-10"^ m. Simultaneously, the current through the channel increases by three orders of magnitude and becomes brighter due to impact and thermal ionization. The primary channel perturbations starting at its origin propagate at a velocity of (1-3)-10^ m/s toward its head. This is the final event of the

96

Chapter 5

first stage of the jerky development of the highly conducting leader channel with longitudinal potential gradients of (2-5)-10^ V/m. Subsequently, a primary channel develops from the head of the leader channel and transforms into a leader channel similar to that described above. The rate of development of a primary channel, the time intervals between the jerks of a leader, and, hence, the effective velocity of propagation of the leader channel, depend on the properties of the liquid and on the parameters of the voltage pulse (Ushakov, 1975; Alfimov et al, 1970). For voltage exposure times from 10"^ s to some nanoseconds, the results of experiments on pulsed breakdown of liquids also suggest the influence of the gas medium. These results are as follows (Ushakov, 1975): a) The electric strength increases with hydrostatic pressure for both nondegassed and degassed liquids. b) The electric strength decreases with increasing temperature. c) For E close to ^br, even in carefiilly cleaned liquids, the energy density near electrode microprotmsions reaches 100 J/cm^ and this may cause local boiling within some fractions of a microsecond. d) Using high-speed shadow photography, local optical structures other than plasmas have been detected. An experiment was performed (Ushakov, 1975) to study the discharge in water on the nanosecond time scale (Figs. 5.2-5.4). The pulse generator used generated voltage pulses of amplitude up to 1 MV and rise time 2 ns with the pulse duration varied in the range 10"^-10"^ s. The water conductivity was a « 10"^Q"^-cm"^ The gap spacing was 0.03-0.12 cm for hemispherehemisphere steel electrodes of diameter 0.8 cm, 0.07-0.8 cm for needleplane electrodes, and 0.15-0.5 cm for blade-plane electrodes. Molybdenum and tungsten needles were used. The blade length was 1.5 cm. For diagnostics, an electron-optical image converter with exposure times of 10"^-lO"^ s was used. For a needle of negative polarity (-N, +P), luminosity appeared, within a few nanoseconds, at the cathode and moved with a velocity of (2-5)-10^ cm/s toward the anode (with the average electric field being 0.8 MV/cm). As the cathode luminosity covered 60% of the gap spacing, another luminosity appeared at the anode and moved with a velocity of-'10^ cm/s toward the cathode, and this was accompanied by a current of 1-5 A. As these two luminosities came together, the switching process began. The discharge from a positive needle had some characteristic features. Limiinosity first appeared at the anode. Its motion velocity was high, no less than 10^ cm/s {E = 0.4 MV/cm), and the current was -30 A. At the opposite electrode (cathode), no luminosity appeared. The switching process in the (+N, -P) gap began as the anode luminosity touched the plane. As the needle was replaced by a blade, the characteristic manifestations of the polarity

ELECTRICAL DISCHARGES IN LIQUIDS

97

effect persisted. When the blade was at a negative potential, an increase in E increased the number of simultaneously developing channels (to 3-7) and the current accompanying their development (to 25-75 A). For a blade of positive polarity, an almost homogeneous luminosity throughout the blade length was observed at the stage of discharge initiation. Subsequently this luminosity became discrete, consisting of 10-15 separate blobs carrying a current of up to 300 A. With a blade of positive polarity, two or three discharge channels were formed, while with one of negative polarity only one discharge channel developed. As the average electric field was increased to 0.7 MV/cm, 15 channels developed on the positive blade and three on the negative one. VWWTXXW^ V \ \ \ \ T C \ \ \ N X W X T X W W C W W T V W W

X W W W W V

y/z/yV////, y///Ay//A yyyyyvyyyy yyyy^vyyy/ yyyyyvyyyy Figure 5.2. Stages of a discharge developing in water in a nonuniform field with a negative needle cathode. £ = 1.2 MV/cm; d=\.5 mm; interframe interval = 10 ns

y///Ay//A y/z/AY///, y/yzryy/y y//yAy//y/ yyyyvyyy/.

xwx^^ww x\\x-\\\\\ v\\\\-\\\\\ \\\v-s\\\\^ x\\v-\\\\x Figure 5.3. Stages of a discharge developing in water with a negative needle anode. F = 0.35 MV/cm; d= 3.2 mm; interframe interval = 10 ns

o ^ \ \ - \ \ \ ^ OCN\V-\\V^ Â^V-XXV^ ^ ^ - ^ ^ ^ ^ ^ V ^ ^ \ \ ^ - \ \ V ^ Figure 5.4. A discharge in a uniform electric field. E = 3.5 MV/cm, d = 0.7 mm; interframe interval = 2 ns

98

Chapter 5

For a discharge in a uniform field of 1.5-3 MV/cm, 6-9 ns prior to the onset of switching, luminosity started propagating from the anode to the cathode with a velocity of--^10^ cm/s (Fig. 5.4). As this luminosity touched the cathode surface, it started growing into a discharge channel, and the switching process began. Considerable progress in the study of the mechanism of electrical discharges in liquids was achieved due to the use of laser technology. Investigations of the prebreakdown phenomena in liquids were carried out with a ruby laser used as an illumination source in a scheme of high-speed schlieren photography (Alfimov et al, 1970; Ovchinnikov and Yanshin, 1985; Abramyan et al, 1971). The nanosecond time resolution made it possible to observe an anode-initiated discharge in a imiform field and to reveal some important features of its initiation and development. In particular, it was established that the electrical discharge had an intricate character and went through several successive stages with different mechanisms and development rates. The fine structure of the discharge at the initial stage was revealed. The results of the experiments (Alfimov etal, 1970; Abramyan et al, 1971) have demonstrated an exceptional importance of the time and space resolution of the recording equipment in studying electrical discharges in liquids. The use of laser illumination in combination with conventional optical methods (schlieren photography, interferometry, etc.) allows one to achieve high time and space resolution simultaneously, which is especially important in studying prebreakdown phenomena in liquids. The optical methods based on measuring the refraction index (density) of the medium make it possible to reveal the earlier stages that precede the occurrence of intense ionization processes (the luminosity stage of an electrical discharge).

4.

THE ROLE OF THE ELECTRODE SURFACE

In liquids, as well as in other dielectric media, a decrease in field uniformity decreases £'br. In this respect, liquids feature a stronger dependence of the electric strength on electrode micro- and macrogeometry than gases. This can be accounted for by the fact that pulsed coronas, whose space charge might screen electrodes and distort the field distribution specified by the electrode geometry, fail to develop in liquids and by the high density of liquids owing to which local fields operating in small volumes are capable of initiating a discharge. An important component of the discharge operation time /a - the time delay to the discharge initiation t\ - is determined for a given liquid by the micro- and macrogeometry of the electrode and by the rate of rise of gap voltage. Obviously, the effect of the electrode geometry on the electric


99

strength of a discharge gap should be most substantial in those cases where t\ makes up a significant portion of the total discharge operation time. The effect of the electrode micro- and macrogeometry on the electric strength of the liquid should be more pronounced for smaller gaps, more uniform electric fields, and higher voltage rise rates (overvoltages). Experimental data support these statements. It has been established (Vitkovitsky, 1987) that the breakdown voltage of needle-plane gaps {d = 3-9.7 cm) in oil for pulses of rise time 1.2 ^s decreases on average by 25-40% as the tip radius of the needle electrode is decreased by more than two orders of magnitude (from 2.5 to 0.01 mm). The measurements performed by Ushakov (1975) have shown that for rectangular pulses of duration 50-60 ns with electrode separations of the order of 1 mm, an increase in tip radius from a few micrometers to several hundreds of micrometers increases Fbr by a factor of 1.5-2. The electrode microgeometry, whose effect on £'br shows up in short gaps with uniform and weakly nonuniform fields, is determined by the surface condition of the electrodes and by the crystalline structure of the electrode metal. It is well known that a way of reducing the number of sites of local field enhancement on electrodes made of polycrystalline metals is their aging by discharges. This operation (sometimes called conditioning) is widely used in vacuum breakdown experiments and in some electrovacuum devices. In some experiments (Lewis, 1959; Felsenthal, 1966; Ward and Lewis, 1963), aging of electrodes was employed in measuring the electric strength of liquids. The exposure of electrodes to discharges prior to measurements is aimed at increasing iE'br and decreasing the spread in £'br and t^. Different experimenters recommend substantially different aging modes. For instance, the recommended number of aging discharges ranges from 5 to 100. Analysis of the experimental data and the aging mechanism itself point to the fact that the conditioning effect depends on a number of factors: the electrode material, area, and surface condition, the voltage exposure time, the amount and rate of release of energy in the spark channel, and the properties of the liquid. Electrode aging has a favorable effect not for all liquids. An increase and stabilization of the discharge time (for E = const) in purified water were observed after 15-20 discharges (Ushakov, 1975). In this experiment, sphere-sphere (0.8 cm diameter) electrode systems and Rogowski electrodes (2.6 cm diameter) were used; the electrodes were made of stainless steel. In the course of aging, the liquid was partially renewed after each breakdown. It can be supposed that no conditioning was observed in oil because not only electrode microprotrusions were destroyed and molten off by the aging discharges, but also hydrocarbon decomposition products deposited on the electrode surfaces, preventing the stabilization of

100

Chapters

the properties of the electrode surface. The foregoing shows that aging of electrodes is an inefficient way of increasing and stabilizing the parameter £br for liquids. In some cases, the most efficient method for reducing the effect of the electrode microgeometry and increasing E\yr of liquids is to cover electrodes with a thin layer of high-strength solid dielectric. It was observed (Ushakov, 1975) that the breakdown voltage of transformer oil and theflashovervoltage of solid dielectrics in a system of coaxial cylinders exposed to microsecond pulses increased by 20-25% if the electrodes were coated with a bakelite lacquer layer of thickness 120-150 |Lim. An increase in breakdown voltage of transformer oil in gaps with a weakly nonuniform field on application of microsecond pulses to electrodes coated with dielectric films was also observed by Standring and Hughes (1962). It should be taken into account that the electric strength of insulating gaps with coated electrodes, which represent a type of combined insulation, depends on the redistribution of the field over the layers of the solid and liquid dielectrics and on the proportion between their £'br values for a given pulse duration. The feature of highly polar liquids, in particular water, as components of a combined insulation is that they have higher conductivity and permittivity compared to solid dielectrics. These factors are responsible for the overloading of solid dielectric layers operating in a sequential combination with highly polar liquids. Ushakov (1975) pointed out that the coating of electrodes with dielectric films increased to some extent the pulsed electric strength of the insulating gap in water; however, this increase was unstable and not in any case this was the consequence of a poor quality of the coating. In analyzing the effect of barriers on the breakdown voltage of insulating gaps in liquids, it should be borne in mind that the dominant factor in the "barrier effect" in liquid is that the barrier behaves as a mechanical obstacle hindering the development of the discharge channel. By the barrier effect is meant the increase in breakdown voltage of a discharge gap due to thin dielectric obstacles mounted in the gap. Since in liquids, in contrast to gases, the ionization zone is extremely small, the barrier is charged to low voltages and its blocking action (by the opposite field) is insignificant; therefore, the barrier effect in liquids is much less pronounced than in gases. The condition for breakdown of an insulating gap in liquid is that the barrier should be broken down under the action of the field localized at the head of the primary discharge channel. The highest electric strength of a gap with a barrier can be achieved by choosing the liquid-to-solid dielectric constant ratio as small as possible and by using high-strength materials for the barrier. For instance, with a celluloid barrier in transformer oil, £'br increases by 24-30%, while in purified water it increases only by 8-19%. The use of


101

high-strength Mylar film in combination with water in a pulse-forming line (Smith et al, 1971) has made it possible to increase the working gradients of the insulation and its resistance with the dielectric permittivity retained high. As the pulse duration is decreased to several nanoseconds, the use of a sequential combination of liquid and solid dielectrics becomes ineffective since under these conditions solid and liquid dielectrics have comparable electric strengths (A. Vorob'ev and G. Vorob'ev, 1966). The electric strength of a liquid insulator decreases with increasing the volume of the dielectric and/or the electrode area for a given degree of field uniformity. An increase in electrode area increases the number of weak points that favor the occurrence of breakdown. These weak points are (solid, liquid, and gaseous) impurity particles in the liquid bulk and geometric irregularities, remainders of polishing agents (abrasive, chromium oxide, etc.), products of oxidation of the electrode metal, adsorbed gases and moisture) on the electrode surface. The available experimental data on the electrode area effect are controversial. The dependence of E'br on electrode area S is very weak: £'br oc S~^'^ (Martin et aL, 1996). Therefore, this effect is not always detectable. In this situation, some inferences can be drawn fi-om experiments performed with different types of voltage pulses, other conditions being comparable. Ushakov (1975) investigated the effect of the electrode area on the electric strength of transformer oil for microsecond pulses and rectangular nanosecond pulses {t^ = 2 ns, /p = 35 ns). The working gaps were formed by four pairs of stainless-steel Rogowski electrodes of different area. The maximum electrode diameter was chosen so that the interelectrode capacitance would not distort the leading edge of the nanosecond pulse. The electrode areas were 1.13, 1.88, 3.14, and 5.24 cm^. The electrode surfaces were carefully polished and a constant time of oxidation of the electrode in air was provided. Preliminary statistical processing of the measurements for electrodes of different area performed to reveal whether they belong to the same or to different categories showed that under these experimental conditions the area effect was observed for microsecond pulses and was absent for nanosecond pulses. The experimental results demonstrate that the electrode area effect depends on the time of voltage action. For a prolonged action of voltage, bridges of foreign inclusions may form where conditions are favorable for breakdown and flashover. Under pulsed voltages, such that impurity microparticles can be considered immobile, an increase in voltage application time enhances the field distortion by impurity particles as they are polarized and, therefore, decreases £'br of the liquid. In a nanosecond breakdown, the major contribution to the area effect should be fi-om weak points on the electrode (anode in a uniform field) surface. However, due to the fact that the discharge is initiated near individual microprotrusions.

102

Chapters

which are present in great numbers on large-area electrodes, comparatively small changes in S change the number of initiating centers only slightly and have no effect on the breakdown. If the electrode area is varied over wide limits, the electrode area effect should be expected on the nanosecond scale as well. Data on the effect of the electrode area on the pulsed electric strength of gaps are given in Chapter 7.

5.

THE ROLE OF THE STATE OF THE LIQUID

An important problem concerns the state of the liquid, namely, its degree of contamination, hydrostatic pressure, and temperature. Weighed solid particles, in high concentrations, have a significant effect on the value of £'br (Ushakov, 1975). The natural moistening of insulating oils does not change their pulsed electric strength at voltage action times of the order of 10"^ s even if the dc breakdown voltage changes three times. It is well known (Skanavi, 1958) that as an oil with 0.03% moisture content is subject to prolonged action of voltage, its E\,^ decreases to one tenth. This implies that the decrease in oil strength by a factor of --3.5, as in the experiment under consideration, is achieved if the moisture content makes up no more than 0.01%. These small variations in impurity concentration fail to change appreciably the pulsed electric strength of oil. At high moisture concentrations in transformer oil corresponding to emulsions of "water-in-oil" (< 30-40%) and "oil-in-water" (> 30-40%) type, the pulsed electric strength of the system decreases with increasing moisture concentration. The decrease in electric strength reaches 40-50% for a pulse duration of-10'^ s and there is almost no decrease for rp 0.5-1 |LIS). U.J

0.4

1 ^

0.3

f\ 1

10 p [atm]

15

20

Figure 5.5. Breakdown electric field E\x for water (a = 5-10"^ Q"^-cm"^) as a function of pressure. Uniform field; t = 0.2 fis;

300

^

Figure 6.6. "Lifetime curve" for a 10.6-m long piece of IC-2 cable

The use of superconductor layers has made it possible to produce a series of type CPV high-voltage cables with polyethylene insulation (CPV-1/20, CPV-1/50, CPV-1/75, CPV-1/300). Experiments performed at TPU have demonstrated that a piece of CPV-1/300 cable of length up to several tens of meters is capable of holding off 6-10 hundred pulses of amplitude 250 kV and 100-200 hundred pulses of amplitude 180 kV. The type IC-4 cable with semiconductor layers, commercially produced in Russia, is designed for prolonged operation under unipolar pulses of amplitude 75 kV. In the United States, a series of special pulse cables with polyethylene insulation and

122

Chapter 6

semiconductor layers is produced. These cables are rated to voltages ranging from 20 to 100 kV and have lifetimes no less than 10^ pulses (for the maximum electric field in the insulation 20-25 kV/mm). Of considerable promise for the use with nanosecond high-voltage generators are coaxial lines with liquid insulators. They have a number of advantages over polymer-insulated cables, such as higher reliability, better conditions for cooling, self-healing of the liquid insulation after breakdown, and less intense damping (Mesyats et al, 1970). The high reliability of this type of coaxial system is ensured by the fact that the solid insulator occupies a small volume and therefore can be carefiilly examined and tested. The properties of liquid-insulated lines are considered in the following chapter.

REFERENCES Belorussov, N. I. and Grodnev, I. I., 1959, Radio-Frequency Cables (in Russian). Gosenergoizdat, Moscow-Leningrad. Delektorsky, G. P., 1963, Mechanism for Breakdown of Polyethylene-Insulated High-Voltage Cables on Application of Voltage Pulses, Vestnik Elektropromyshlennosti, 1:55-57. Howard, P. R., 1951, The Effect of Electric Stress on the Life of Cables Incorporating a Polythene Dielectric, Proc. lEE. 98:365-370. Kalyatsky, I. L, Dulzon, A. A., and Zhelezchikov, B. P., 1965, Distortion of Monopolar HighVoltage Pulses in Coaxial Cables, Izv. SOANSSSR, Tekh. Nauki. 10:151-154. Korolev, V. S. and Torbin, N. M., 1970, Electric Strength of Some Polymers under the Action of Short Voltage Pulses. In Electrophysics Apparatus and Electrical Insulation (in Russian). Energia, Moscow. Lewis, I. A. D. and Wells, F. H., 1954, Millimicrosecond Pulse Techniques. Pergamon Press, London. Meinke, H. and Gundlach, F. W., eds., 1956, Taschenbuch der Hochfrequenztechnik. Springer, Berlin. Mesyats, G. A., Nasibov, A. S., and Kremnev, V. V., 1970, Formation of Nanosecond HighVoltage Pulses (in Russian). Energia, Moscow. Morugin, L. A. and Glebovich, G. V., 1964, Nanosecond Pulse Power Technology (in Russian). Sov. Radio, Moscow. Vorob'ev, A. A. and Vorob'ev, G. A., 1966, Electrical Breakdown and Destruction of Solid Dielectrics (in Russian). Vyssh. Shkola, Moscow. Vorob'ev, G. A. and Mesyats, G. A., 1963, Techniques for the Formation of Nanosecond High-Voltage Pulses (in Russian). Gosatomizdat, Moscow. Zhekulin, L. A., 1941, Propagation of Electromagnetic Signals through Coaxial Cables, Izv. ANSSSR, Tekh. Nauki. 3:11-24.

Chapter 7 LIQUID-INSULATED LINES

1.


As the methods for production of nanosecond high-power pulses were developed, a need aroused in pulse generators with currents of 10^-10^ A, voltages of 10^-10'' V, and pulse durations of 10"^-10"^ s. Generally used as energy stores in generators of this type are capacitors and coaxial or strip lines filled with liquid dielectric (as a rule, transformer oil or water). The nanosecond high-power pulse generators commonly use lines of two types (corresponding to their purposes): energy-storage lines and transmission lines. The former operate with pulse transformers charged by Marx generators or they are charged by a pulse of rise time > 10"^ s. The latter are intended to transfer energy by pulses of duration 10"^-10"^ s. Therefore, it is important to know how oil and water behave imder exposure to microsecond and nanosecond electric fields. Distilled water was first used as a dielectric for an energy-storage capacitor in experiments with electrically exploded wires (Chace and Moore, 1959). Early low-inductance nanosecond generators capable of producing high pulsed electron currents and intense electric fields were developed at the Institute of Nuclear Physics (Novosibirsk) (Lagunov and Fedorov, 1978). Recall that, according to formula (6.5), the wave impedance of a coaxial line is given by ZQ =(60/v8)In(Z)2/A) [^l? where s is the relative dielectric permittivity and D2 and D\ are the respective diameters of the outer and inner conductors. For a strip line, we have Zo=^^[Q],

(7.1)

124

Chapter 7

where b is the strip width and d is the distance between two strips. The general case is dJ|l + ^ |

-1,

(8.2)

where Fis the potential difference between the inner and the outer conductor of the line. (a)

450

- y-

.

1 ^

^

20

J'

1

/I - 1

26\

40 60 t [ns]

/ ^80

19 -

Figure 8.2. Oscillograms of voltage F, currents at the line input, /nne, and output, /output? and leakage current (dashed curve)

The origin of the limiting voltage and current values can readily be understood proceeding from the following considerations: As the gap spacing d, and, hence, the impedance of the acceleration gap, is increased, the voltage should increase and the current should decrease, since the resistance of the line in relation to the leakage electron currents that appear between the line electrodes because of their large area, is much lower than the resistance of the generator. Therefore, a small excess of the line voltage above its limiting value suffices for the appearance of a leakage current toward the outer electrode, which restricts fiirther increase in voltage. As a result, a self-consistent mode is established in the line, such that both the current and the voltage reach their limiting values. Let us consider in more detail the nature of the leakage current toward the opposite electrode of a line. The dynamics of the establishment of magnetic self-insulation was investigated with the help of Faraday cups placed on the outer coaxial tube (Baranchikov et al, 1978). The leakage currents toward the outer electrode appeared within the rise time of the line current pulse with /pp < /mm. The leakage current ceased or decreased by an order of magnitude when the line current became 10-20% greater than /min.

138

Chapters

In the experiment, the leakage was observed at low voltages during the current drop (Fig. 8.2). To explain this effect, we shall consider the distribution of the leakage current near the end face in the limiting mode. Once the cathode has acquired an emissive power necessary to pass /min, the current, according to the estimates obtained with the help of the ChildLangmuir law, closes at the end of the line over a length equal to about the electrode gap spacing. Decreasing voltage increases the width of the leakage region at the end of the line. For y > 2, the width of the leakage region, A, is of the order of the electrode gap spacing, A - (r2 - r\\ and for (y - 1) «c 1, the leakage region may be considerably grater than the electrode gap, A « 9nd/S(y - 1) » t/, and be comparable to the length of the line (Korolev, 1990; Gordeev, 1990). The duration of the first leakage current pulse is determined by the processes initiating explosive electron emission and by the inductance of the line. The leakage currents have the highest values early in the pulse and then decrease quicker than the difference between the line and the anode current. This testifies to a displacement of the leakage currents toward the load with increasing current and magnetic field in the line. (A diode with explosive electron emission is usually used as a load.) This conclusion is confirmed by direct measurements of the density distribution of the electron leakages along the line (Baranchikov, 1978; Aranchuk et al, 1989). The dynamics of the distribution of leakage currents at the end of the line was additionally measured with x-ray gages by scanning the lateral surface of the outer electrode with a resolution of 4 mm. Early in the current pulse, the characteristic length over which the electron flow was concentrated, was 2-3 cm, which was equal to 4-6 electrode gaps. Once plasma had appeared at the internal surface of the outer electrode, ion currents were detected at the negative electrode of the line. The electron current density increased at the stage of growth of the ion current, and this was judged from the observation that the electron leakage region halved in size while the total current varied only slightly. Generally, the electron layer occupies not the whole of the electrode gap. The current /une - /c is transferred by electrons in the coaxial gap. The cathode current is given by the relation (Gordeev, 1990) /c = /iine/y*

(8.6)

For a line operating in the limiting mode, we have /c//min=l/y-l

(8.7)

for low voltages [(y -1) «: l] and IJImin-y-'^'

(8.8)

VACUUM LINES WITH MAGNETIC SELF-INSULATION

139

for high voltages. Thus, at large y most of the current is transferred by electrons accelerated in the electrode gap. Once magnetic insulation has been established, electrons fill the whole of the electrode gap. Numerical calculations that have been carried out for a line with ^2/^1 =2.7/1.1 (cm) operating in the limiting mode at a voltage of 410 kV confirm the conclusion that the motion of particles far from an end face of a line occurs in an electron layer adjoining the inner electrode (Fig. 8.3). However, this layer is wider than that predicted by hydrodynamic calculations. Thus, according to the hydrodynamic theory, for the above values of current and voltage, the layer width is 0.7 cm (dashed line), while the numerical calculations yield 1.0 cm. This discrepancy can be accounted for by the initial spread in particle velocities. The leakage electron current depends on the gap spacing d. For d > do (do being the gap spacing that corresponds to the peak power dissipated in the load), the amplitude of the leakage current pulses increased during the current rise time and fall time, and the plateau between the pulses was more pronounced. This can be explained by the fact that for d > do, as mentioned, V and Fune tend to their limiting values depending on the wave impedance of the line.

z [cm]

Figure 8.3. Trajectory of electrons in the steady-state insulation mode (F= 410 kW,d=2 cm)

The efficiency of the energy transfer through a cylindrical line in a steady-stated mode for a quasi-stationary case with /une > Imm is close to 100%. The energy flux density achieved in lines of length up to 1 m on the MITE system and on one module of the Angara-5 system is over 10^^ W/cm^ at an electric field E 500

0

^

19 /^

.s

0 ^

-y^. ^ / Av ^-^

V

17

\ - ^

1

'lAX. \.^^

0

50

100 / [ns]

Figure 8,4. Oscillograms of the voltage V and currents at the line input, /une, and output, Output, for / = 4.5 m and r2/ri = 2.6/2.0 (cm) and of leakage currents (dashed curves) measured at 0.4 and 3.9 m from the beginning of the line

As a current pulse propagated along the line, its waveform varied. The wave front became more abrupt. This effect had been predicted and termed the magnetron effect by Kataev (1963) who studied shock electromagnetic waves in lines. The current measured by a Faraday cup at the end of the line had a characteristic spike preceding the main front. It should be noted that the signals from the x-ray gages that detected the radiation from the anode practically followed the waveform of the current measured by the Faraday cup placed at the end of the line. The current and the intensity of x rays from the surface of the outer electrode measured at the output of the line suggested that there existed a vacuum forerunner of small amplitude, which was followed by the wave front. The velocity of propagation of the forerunner was equal to the velocity of light. The interval between the onset

142

Chapters

of explosive electron emission, determined by breaks in oscillograms of the voltage at the line input, and the pedestal of the main current pulse measured by the Faraday cup placed at the line end determined the velocity of propagation of the magnetic self-insulation wave. The velocity of propagation of the leading edge of the main pulse over the base / = 4.5 m was much lower than the velocity of light and for a medium amplitude of the voltage pulse at the line input of 460 kV it was 0.45 ± 0.05c. The same values were obtained by the delay of the signals from the x-ray gages that detected the radiation from the line lateral surface and by the occurrence of maximum leakage currents measured by the Faraday cups located along the line. The velocity of the wave front increased with the amplitude of the voltage pulse. In experiments performed on the PULSERAD-1500 machine (F= 3 MV, Zo = 50 Q, ^p = 50 ns) (DiCapua and Pellinen, 1979), the velocity of the magnetic self-insulation wave, determined from oscillograms of currents measured at different places of a coaxial line with rilrx = 11.43/5.72 (cm) and length 10 m at a voltage of 1.8 MV, made up 0.70 ± 0.06 of the velocity of light. As follows from these experiments, a minimum current is established behind the wave front, which corresponds to the configuration of the electron layer adjoining the inner electrode of the line. Figure 8.5 presents the results of experiments carried out at I. V. Kurchatov Institute of Atomic Energy on strip and coaxial lines with diode and resistive loads (Aranchuk etal., 1989; Airapetov et al, 1981; Ware et al, 1985). The polarity of the inner electrode of length up to 10.7 m was either positive or negative and the voltage was 3 MV. Also given in Fig. 8.5 are theoretical expressions for currents i^lellmc^g [g = (lnr2/ri)"^ for the cylindrical case and g = (2nd/by\ where d and b are, respectively, the gap spacing and the line width, for the plane case] obtained in the one-body approximation, / = (y^ -1)^^-^, and in the MHD approximation corresponding to a minimum current /mm and a parapotential current /pp =Yln[y + (Y^ -l)^^^] are given as well. The measured velocities of propagation of the wave front fit well to the formula obtained on the assumption that a minimum current is established behind the wave front and that there exists an electric layer adjoining the negative electrode (Gordeev, 1990)

.^MziOlzI). c

(8.10)

YY* - 1

From oscillograms of the leakage currents and the line input and output currents (see Fig. 8.4), it follows that after the onset of explosive electron emission the wave front in the line becomes steeper. In the experiments on


143

the MS system, the rise time of the output current was 7-10 ns, which made up one-third of the input current. At small amplitudes, as follows from formula (8.9), the velocity of forward areas at the front of a magnetic selfinsulation wave is low, and these areas will be caught up with the areas of the wave front with a higher voltage. This process results in an increased steepness of the wave profile at the front and in the generation of shock waves. 0-7

12

/^C

A-5

9 A^

6

D^

S-""^

^b ^ ^

3 r

1.

J

J

_l

Figure 8.5. Limiting current / versus voltage y = 1 + eV/mc^: a - one-body approximation, / = (y2 - 1)1/2. ^ _ curve corresponding to the minimum current Imm', c - curve corresponding to the parapotential current /pp = y ln(y + (y^ - 1)^^^); 1 - data, of Aranchuk et al. (1989), 2 Airapetov et al. (1981), S - Woodall and Stinnett (1985)

The width of the wave front calculated by the measured velocity and duration of the main leakage pulse is 1-1.5 m, which is 3-4 times less than the length of the line (Baranchikov et al, 1978). The reliability of this estimate of the front width is testified by the fact that the measured amplitude of the leakage current density, 3-4 A/cm^, is in agreement with the value calculated from the leakage current at the main front and the surface of the section of the outer electrode equal to the length of the front: Jieak =I\Qak/2nrvtr. As reported by DiCapua and Pellinen (1979), as a wave propagated through a line, the duration of the wave front decreased to less than 4 ns over a base of 10 m. This corresponded to the front width equal to 0.6 m, which was substantially smaller than the length of the line. The rate of current rise reached 10^^-10*^ A/s. Prior to the onset of explosive electron emission, a vacuum forerunner, an ordinary electromagnetic wave, propagates through the line ahead of the front of the magnetic self-insulation wave. The structure of the wave front strongly depends on the emissive power of the cathode material. For example, for the inner electrode coated with Aquadag, the wave front becomes narrower and the vacuum forerunner

144

Chapters

ahead of the main wave disappears. In the limiting case of "instantaneous" explosive electron emission, the width of the wave front is of the order of the electrode gap of the transmission line. In the actual case of a finite time of explosive electron emission, the structure of the wave front appears to be more intricate (see Fig. 8.4) and its width is larger than the electrode gap. As the potential at the wave front increases, there occurs the moment when the electron emission from the cathode becomes substantial. This is followed by a valley in current and voltage waveforms, and the leakages at the wave front are associated with the valley. As the voltage increases, the current downstream of the deep is observed to increase, which is accompanied by the cessation of the leakage currents. The nonlinear magnetic self-insulation wave can be reflected from the end of the line. This reflection is substantially different from that occurring in a conventional vacuum line. The reflection of the magnetic self-insulation wave was investigated by Van Devender (1979) for 2-m long cylindrical lines with the electrode diameter ratio equal to 1/0.2, 1.8/0.2, and 1/0.1 (cm) and the respective wave impedances 96, 132, and 138 Q for a positive and negative incident pulse of amplitude up to 500 kV. The line carried a resistive load based on a water solution of CUSO4 whose resistance could be varied from a few ohms to several hundreds of ohms. The presence of a resistive load with a known resistance facilitated the interpretation of experimental data. As a voltage pulse was applied to the line with a wave impedance Zo = 138 Q during a time of 35-40 ns, which was equal to the time of double run of the wave through the line, the input current did not depend on the load resistance. For r > 40 ns the pattern was different. In the case R\oad ^ Zo (with the "hot" impedance of the line Zune = 40 Q), since there was no reflected wave, the input current did not depend on the load and the input impedance was close to the line "hot" impedance Znne. This is related to the fact that the resistance of a load at the end of a line cannot be over V/Imm- For resistances i?ioad > V/Imm, the mode of magnetic self-insulation is provided by the passage of some portion of the current to the positive electrode at the end of the line near the load, resulting in a decrease of i?ioad to V/Imm- Therefore, the input current-voltage characteristics remain unchanged. For iJioad < Znne, the input current-voltage characteristics of the line, because of the occurrence of a reflected wave, depend on /Jioad, and as the load resistance is decreased, the input current increases, while the voltage decreases. Similar characteristics have been obtained for other values of the line impedance and voltage. The efficiency of the energy transfer through a line is determined by the load. The highest efficiency is achieved in the matched mode with the load resistance equal to the line "hot" impedance Zune. As the impedance of a line becomes lower or higher than its^ "hot" impedance, the efficiency decreases.


145

As Ziine is decreased relative to its matched value, a line with magnetic selfinsulation behaves as a conventional long vacuum line: the current /load increases, while Fout decreases. As i?ioad is increased relative to its matched value, the output voltage of the line does not vary and is close to the voltage in the matched mode, while /bad decreases. This behavior of the load current and output voltage implies that for i?ioad > ûne the match is achieved due to the passage of a current near the load that shunts the load resistance. Additional losses that occur at the front of the nonlinear magnetic selfinsulation wave propagating through the line are due to the leakage electron current. The energy transfer efficiency r| is estimated by the formula (8.11) Ctr, \V

Ve

where / is the length of the line, tp is the pulse duration, and VQ is the velocity of propagation of an electromagnetic wave in the steady-stated mode. The experimentally found efficiency r| of the beam transport on the MS machine at a voltage of 0.5 MV across the line made up 50%, while the theoretically predicted efficiency was 70%. A high efficiency of energy transfer (90%) through magnetically self-insulated plane lines of length 7 m was obtained on the MITE system at Sandia National Laboratories (Van Devender, 1979).

Figure 8.6. Relative wave front velocity v^/c versus magnetization current / for the line voltage V= 220 (open circles) and 612 kV (solid circles). The solid and dashed lines represent the respective calculated dependences for the above voltages

A method for increasing the efficiency of energy transfer in magnetically self-insulated lines by applying an additional magnetic field to suppress the leakage electron currents at the wave front has been proposed by Van Devender (1979). If the magnetic field is intense enough, the electron layer adjoins the cathode and the line is close by its parameters to a vacuum line.

146

Chapters

In this case, the energy transfer may occur practically without loss. In this experiment, a line with a diameter ratio of 18/2 (mm) (wave impedance Zo= 138 Q) was additionally magnetized by a current passed through the inner electrode. As the magnetization current was increased, the velocity of the wave approached the velocity of light (Fig. 8.6) and the current pulse waveform was close to that typical of a vacuum line because the forerunner disappeared. The "hot" impedance of the line increased with magnetization current, testifying to a decrease in width of the electron layer. At a fixed value of the load impedance there is a magnetization current at which the greatest efficiency of energy transfer is achieved. In this case, the efficiency is low at a small magnetization current and it increases with current, reaching a maximum at the "hot" impedance of the line equal to the resistance of the load.

4.

PLASMAS AND IONS IN A LINE

Among the processes capable of restricting the energy fluxes and energy delivery to the load is the generation of plasma at the electrode surface. The plasma arises at the line electrodes during the action of a high-voltage pulse. The cathode plasma is generated due to the explosive electron emission from the cathode and the bombardment of the cathode by positively ionized atoms emitted from the anode plasma, while the anode plasma results from the interaction of electrons accelerated in the electrode gap with the anode surface. At both electrodes, plasma can be produced by intense illumination of the electrode surface with low-energy x rays, which is most likely to occur in the transition region between the line and the (diode or z-pinch) load. The moving plasma may cause the line gap to close and thus destroy magnetic insulation. Moreover, because of the decrease in effective gap spacing, electron and ion leakage currents may appear. The cathode plasma properties and dynamics in lines were investigated experimentally at electric fields of up to 2 MV/cm (Airapetov et aL, 1981; Woodall and Stinnett, 1985; Stinnett and Woodall, 1985). In these experiments, it has been established that the plasma is produced at the cathode within several nanoseconds. Its density is nonuniform, and at a distance less than 1 mm from the cathode it is 10^^-10^^ cm"^ and its temperature is several electron-volts. The plasma expands, with a velocity of (1-2)-10^ cm/s, in a diffusion manner since the pressure of the magnetic field on the plasma surface is greater than the gas-kinetic pressure. From spectroscopic measurements of the plasma composition, it follows that the basic contribution to the plasma luminosity is firom the lines of hydrogen.


\A1

The reduced velocity of the plasma corresponds to the thermal velocity of hydrogen ions with a temperature of 2 eV. A model, which takes into account the influence of the expanding cathode plasma on the power transfer through a magnetically insulated vacuum line, is proposed by Stinnett et al (1985). The plasma was considered to appear at an electric field of 0.3 MV/cm. Calculations were carried out for a line of length 2 m with an aluminum cathode of radius 6.2 cm and an electrode gap of spacing 0.5 cm. The line carried an inductive load of 18 nH at an applied voltage pulse of amplitude 0.5 MV and duration 150 ns. With the initial plasma parameters used in these calculations (temperature 5 eV, density per unit area 8.7-10"^ g/cm^, and layer width 1 |im), the plasma is practically not decelerated by the magnetic field up to / = 60 ns (or up to the 50th nanosecond from the onset of explosive electron emission) and later the plasma front velocity decreases (at / = 120 ns it was 4-10^ cm/s). Up to the 120th nanosecond, the average velocity of the plasma front was 2.4-10^ cm/s. From the results of these calculations it follows that a considerable portion of the current (up to 50% of the total line current) is transferred in the plasma sheath and the expansion of the cathode plasma results in a change in the effective gap spacing of the line and in an increase in the line current by 10-20% compared to the no plasma case. The evolution of the spatial distribution of losses at the anode was studied with the help of a three-frame electron-optical system. A thin plastic scintillator attached to the anode served as a converter of braking radiation. Typically, the luminosity consisted of luminous spots, each about 1 mm in size. The spots appeared and disappeared within the interframe interval (5 ns). Putting in correspondence the dynamics of spots observed on electron-optical pictures and the level of the leakage current density at the anode, one could estimate the current in individual local spots (about 1 kA). The plasma sheath at the anode serves as an emitter of ions, which, in actual accelerators, are not magnetized and are freely accelerated by the electric field in the vacuum gap. The leakage ion current is due to the distribution in the gap of the ion and electron space charge and depends on the position and dimensions of the electron layer. The equilibrium position of the layer should in turn vary, as ion leakages appear, because of the redistribution of the electric field. For practical use of an MIVL, it is important to determine the minimum current starting from which there is an equilibrium layer of electrons in the presence of an ion flow and the dependence of the leakage ion currents on the voltage and the gap width. The presence of ions in an electrode gap increases the minimum electron current of magnetic self-insulation. Qualitatively, this can be explained using the analogy to a conventional diode. In a planar vacuum diode with no electron emission, the electric field in the gap is a constant. As an electrode

148

Chapters

emits charged particles, the electric field at the electrode decreases to zero. The field in the electrode gap becomes nonuniform, increasing at the other electrode by 1/3 compared to that in a vacuum diode. A similar effect arises in a line with magnetic self-insulation of electrons in which emission of ions takes place. For y ^ 1, when the electron layer is narrow, the minimum current is greater by 1/3 than /min in a line without ions. For practical applications, the problem of the excess of the ion leakage current above its values obtainedfi*omthe Child-Langmuir law is important. In experiments, the maximum (sixfold) excess has been obtained mainly due to the nearelectrode plasma layers expanding with a velocity of about 10^ cm/s. In contrast to positive ions, negative ions present in a line increase the electric field in the electrode gap. Therefore, to realize magnetic insulation calls for a stronger magnetic field. Moreover, an increase in ion density can have the result that the balance of pressures in the electron layer fails to be maintained and magnetic insulation is disrupted (Sincemy et al, 1983). In experiments (Waisman and Chapman, 1982; Korolev et al, 1983) carried out on 2-MV, 400-kA, 35-ns accelerators, in a line of length 6 m with magnetic self-insulation, leakage currents of negatively charged ions (H", H2, C", O", O2) were detected with the help of a time-of-flight spectrometer and Faraday cups set on the diode. Although the current density in these experiments reached high values (50 A/cm^), the regions of ion leakages were localized in the line and did not give considerable losses. The losses depended on the distance along the line and were determined by the conditions of production of cathode plasma (the rate of variation of the electric field, the amplitude of the voltage forerunner, and the electric field strength). Magnetically insulated vacuum lines are widely used as transmission and energy storage units (Al'bikov et al, 1990; Van Devender et ai, 1981; Turman et al, 1985; Stinnett and Stanley, 1982; Gordeev et al, 1983; Yonas, 1981; Ware et al, 1985; McClenanan et al, 1983; Babykin et al, 1991; Koval'chuk and Mesyats, 1985). This will be discussed in detail in Chapter 16.

REFERENCES Airapetov, A. Sh., Krastelev, E. G., and Yablokov, B. N., 1981, Operation of a Magnetized Vacuum Transmission Line, Zh Tekh. Fiz. 51:1548-1550. Al'bikov, Z. A., Velikhov, E. P., Veretennikov, A. I., Glukhikh, V. A., Grabovsky, E. V., Gryaznov, G. M., Gusev, O. A., Zhemchuzhnikov, G. N., Zaitsev, V. I., Zolotovsky, O. A., Istomin, O. V., Kozlov, I. S., Krasheninnikov, S. S., Kurochkin, G. M., Latmanizova, V. V., Matveev, Yu. A., Mineev, G. V., Mikhailov, V. N., Nedoseev, S. L., Oleinik, G. M., Pevchev, V. P., Perlin, A. S., Pechersky, O. P., Pismenny, V. D.,


149

Rudakov, L. I., Smimov, V. P., Tsarfin, V. Ya., and Yampolsky, I. R., 1990, The Angara-5-1 Experimental Facility, .4/. Energ. 68:26-35. Aranchuk, L. E., Baranchikov, E. I., Gordeev, A. V., Zazhivikhin, V. V., Korolev, V. D., and Smimov, V. P., 1989, Investigation of a Magnetically Self-Iinsulated Line with Ion Leakages, Zh Tekh. Fiz. 59:142-151. Babykin, V. M., Gordeev, G. T., and Korolev, V. D., 1991, Dynamics of an REB in a HighCurrent Diode with a Blade Cathode, Fiz. Plazmy. 17:1102-1110. Baksht, R. B. and Mesyats, G. A., 1970, Effect of a Transverse Magnetic Field on the Current of the Electron Beam at the Initial Stage of a Vacuum Discharge, Izv. Vyssh. Uchebn. Zaved.Fiz. 7:144-146. Baranchikov, E. I., Gordeev, A. V., Korolev, V. D., and Smimov, V. P., 1978, Magnetic SelfInsulation of Electron Beams in Vacuum Lines, Zh. Eksp. Teor. Fiz. 75:2102-2121. Baranchikov, E. I., Gordeev, A. V., Korolev, V. D., and Smimov, V. P., 1977a, Transportation and Focusing of Relativistic High-Current Electron Beams in Magnetically Insulated Coaxial Lines. In Proc. 2nd Symp. on Collective Acceleration Techniques (Dubna, 29 Sept. -2 Oct., 1976) (in Russian), Dubna, pp. 271-274. Baranchikov, E. I., Gordeev, A. V., Korolev, V. D., and Smimov, V. P., 1977b, The Wave Mode of Magnetic Self-Insulation in a Vacuum Line, Pis 'ma Zh. Tekh. Fiz. 3:106-110. Bemstein, B. and Smith, I., 1973, "Aurora", an Electron Accelerator, IEEE Trans. Nucl. Sci. 20:294-300. Brillouin, L., 1951, Electronic Theory of the Plane Magnetron. In Advances in Electronics (L. Marton, ed.), Vol. 3. Academic Press, New York, pp. 85-144. Danilov, V. N., 1963, The Generalized Brillouin Mode of Electron Flows, Radiotekh. Elektron. 11:1892-1900. Danilov, V. N., 1966, On the Theory of Brillouin Electron Flows, Ibid. 11:1994-2007. DiCapua, M. S. and Pellinen, D. G., 1979, Propagation of Power Pulses in Magnetically Insulated Vacuum Transmission Lines, J. Appl. Phys. 50:3713-3720. DiCapua, M. S., Pellinen, D. G., Champney, P. D., and McDaniel, D., 1977, Magnetic Insulation in Triplate Vacuum Transmission Lines. In 2nd Intern. Conf. High Power Electron and Ion Beams, Ithaca, USA, Vol. 2, pp. 781-792. Gordeev, A. V., 1990, Theory of Magnetic Insulation. In Generation and Focusing of Relativistic High-Current Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 81-122. Gordeev, A. V., Korolev, V. D., Sidorov, Y. L., and Smimov, V. P., 1975, Production and Focusing of High-Current Beams of Relativistic Electrons up to High Densities, Ann. N. Y. Acad Sci. 251:668-678. Gordeev, E. M., Zazhivikhin, V. V., Korolev, V. D., Liksonov, V. I., Tulupov, M. V., and Chemenko, A. S., 1983, Effects of Local Plasma Generation during Energy Concentration in Magnetically Self-Insulated Vacuum Lines, Fiz. Plazmy. 19:1101-1109. Kataev, I. G., 1963, Electromagnetic Shock Waves (in Russian). Sov. Radio, Moscow. Korolev, V. D., 1990, Magnetically Insulated Vacuum Transmission Lines. In Generation and Focusing of Relativistic High-Current Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 43-81. Korolev, V. D., Smimov, V. P., Tulupov, M. V., Tsarfm, V. Ya., and Chemenko, A. S., 1983, Formation of Plasma Flows in High-Current Diodes, Dokl. ANSSSR. 270:1109-1112. Koval'chuk, B. M. and Mesyats, G. A., 1985, Nanosecond Pulse Generator with a Vacuum Line and a Plasma Opening Switch, Dokl. ANSSSR. 284:857-859. Lovelace, R. N. and Ott, E., 1974, Theory of Magnetic Insulation, Phys. Fluids. 17:1263-1268.

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McClenahan, C. R., Backstrom, R. C , Quintenz, J. P., et al, 1983, Efficient Low-Impedance High Power Electron Beam Diode. In Proc. 5th Int. Topical Conf. High Power Electron and Ion Beam Research and Technology, San Francisco, CA, pp. 147-150. Ron, A., Mondelli, A. A., and Rostoker, N., 1973, Equilibria for Magnetic Insulation, IEEE Trans. Plasma Sci. 1:85-93. Sincemy, P., DiCapua, M., Stingfield, M., et al., 1983, The Limit of Power Flow along a High-Power MITL. In Proc. 5th Intern. Conf. High Power Particle Beams, San Francisco, pp. 267-271. Smith, I. D., Champney, P. D., and Creedon, J. M., 1976, Magnetic Insulation. In Proc. 1st IEEE Intern. Pulsed Power Conf., Lubbock, TX, pp. 11-8. Stinnett, R. W., Allen, G. R., Davis, H. P., Hussey, T. W., Lockwood, G. J., Palmer, M. A., Ruggles, L. E., Widman, A., and Woodall, H. N., 1985, Cathode Plasma Formation in Magnetically Insulated Transmission Lines, IEEE Trans. Electr. Insul. 20:807-809. Stinnett, R. W. and Stanley, T., 1982, Negative Ion Formation in Magnetically Insulated Transmission Lines, y. Appl. Phys. 53:3819-3823. Stinnett, R. W. and Woodall, H. N., Kinetic Loss Experiments on MITE. In Proc. 5th IEEE Pulsed Power Conf, Arlington, VA, Pt III, pp. 503-506. Turman, B. N., Martin, T. H., Neau, E. L., et al, 1985, PBFA-II, a 100 TW Pulsed Power Driver for the Inertial Confinement Fusion Program. In Proc. 5th IEEE Pulsed Power Conf, Arlington, VA, pp. 155-161. Van Devender, J. P., 1979, Long Self-Magnetically Insulated Power Transport Experiments, J. Appl. Phys. 50:3928-3934. Van Devender, J. P., Stinnett, R. W., and Anderson, R. V., 1981, Negative Ion Losses in Magnetically Insulated Vacuum Gaps, Appl. Phys. Lett. 36:229-233. Voronin, V. S. and Lebedev, A. N., 1973, Theory of the Magnetically Insulated High-Voltage Coaxial Diode, Zh. Tekh. Fiz. 43:2591-2598. Voronin, V. S., Kolomensky, A. A., Krastelyev, E. G., et al., 1979, Energy Transport in Magnetically Insulated Vacuum lines. In Proc. Ilird Intern. Topical Conf on High Power Electron and Ion Beams, Novosibirsk, Vol. 2, pp. 593-602. Waisman, E. and Chapman, M., 1982, Vacuum Transition Lines in the Presence of Resistive Cathode Plasma, J. Appl. Phys. 53:724-730. Ware, K., Loter, N., Montgomery, M., et al., 1985, Source Development on Black Jack 5. In Proc. 5th IEEE Pulsed Power Conf, Arlington, VA, pp. 118-121. Woodall, H. N. and Stinnett, R. W., 1985, Injector Losses on MITE. Ibid. pp. 499-501. Yonas, G., 1981, Inertial Fusion Research Using Pulsed Power Drivers. In Proc. 10th European Conf. Control. Fusion and Plasma Physics, Moscow, Vol. 2, pp. 134-138.

PART 4. SPARK GAP SWITCHES

Chapter 9 HIGH-PRESSURE GAS GAPS

1.

CHARACTERISTICS OF SWITCHES

Depending on the means of energy storage in a pulse generator, closing or opening switches are used for capacitive and inductive energy storage, respectively. In this chapter, we consider closing spark gap switches with a high-pressure gas discharge. This implies that the conditions in the discharge gap correspond to the right branch of the Paschen curve. Besides, lowpressure discharges, vacuum discharges, discharges in liquid and solid electrolytes, and discharges over the surface of a dielectric are used. The characteristics of spark gap switches depend on the functions they perform in generators. First, these are time characteristics. It is necessary to have a short switching time ts (lO'^^-lO"^ s), a short triggering delay time /d (10-^-10-^ s), and a low jitter A/a (10-^^-10"^ s). Second, these are characteristics associated with the switch current and voltage. The peak current passed by one switch is generally / « 10^-10^ A at a voltage F« 10^-10^ V. In some cases, a wide range of operating voltages is necessary which is characterized by the ratio of the greatest operating voltage Fmax to the least one Vmm, i-e., 8 = Fmax/'^min • Third, important parameters that are responsible for the efficiency of a generator are its residual resistance and inductance, and, while the first parameter is determined by the physical properties of the discharge plasma in the gap, the second one depends, besides, on the geometry and design of the switch components. Fourth, in some cases, generators should be capable of operating repetitively, and the pulse repetition rates range from some fractions of a hertz to 10"* Hz and more.

154

Chapter 9

It should be noted that there are no generators whose switches meet all above requirements. However, there is one parameter of critical importance in nanosecond pulse power technology. This is the switching time /§ that must be short. We already mentioned that one way of attaining short 4 is to increase the gas pressure in the spark gap and the other is to increase the overvoltage across the gap. For qualitative estimation of the dependence of/§ on gas pressure/? for a gap operating under the conditions of dc breakdown, we shall use the model of Rompe and Weizel. According to this model, we have pt^ - (E/p)'^. For a constant voltage of dc breakdown of gas, Fdc = const, according to Paschen's law (see Chapter 4), the product of gas pressure by gap spacing, pd, should also remain constant, and, hence, the quantity E^Jp = V^Jpd will be constant as well. This implies that the time 4 decreases with increasing gas pressure as ^s '^ 1/p (Vorob'ev and Mesyats, 1963). Figure 9.1 gives t^ as a function ofj^ for different gases (Mesyats, 1974). The time /§ was measured using the switching characteristic V{t) between the 80% and 10% levels of the dc breakdown voltage, which was equal to 15 kV. A charged coaxial cable was discharged through a switch. The peak current was 100 A. Figure 9.1 demonstrates that the time ^s actually decreases with increasing gas pressure p. For instance, U « 20 ns for air at atmospheric pressure and about a nanosecond at 10 atm. Different gases have different switching characteristics. For example, argon has the best switching characteristic of those xmder consideration. Even at atmospheric pressure it shows the time /s ^ 5 ns, while for helium, even atp « 10 atm, U « 30 ns. For hydrogen, we have /s« 100 ns at atmospheric pressure and /s« 3 ns at 6 atm. For some ts(p) curves, the decrease in U with pressure becomes more abrupt when going from low to high pressures. This is due to the prolonged stepped decrease in gap voltage (Kunhardt, 1990) that takes place for some gases at low pressures (p < 1 atm). For a dc breakdown, a decrease in gap spacing leads to a decrease in ^sActually, for the right branch of Paschen's curve, in the region close to the minimum, we have

^= 4 . 4 .

(9..)

P Pd For air, .4] = 62-10^ V/cmatm and B\ = 340 V. Hence, (Aipd-^BiY that is, at a constant gas pressure, the time ^s will decrease with decreasing gap spacing d. This conclusion is illustrated by the plots oftsip) for different

HIGH-PRESSURE GAS GAPS

155

d in Fig. 9.2. For d = 0.2 mm, we have a short time ts « 10"^ s even for air at atmospheric pressure. This effect is used in closing multielectrode switches (see Section 6 in Chapter 9), which have the time ts « 10"^ s even for air and nitrogen at atmospheric pressure (Mesyats, 1974).

10^ p [mmHg] Figure 9.1. Pulse rise time as a function of fill gas pressure: I - air, 2 - carbon dioxide, 3 nitrogen, 4 - hydrogen, 5 - freon, 6 - helium, and 7 - argon

Figure 9,2. Time U as a function of air pressure for rf= 2.2 (7), 0.98 (2), 0.7 (i), 0.4 (4\ and 0.2 mm (5)

156

Chapter 9

A switch is generally triggered by some action on its gap (or gaps), such that the condition E>E^,

(9.3)

is fulfilled. Here, £'dc is the dc breakdown electric field and E is the electric field in the gap. Condition (9.3) can be fiilfilled by increasing E or decreasing J^dc- Therefore, there are switches of two types. Three-electrode switches and numerous modifications of muhielectrode switches, switches with low-energy electrons injected into the gas, and capacitive two-electrode spark gaps with gas depressurization pertain to the first type. The secondtype switches are gas spark relays, trigatrons, laser-triggered switches, etc.

2.

TWO-ELECTRODE SPARK GAPS

The elementary type of switch used in nanosecond pulse generators is the two-electrode spark gap with compressed gas, which is triggered by an applied voltage. Switches of this type are also referred to as self-breakdown spark gaps. The discharge in them occurs when, in accordance with (9.3), the electric field E becomes greater than the dc breakdown electric field ^dc. Generally, an energy storage line or capacitor, which is pulsewise charged from a Marx generator or pulse transformer, is discharged through such a switch into a load. When using this type of switch, fast charging of the line is desirable to reduce the switch dimensions, and, hence, inductance. However, during fast charging, a jitter may appear in the breakdown of the gap; therefore, the gap should be adjusted so that the breakdown would occur not when the charge voltage peaks, but some time earlier. This would decrease the amplitude of a nanosecond voltage pulse across the load. It seams that the optimal time it takes for the charging pulsed voltage to reach a maximum ranges between a microsecond and several microseconds. With these times, a two-electrode spark gap operates in fact in the mode described by Paschen's law. Therefore, it can be triggered up not only by increasing the voltage between the electrodes, but also by reducing gas pressure p or decreasing gap spacing d between cathode and anode. Twoelectrode switches are used in Marx generators and as the main switches in nanosecond pulse generators. Vorob'ev and Mesyats (1963) describe a nanosecond relaxation generator in which a spark gap filled with nitrogen at 10 atm was broken down during the charging of a capacitor C through a resistor R, In this generator, the pulse repetition rate was determined by the time constant RC. Two-electrode spark gaps with SFe that operated at megavolt voltages and Zioad = 10 Q (Fig. 9.3)


157

are described by Harrison et al, (1974). The characteristics of generators with two-electrode spark gaps are given in Table 9.1. ib) 3 — y

2

4

5 p.

1-^

J_. "^ L^ —=t

V

1

/

—

6

r- ^^^^==^ _

Figure 9.3. Schematic diagrams of nontriggered gas switches: (a) 1,4 - electrodes, 2 - pins, 3 - SF6 at 4-5 atm, 5 - housing; {b) 1 - electrodes, 2, 6 - inner conductors, 3, 5 - outer conductors, 4 - SFe at 4-5 atm, 7 - insulators; (c) 1 - electrodes, 2, 5 - inner conductors, 4 SF6 at 12-15 atm, 3 - outer conductor, 6 - slab insulator Table 9.1. Output voltage, MV 0.5 1.0 2.0

Spark gap types in Fig. 9.1,(2, Z> Inductance ^load*r» L,nH Qns 90 116 169 135 305 248

Spark gap type in Fig. 9.1, c Inductance ^load*r» I,nH Qns 80 55 130 100 240 190

From the data listed in this table it follows that the pulse rise time is determined in the main by the inductance of the spark gap, that is, U « LIZ\o^^, High-pressure two-electrode spark gaps are widely used in generators operated repetitively with pulse repetition rates of 10^-10^ Hz (SINUS, Radan, SF, etc.) at voltages of 10^-10^ V and average powers of 100 kW and more, which have been created at the Institute of High Current Electronics (IHCE) in Tomsk and at the Institute of Electrophysics (lEP) in Ekaterinburg. In the spark gaps of the SINUS generators, the gas is forced to flow at an optimum velocity. The gas flow velocity should be high enough to remove plasma from the gap within the pulse interval, but not too high to keep the discharge region at the cathode heated in order that initiating electrons could appear during the discharge initiated by the next pulse. This will be discussed in detail below. One of the factors that limit the repetitive operation capability of twoelectrode switches is the discharge chaimel through which the current flows. This channel, on the one hand, has a high inductance, which gives no way of obtaining the required short pulse rise times. On the other hand, because of the high current density in the channel, the latter leaves at the electrodes a strongly heated metal, slowly deionizing plasma, and a strongly heated gas.

Chapter 9

158

To resolve these problems, it was proposed to use spark gaps with a multiavalanche volume discharge (Mesyats, 1974). In such a spark gap, the inductance is very low (< 1 nH), and the gas and electrodes are not heated because of the low current density in the spark gap, since y - IIS, where / is the current and S is the electrode area. Generators of this type are capable of operating with pulse repetition rates of up to 10"^ Hz and more in the picosecond pulse mode. The construction of a switching device used in a generator is shown schematically in Fig. 9.4. Between plates 1 and 3 there is gas interlayer 5, which is formed because the plates adjoin one another at the places of microprotrusions present on the ceramic and metal surfaces. The average width of the gap between elements / and 2 is determined by the condition of the surfaces and generally lies in the range 10-30 |Lim. When a pulsed voltage is applied between the electrodes, a surface discharge develops along the ceramics through the points where the latter touches the metal. The luminescence of this discharge causes the appearance of electrons near the cathode that initiate an avalanche discharge in the air gap between ceramics 1 and metal electrode 3,

Figure 9.4. Schematic diagram of an avalanche gas switch: 1 electrodes; 4 - silver coating; 5 - air gap

BaTiOs tablet; 2, 5 - metal

Detailed information on the operation of two-electrode gas gap switches can be found in the monographs by Koval'chuk et al (1979) and Vitkovitsky (1987) and in the review by Buttram and Sampayan (1990).

3.

THREE-ELECTRODE SPARK GAPS

A three-electrode spark gap is arranged as follows (Fig. 9.5, a): Electrode 2 is generally connected to a source of high dc voltage V and electrode 1 is grounded through a load. The width of the gap 2-3 is chosen such that the


159

gap is not broken down at the voltage V, and the gap 1-3 has such a width that it is not broken down at the voltage of the trigger pulse. As the trigger pulse, whose polarity is inverse with respect to F, arrives at the electrode 3, the gap 2-3 is broken down and the middle electrode acquires the potential V. For the gap spacing ratio (^2-3/^1-3 « 2, the spark gap has the greatest double range of operating voltages. Investigations of the operation of three-electrode spark gaps (Mesyats, 1974; Stekol'nikov, 1949) have shown that to decrease the triggering delay time and jitter, it is necessary to increase the amplitude and rate of rise of the trigger pulse. For the trigger pulse dV/dt = 40-50 kV/|Lis and amplitude making up 50-70% of V, the jitter was of the order of 10"^ s.

Figure 9.5. Schematic arrangement of electrodes for various types of triggered switch: a three-electrode spark gap switch, h - trigatron, c - spark relay

A generator was developed (Vorob'ev and Mesyats, 1963) in which the gas in the three-electrode spark gap was illuminated with ultraviolet radiation generated by an auxiliary spark gap connected in series in the cable by which a trigger pulse was supplied. At voltages of 10-15 kV the threeelectrode gap was triggered with 1 ns jitter. Schrank et al (1964) described a three-electrode switch whose gaps were illuminated with the ultraviolet radiation of a surface discharge along a high-s ceramics (barium titanate) to decrease and stabilize the triggering time. The spark gap was utilized in a pulse generator for powering a spark chamber. The voltage across the spark gap was 30 kV and the current was 5 kA. The working gas was a mixture of 90% N2 and 10% CO2 at a pressure of 3.5 atm. The triggering delay time of the spark gap was 25 ns with a jitter of several nanoseconds. Short and stable triggering times are typical of three-electrode spark gaps triggered by the principle of field distortion (Mercer et ai, 1976). Figure 9.6 illustrates the distortion of the field in a typical spark gap operating in the megavolt region. The trigger electrode is generally placed in the middle of the electrode gap. This electrode has the shape of a thin plate with a sharp edge, but in the initial state, there is no enhanced electric field at this electrode because it is under the voltage corresponding to the equipotential line along which it is located. Then the trigger pulse changes the trigger

160

Chapter 9

electrode voltage to a value usually lower than the potential of the nearest main electrode. This distortion of the natural fields in the gap results in a very strong field at the edge, giving rise to a corona and a streamer. Initially, the gap between the trigger and the high-voltage electrode is generally broken down which is followed by the breakdown of the gap between the trigger and the grounded electrode. (^) I

Main

I

(^)

electrodes

^.==^^)V Trigger electrode Figure 9.6. Circuit diagram of a three-electrode spark gap triggered due to field distortion: a without a trigger pulse, h - with a trigger pulse. The trigger electrode is located in the K/3 potential line

To ensure small jitters of breakdown (about 1 ns) and triggering, it is necessary to have a short breakdown delay time, about 10 ns. The breakdown delay time is determined by the development time of the streamer and depends in the main on the time of occurrence of the streamer at the edge of the trigger electrode; the elongation of the streamer occurs rather quickly. Hence, the efficiency of triggering of a spark gap is determined by the electric field created by the trigger pulse at the edge of the trigger electrode, and this field, in turn, appreciably depends on the amplitude of the trigger pulse and the radius of curvature of the edge. For multimegavolt spark gaps, the trigger electrode can be placed near the middle of the gap, applying a trigger pulse that changes its potential only by several hundreds of kilovolts. However, higher fields can be obtained at the edge of the trigger electrode if it is placed near one of the electrodes lengthways an equipotential line corresponding to several hundreds of kilovolts. The arrangement of the trigger electrode near a fixed equipotential line helps one to localize field distortion in a small region. Since spark gaps with field distortion are used at higher and higher voltages, this geometry appears very convenient. A spark gap of this type with an operating voltage of 3 MV and a breakdown delay time t^ = 20 ns with about 1 ns jitter is described by Mercer et al (1976). Short values of t^ are realized due to high average electric fields in a discharge gap; therefore, the SFe fill gas was used at a pressure of --10 atm. This has also made it possible to reduce the dimensions of the

HIGH'PRESSURE GAS GAPS

161

spark gap and its inductance. In SF6, the streamers from the positive electrode propagate with a higher velocity than those from the negative one. Therefore, the trigger electrode was mounted near the grounded electrode, since the main voltage was of negative polarity. A previously developed spark gap of similar design was used a trigger spark gap in the Aurora accelerator (Bernstein and Smith, 1973). For a 1.8-mm gap spacing between the trigger and the grounded electrode, the breakdown jitter was 2-3 ns. To reduce the jitter, it was decided to increase the field at the edge of the trigger electrode by increasing the gap spacing to 5 mm with a corresponding increase of the trigger pulse amplitude. Three-electrode spark gaps of other types can also be operated in parallel that to reduce the inductance of the discharge circuit at voltages of up to 100 kV. For instance, two parallel-connected three-electrode spark gaps were operated with 2 ns jitter (Mesyats, 1974) describes the operation of is described; the jitter of the operation of these spark gap was 2 ns.

4.

TRIGATRONS

A trigatron (Fig. 9.5, b) consists of two main electrodes - cathode 1 and anode 2 - and trigger electrode 3 made as a metal rod, which is sometimes enclosed in a dielectric tube, and placed along the main axis. There are two mechanisms of the operation of a trigatron, depending on the construction of the trigger unit and the applied voltage. Let us first consider the operation of a trigatron at voltages of some tens of kilovolts. As a voltage pulse arrived at the trigger electrode, a discharge occurs between the rod 3 and the electrode 7. The ultraviolet radiation of this discharge initiates breakdown between the main electrodes 1 and 2. The triggering delay time of this type of trigatron is generally 10"^ s with a jitter of 10"^ s. Theophanis (1960) examined the possibility of triggering a trigatron with nanosecond jitter. The trigatron was in the atmosphere of freon at a pressure of 100 mm Hg. The operating voltage was 50 kV. The examination has shown that the operation time of the trigatron is shorter if the polarity of the trigger pulse is opposite to that of the potential of the ungrounded electrode. As a capacitor was discharged through the trigatron, a trigger pulse of amplitude 16 kV and rise time 20 ns appeared. When the trigatron voltage was 10% lower than Fdc, the delay time was 20 ns with a jitter of 1 ns. The delay time and jitter decrease with a decrease in rise time of the trigger pulse because of the increase in overvoltage between the electrodes I and 3, In the experiment performed by Lavoie et al (1964), to reduce the amplitude of the pulse triggering a trigatron, the trigger electrode was coated

162

Chapter 9

with barium titanate (BaTiOs), a dielectric with a high permittivity (8> 1000). Between the dielectric coating of electrode 3 and electrode 1 there was a small gap across which almost all the voltage appeared to be applied on application of the trigger pulse. In spark gaps of this type, filled with air at atmospheric pressure, the highest operating voltage was 25 kV, the delay time ranged from 17 to 65 ns, depending on the required operation mode, and the jitter was not over 3 ns. The trigger pulse amplitude and rise time were, respectively, 0.5-1 kV and 5 ns. Markins (1971) has demonstrated the possibility to achieve nanosecond jitters for a trigatron switch at voltages of the order of 10^ V. The trigger voltage generally used ensured breakdown of the trigger gap in the absence of the main charge voltage. In the experiment, the ampHtude of the trigger pulse was diminished to a value at which there was no breakdown of the trigger gap in the absence of the main voltage. However, when the main voltage was applied, no difference in the operation of the spark gap in these two modes was noticed. At a pressure of -5 atm, the breakdown of the trigger gap occurred with a delay of--10 ns and the delay to the breakdown of the main gap was 20-70 ns; the average velocity of the streamer in this case was --10^ cm/s. Thus, for a trigatron operating at high voltages, it is necessary that breakdown first occurred between the electrodes 1 and 2 rather than between the electrodes 1 and 3. This is the second mechanism of operation of a trigatron. At a self-breakdown voltage Fdc = 0.95 MV, the triggering jitter varied from 1.5 ns at F = 0.95 Fdc to 7 ns at F= 0.6 Fdc. Thus, the stable triggering range was (0.55-1.0)Fdc. Four trigatrons of this type connected in parallel switched a line with a wave resistance of 1.5 Q, which was charged to 2 MV and produced a pulse of duration /p = 70 ns and rise time t^ = 20 ns (Markins, 1971). Similar spark gaps were used in the experiments described by Martin (1973) and on the improved Gamble I generator (Cooperstein et al, 1973). In the latter case, an eight-channel trigatron was used which operated at voltages of 1-3 MV with 2 ns triggering jitter of each channel. The inductance of such a spark gap was 70 nH, which made it possible to obtain the rise time of the output pulse equal to 20 ns in switching a 4-Q line into a matched transformer line. Trigatrons having a considerably shorter and more stable delay time were tested in experiments performed by Koval'chuk et al (1979) and El'chaninov et al (1975). Figure 9.7 presents the delay time of operation of a trigatron, t^, as a function of the voltage at trigger electrode 3 for different self-breakdown voltages between electrodes 1 and 2. The gap spacing was d=5,5 cm and the pressure of the working gas mixture 8% SF6 + 92% N2 was 6 atm. This function has a minimum. The current-voltage characteristic

HIGH'PRESSURE GAS GAPS

163

of a trigatron depends on the polarities of the main and trigger voltages. The least delay time is generally obtained with negative main voltage and positive trigger voltage.

150 200 Ftr [kV]

300

Figure 9.7. Delay time as a function of trigger electrode voltage for V^JV^ = 0.93 (i), 0.75 (2), and 0.7 (i)

The delay time U and jitter tst^ are affected by the composition of the working gas mixture. Generally, a mixture of nitrogen and SFg is used. An admixture of argon to this mixture noticeably improves t^ and A/a (Table 9.2) (Koval'chuk et al, 1979; El'chaninov et al, 1975). Table 9.2. Gas mixture

N2

90%N2+ 10% SF6

80%N2+ 10%SF6 + 10% Ar

50%N2 + 50% Ar

40%N2 + 50%Ar + 10% SF6

/d ± A/d, ns

4.810.7

510.7

3.210.5

3.110.4

2.310.3

Thus, trigatron initiation of a spark discharge at megavolt voltages makes it possible to obtain the discharge delay time t^ equal to a few nanoseconds and its straggling A/d equal to some fractions of a nanosecond. This makes feasible parallel operation of a great number of spark channels in trigatrons. Now we shall consider in more detail the mechanism of the nanosecond discharge in a trigatron. There are two points of view on the mechanism of the operation of a trigatron. According to one of them, the excitation of the discharge in the main gap occurs because of the photoionization caused by the short-wave radiation from the spark of the trigger discharge. The second point of view (Shkuropat, 1969) is based on the assumption that a discharge can be initiated in a trigatron before the breakdown of the trigger gap.

164

Chapter 9

In the experiment performed by Erchaninov et al (1975), the second mechanism of the breakdown of a trigatron was reahzed. The width of the trigger gap in these experiments made up not above 10-15% of the width of the main gap. Delay times of about 3--5 ns were obtained at an amplitude of the trigger pulse making up no more than 10-15% of that of the main voltage. To provide shorter t^, it is necessary that, on application of a trigger pulse, the main gap become closed earlier than the breakdown of the trigger gap takes place. To meet this requirement, one should adjust correctly the proportion between the trigger gap formed by the electrodes 1 and 3, d\-2,, and the main gap d and choose an optimum trigger voltage Fir. For too high Ftr, the trigger gap is broken down first, the triggering potential is shunted by the low impedance of the spark in this gap, and t^ increases. When Ftr is low, the electric field gradient at the edge of the trigger electrode decreases, and this leads to an increase in t^ as well. It is necessary to have the ratio dxîldx-^, = 5-10, since at smaller ratios the overvoltage across the trigger gap of width dxv decreases after the closure of the main gap, while at large dld^r the voltage Fir should be substantially reduced. The short and stable delay time obtained for the trigatron ignition of spark gaps was good reason to hope that parallel operation of several spark gaps could be arranged with small transit time isolation, /trans- Initially, experiments on the initiation of two parallel spark channels were carried out (Koval'chuk et al, 1979). Taking into account the small jitter (some fractions of a nanosecond) of the delay time in this type of triggering, two trigatron units were mounted in one spark gap at a distance of 8 cm (^trans = 0.27 us) from cach other (Fig. 9.8). Electrode 1 was made as a plate with rounded (i? = 15 mm) edges. The electrode gap spacing was 5.5 cm and the gas (8% SFe + 92% N2) pressure was 6 atm. The trigger pulse of amplitude 140 kV was applied simultaneously to both trigger electrodes 3 through resistors of resistance /? = 10^ Q. The main discharge current in each channel was measured with the help of shunts of resistance 0.2 Q, which were placed between the grounded electrode and the metal rings onto which the main discharge occurred. It has been shown that with two channels the switching time almost halves if the current is the same in both channels (32 ns with one channel and 18 ns with two ones). In these experiments, the switching time of the trigatron was determined by the ohmic resistance of the spark. The effect of the inductance was insignificant, and the total current in the two channels was 26 kA. Further investigations of the characteristics of a trigatron and of the multichannel operation of a high-current switch (Koval'chuk et al, 1979) were performed on a system with an eight-channel spark gap rated at 500 kV and a 3-Q coaxial line with a double electric length of 18 ns.


165

rf cable

Figure 9.8. Schematic diagram of a double-chamiel trigatron: 1 - high-voltage electrode, 2 • ground electrode, 3 - trigger electrode, 4 - dielectric sleeve, 5 - Marx generator 1, and 6 • Marx generator 2, VD - voltage divider

40% N2 80% N2 90% N2 50% AT 10% Ar 10% SF, 10% SF, 10% SF,

50% N2 50% Ar

N,

"1—r

-|—r

"1—r

1—r

"1—r

"1—r

n—r

1—r

n—r

1—r

(a)

(b)

(c)

3

2

2

^

1 1—r

"I—r

id) h1 T

I

I

I

I

I

I

i

I

I

I

I

r

0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 15 t [ns] Figure 9.9. Oscillograms showing the drop in discharge gap voltage for different gas mixtures and one {a\ two {b\ four (c), and eight channels (d)

166

Chapter 9

The switching characteristic of a switch depends on the fill gas. For instance, it is well known that an admixture of 50% argon to a mixture of N2 and SF6 improves the performance of the switch (Moriarty et al, 1971). For an eight-channel trigatron, the highest rate of current rise was obtained with a mixture of 80% N2 + 10% SF6 + 10% Ar. The switching characteristics were obtained for one-channel and multichannel operation of a high-current spark gap filled with mixtures of SFe, N2, and Ar in different proportions (Koval'chuk et al, 1977). Typical oscillograms of the voltage across the spark gap are given in Fig. 9.9. From these oscillograms, it can be seen that addition of argon in great amounts to the gas mixture substantially delays the decrease in voltage. As the number of spark channels is increased, the rate of voltage drop increases early in the switching process. However, even for an eight-channel discharge, at the terminating stage of switching in a mixture containing 30-50% Ar, no less than 10-15% of the initial voltage remains across the gap. The inductive resistance of a switch weakly depends on the gas type. Therefore, perhaps, the residual voltage is due to the high active resistance of the switch. This is also testified by the nonexponential voltage drop during the terminating stage of switching.

5.

SPARK GAPS TRIGGERED BY EXTERNAL RADIATION

5.1

Ultraviolet triggering

A spark gap triggered by the ultraviolet radiation of an auxiliary spark gap is referred to as a spark relay. This device has two spark gaps (see Fig. 9.5, c): the main spark gap between electrodes 1 and 2 and trigger spark gap 3 (StekoFnikov, 1949). The ultraviolet radiation of the spark in the gap 3, when hitting the cathode 2, gives rise to a photoelectric current from the cathode that initiates breakdown of the main gap. It has been demonstrated (Stekol'nikov, 1949) that at a 1-2% undervoltage across the main gap and an operating voltage of about 10 kV the delay time t^ between the breakdowns of the trigger and the main gap is 10"^ s. Spark relays played an outstanding role in developing triggered pulsed devices for first fast oscilloscopes. Stekol'nikov (1949) has shown that such relays, when properly adjusted, have t^ « 10"^, and A/d d. After the ignition of a discharge in the hollow cathode, the discharge plasma penetrates into the region of the hole, and an electron beam with a current of 10-100 A is formed. At this stage there occur desorption of the gas from the surface and its ionization, and the gas density in the hole region reaches 10^^ cm"-^. In Fig. 10.5, a pseudospark gap is shown in which an auxiliary glow discharge is used. The discharge operates in the system of electrodes 8 and 9. The distance between the electrodes is chosen large enough to provide the ignition of a discharge at voltages of 1-2 kW corresponding to the left branch of Paschen's curve. As a voltage pulse is applied to the electrode 9,

LOW-PRESSURE SPARK GAPS

197

there occurs an amplification of the current between the electrodes 8 and 9 and, besides, a discharge is ignited over a long path between the electrode 9 and the cathode cavity of electrode 4, Thus, plasma appears in the cavity beneath the electrode 4, and electrons are extracted into the main discharge gap, initiating the breakdown of this gap. Trigger systems of this type make it possible to achieve pulse repetition rates of up to 100 kHz. However, their disadvantage is that an auxiliary glow discharge permanently operates in the device.

Figure 10J. Schematic of a two-electrode pseudospark switch triggered by a pulsed glow discharge. The complex design of the electrodes is necessary to prevent metallization of the insulator by the sputtered material of the electrodes (7, 2, 5 - anode; 4, 5 - cathode; 6 hollow cathode; 7 - blocking electrode; 8,9- trigger electrodes)

The geometry of a modem pseudospark gap with ultraviolet illumination is given in Fig. 10.6. The spark gap has a hollow cathode and a hollow anode. The ultraviolet radiation ignites a discharge in the hollow cathode. The plasma of this discharge penetrates into the region of the cathode hole. The diameter of the glow channel is approximately equal to the hole diameter. A high-current discharge with a current density of 10"^ A/cm^ is formed when the plasma glow, expanding with a velocity of 10^ cm/s, fills the electrode gap. The discharge voltage decreases to several hundreds of volts. It is localized within a layer of thickness 10"^ cm and creates a field of strength £ = (1-5) -10^ V/cm at the cathode (Christiansen, 1989; KirkmanAmemija et al, 1989; Hartman and Gundersen, 1989).

198

Chapter 10

Figure 10.6. Triggered pseudospark gap. 1 - cathode, 2 - anode, S - triggering ultraviolet lamp, 4 - glass case, 5 - gas supply, 6 - quartz window

The cathode microrelief resulting from the operation of pseudosparks is similar to that formed under the action of an arc discharge. The erosion rate, measured by Christiansen (1989), is -10"^ g/C, which is typical of an arc discharge [(5-8)-10"^ g/C for a molybdenum cathode]. Taking into account the character of cathode erosion, one can suggest that the high average current density of a pseudospark is provided by explosive emission of electrons. The studies of the physical processes of initiation and development of a vacuum breakdown and the mechanism of emission in the cathode spot of a vacuum arc and in a volume gas discharge, considered above, have made it possible to establish a number of relationships which prove that the phenomenon underlying the mechanism of operation of a pseudospark is explosive electron emission (Mesyats and Puchkarev, 1992). The erosion traces, as in a vacuum discharge, are microcraters produced by individual microexplosions. Let us proceed from the estimates that the average current density -10"^ A/cm^ in a pseudospark is provided by ---10^ ectons, each carrying a current of ---10 A. The current density in an ecton can reach 10^ A/cm^. Ectons may appear within a time td, provided thaXj% = const. For an initial current of-10^ A/cm^, the value of t^ lies in the nanosecond range. It has been shown (Mesyats, 2000) that for a molybdenum cathode conditioned in high vacuum, at an average electric field at the cathode E > 2-10^ V/cm, /ci< 10 ns. The field created by a volume discharge at the initial stage of formation of a pseudospark is of the same order of magnitude, and, hence, there are conditions for the formation of an ecton within r < 10 ns. It is important to note that one or several ectons are not able to shunt the layer and, hence, the voltage across the layer does not change. The number of ectons increases until the total current causes a redistribution of the voltage between the current source and the diode. The situation is similar to that with the formation of a high-current volume discharge in gas for which

LOW-PRESSURE SPARK GAPS

199

it was also noticed that the cathode spot appears as the field in the nearcathode layer reaches E > (1-2)-10^ V/cm. The subsequent transition of the discharge into a constricted spark depends on Elp and, for the conditions of a pseudospark, it is hampered by the low pressure in the electrode gap and by the great number of simultaneously appearing ectons. Kirkman-Amemija et al (1989) observed the occurrence of ectons at the cathode of a BLT switch and a constricted spark during some first operations of the switch. Subsequently, as the electrodes were conditioned by discharges, sparks disappeared and the discharge went into a diffuse stage. Based on this observation, the authors have concluded that there was a socalled superemission. This effect can be explained as follows (Mesyats and Puchkarev, 1992): In first operations of a spark gap with fresh electrodes, the electric field in the gap is £"« 10^ V/cm. The field at the cathode is enhanced many times and this results in field emission followed by explosive electron emission. The discharge develops, like a vacuum discharge, from individual cathode microregions. In the course of conditioning, the electric strength increases and, as soon as bulk ionization begins in the electrode gap and the field becomes localized in a thin near-cathode layer within 1 ns, conditions are created for spontaneous occurrence of explosive electron emission followed by the formation of ectons over a large area. Since the current of one ecton seems to be not over 10 A and the plasma in an ecton is completely ionized and radiates in the ultraviolet region with the spot size being less than 0.1 mm, these cathode spots are imperceptible on the background of the bulk luminescence. The statement that the so-called superemission in pseudosparks is explosive electron emission is confirmed by the results of experiments on electrode erosion. The electrode erosion is more pronounced in that place where the electric field is a maximum, i.e., on the edge of the hollow cathode.

REFERENCES Abramovich, L. J., Klyarfeld, B. N., and Nastich, Yu. N., 1966, A Superdense Glow Discharge with a Hollow Cathode, Zh Tekh. Fiz. 36:714-719. Bochkov, V. D., Dyagilev, V. M., Ushich, V. G., Frants, O. B., Korolev, Yu. D., Shemyakin, I. A., and Frank, K., 2001, Sealed-off Pseudospark Switches for Pulsed Power Applications (Current Status and Prospects), IEEE Trans. Plasma Sci. 29:802-808. Brish, A. A., Dmitriev, A. B., Kosmarsky, L. N., Sachkov, Yu. N., Sbitnev, E. A., Heifets, A. B., Tsitsiashvili, S. S., Eig, L. S., 1958, Vacuum Spark Relays, Prib. Tekh. Eksp. 5:53-58. Bugaev, S. P. and Mesyats, G. A., 1966, A Spark Peaker. USSR Inventor's Certificate No. 186 033 (October, 1964). Christiansen, J., 1989, The Properties of the Pseudospark Discharge. In Physics and Applications of Pseudosparks (M. A. Gundersen and G. Schaefer, eds.), Plenum Press, New York, pp. 1-13.

200

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Christiansen, J. and Schultheiss, C, 1979, Production of High Current Particle Beam by Low Pressure Spark Discharges, Z.furPhysik. A. 290:30. Creedon, J., 1990, Design Principles and Operation Characteristics of Thyratrons. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 379-407. Fo^t-kv, V. E., ed., 2000, Encyclopedia of Low-Temperature Plasmas (in Russian). Nauka, Moscow. Gundersen, M. A. and Schaefer, G., eds., 1989, Physics and Applications of Pseudosparks. Plenum Press, New York. Hagerman, D. C. and Williams, A. H., 1959, High-Power Vacuum Spark Gap, Rev. Set Instrum. 30:182. Hartman, W. and Gundersen, M. A., 1989, Cathode-Related Processes in High-Current Density, Low Pressure Glow Discharge. In Physics and Applications of Pseudosparks (M. A. Gundersen and G. Schaefer, eds.), Plenum Press, New York, pp. 77-88. Kirkman, G. F. and Gundersen, M. A., 1986, Low Pressure, Light Initiated, Glow Discharge Switch for High Power Applications, Appl. Phys. Lett. 49:494. Kirkman-Amemija, G., Liou, R. L., Hsu, T. H., and Gundersen, M. A., 1989, An Analysis of the High-Current Glow Discharge Operation of the BLT Switch. In Physics and Applications of Pseudosparks (M. A. Gundersen and G. Schaefer, eds.), Plenum Press, New York, pp. 155-165. Korolev, Yu. D. and Frank, K., 1999, Discharge Formation Processes and Glow-to-Arc Transition in Pseudospark Switch, IEEE Trans. Plasma Sci. 27:1525-1537. Kovalenko, V. P., Makarevich, A. A., Rodichkin, V. A., and Timonin, A. M., 1974, Study of the Laser-Triggered Vacuum Discharge, Zh. Tekh Fiz. 44:2317-2321. Lobov, S. I., Tsukerman, V. A., and Eig, L. S., 1960, A Triggered Low-Pressure Spark Gap, Prib. Tekh. Eksp. 1:89. Makarevich, A. A. and Rodichkin, V. A., 1973, A Laser-Triggered Vacuum Spark Gap, Ibid. 6:90-91. Mather, J. W. and Williams, A. H., 1960, Some Properties of a Graded Vacuum Spark Gap, Rev. Sci. Instrum. 31:297. Mechtersheimer, G., Kohler, R., Lasser, T., and Meyer, R., 1986, High Repetition Rate Fast Current Rise Pseudospark Switch, J. Phys. E. 19:466. Mesyats, G. A., 1974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A., 2000, Cathode Phenomena in a Vacuum Discharge: The Breakdown, the Spark and the Arc. Nauka, Moscow. Mesyats, G. A. and Puchkarev, V. F., 1992, On Mechanism of Emission in Pseudosparks, Proc. XVISDEIV, Darmstadt, Germany, pp. 488-489. Penetrante, B. M. and Kunhardt, E. E., 1990, Fundamental Limitations of Hydrogen Thyratron Discharges. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.), Plenum Press, New York, pp. 451-472. Slivkov, I. N., 1986, Processes at a High Voltage in Vacuum (in Russian). Energoatomizdat, Moscow. Thompson, J. E. 1990, Triggered Vacuum Switch Construction and Performance. In Gas Discharge Closing Switches (G. Schaefer, M. Kristiansen, and A. Guenther, eds.). Plenum Press, New York, pp. 271-285. Wilson, J. M., Boxman, R. L., Thompson, J. E., and Sudarshan, T. S., 1983, Breakdown Time of a Triggered Vacuum and Low-Pressure Switch, IEEE Trans. Electr. Insul. 18:238-242.

Chapter 11 SOLID-STATE AND LIQUID SPARK GAPS

1.

SPARK GAPS WITH BREAKDOWN IN SOLID DIELECTRIC

In high-power pulse generators with high rates of rise of the discharge current (up to 10^"^ A/s and more), switches with a discharge in a solid dielectric, having a number of advantages, are often used. Due to the high dielectric strength of solid dielectrics (Mylar, polyethylene, polypropylene, etc.), the discharge gap can be very small and the inductance and active resistance of the spark gap can be rather low. This makes it possible to switch currents as high as millions of amperes and produce current and voltage pulses with very short rise times. The breakdown delay time for solid dielectrics quickly decreases with increasing overvoltage, being a few nanoseconds at an overvoltage factor of 1.5 and more (Mesyats, 1961). The first solid-state spark gaps with mechanical triggering (puncturing a dielectric with a sharp metal punch) intended for the production of microsecond current pulses of amplitude up to 10^ A were developed by Komelkov and Aretov (1956). Mesyats (1961) paid attention to the opportunity of using solid-state spark gaps in generators of high-power nanosecond pulses when, in his experiment on the breakdown of NaCl crystals and fluoroplastic, he obtained a switching time of 10""^ s. More often solid-state spark gaps are used in generators with strip transmission lines in which a stack of thin dielectric sheets is used for insulation. In this case, there is no need in bushing insulators, the nonuniformity at the joint of the line with the switch is absent, and multichanneling is possible, which enables the inductance and active resistance of the switch to be made extremely low. The dc breakdown

202

Chapter 11

electric field of a dielectric, E^c, usually equals several megavolts per centimeter, and it increases with decreasing dielectric thickness. For example, in thin (5-10""^ cm) Mylar films, E^c « 8 MV/cm has been achieved. Therefore, solid-state spark gaps, similar to strip lines, are made of stacks of dielectric films impregnated with liquid dielectric. However, ^dc depends not only on the film thickness, but also on the area of the film surface on which the electrode is put. Hence, we can speak of the dependence of E^c on the volume V of the dielectric to which the field is applied. J. C. Martin (Martin et al, 1996) recommended the empirical formula JFdcV^/io=i^,

(11.1)

where the electric field J^dc is measured in megavolts per centimeter and the volume V in cubic centimeters. The quantity K is equal to 2.5 for Teflon and polyethylene, 2.9 for polypropylene, 3.3 for Lucite, and 3.6 for thin Mylar. Solid-state spark gaps can operate based on the self-breakdown principle or be triggered by some external action. Self-breakdown can be realized by destroying the dielectric placed between the spark gap electrodes. In the simplest case, to destroy the insulation and close the gap, an electrodynamic hammer is used that is brought in motion by a pulsed magnetic field (Rogers and Whittle, 1969). Such a spark gap has a rather low active resistance (-^10"^ Q), which is determined by the resistance of the metal bar that connects the electrodes. However, the triggering delay time of spark gaps of this type is at the best some tens of microseconds, which substantially restricts the field of their application. Another type of self-breakdown is the breakdown resulting from the action of a pulsed voltage much in excess of the dc breakdown voltage. However, in this case, the triggering delay time of the spark gap is rather unstable since the breakdown occurs over irregularities and inclusions, which are always present in commercially produced dielectrics. To eliminate the statistical influence of these inclusions, it was proposed (Martin et al, 1996) to stabilize the breakdown voltage by creating artificial irregularities in the dielectric. These irregularities can be created, for example, by caving small metal cones or thin wires into the dielectric. In such a spark gap, with the help of heated thin needles pressed into the dielectric, blind channels were made in which a discharge developed. Such a channel is capable of transmitting a limited current, and the breakdown voltage for one channel is stable within -6 %. Therefore, many channels - no less than 30 - were made in the dielectric. In this case, the breakdown voltage was stable within -2 %. An increase in number of channels substantially reduces the inductance of the discharge circuit and increases the rate of rise of the pulsed voltage produced. The simultaneity of formation of a great number of channels depends on the rise rate of gap

SOLID-STATE AND LIQUID SPARK GAPS

203

voltage. It has been revealed that as a pulsed voltage with dVldt < 10^^ V/s was applied to the dielectric, only one channel was formed. For all channels to be broken down simultaneously, it is necessary to have dVldt > W^ V/s. In this case, all channels are formed within -10"^ s (Vitkovitsky, 1987). To trigger solid-state spark gaps, various methods are used. The simplest one is based on the principle of operation of a three-electrode spark gap, such that a metal plate is built in between two dielectric sheets clamped between the cathode and the anode. On application of a trigger pulse, the dielectric between the trigger electrode and one of the main electrodes is broken down and then, due to overvolting, the second dielectric is broken down. Spark gaps in which the dielectric is destroyed by exploding a small charge of explosive, a wire (Huber, 1964), or a foil (Henins and Marshall, 1968) are also used. With an exploding wire, breakdown occurs along the cracks formed in the dielectric imder the action of the shock wave. Spark gaps with the use of an explosive have a somewhat lower resistance since the electrode gap is bridged by the metal jet formed on explosion. The triggering delay time of "explosive" switches is a few microseconds. Bayes et al (1966) describe a spark gap in which a dielectric is destroyed under the action of the gas-kinetic and magnetic pressure produced by a spark. The spark is initiated between two auxiliary foils that are separated with a dielectric having a hole, in which the triggering discharge occurs. To trigger such a spark gap, high-power capacitor banks are used, and the triggering current is several hundreds of kiloamperes. A detailed review of solid-state spark gaps is given in the monograph by Vitkovitsky (1987).

2.

SPARK GAPS WITH BREAKDOWN OVER THE SURFACE OF SOLID DIELECTRIC

The mechanism of the operation of surface-discharge spark gaps in gas is determined by the presence of triple (metal-dielectric-gas) junctions (TJ's) at the places of contact between the cathode and the dielectric. Even a single electron appearing at this junction and hitting the surface of the dielectric produces plasma necessary to initiate a discharge over the dielectric surface. Depending on the electric field at the surface of a metal protrusion in the TJ, there are three options for a discharge to develop. First, if the field is high enough (-10^ V/cm) to cause field emission, the protrusion is heated by the Joule mechanism and explodes, a cathode spot appears, the plasma starts expanding over the dielectric, and a discharge is initiated. High electric field at the protrusion may be due to high dVldt or high permeability of the dielectric. Second, if the field at a TJ is not very high (5-10^ V/cm), the number of electrons appearing during the voltage pulse suffices to initiate a

204

Chapter 11

surface discharge. The moving plasma gives rise to a displacement current, which passes through a metal protrusion in the TJ, heating the protrusion by the Joule mechanism and then exploding it. As a result, a cathode spot and cathode plasma appear, and the latter speeds up the surface discharge process. Finally, the third option takes place, in particular, in a dc breakdown when a few electrons get from a TJ on the cathode, initiate an avalanche of secondary emission electrons, positively charge the dielectric, and ionize the gas near the dielectric surface. In this case, a cathode spot can appear either on the interaction of the discharge plasma with the cathode surface or as the gap is bridged by the plasma. In the second and third cases, a corona discharge develops over the dielectric surface. The mechanism of surface discharges in gas was investigated on the nanosecond scale in the experiment described by Mesyats (1974). The rate of voltage rise in this experiment was > 10^^ V/s with a time delay to breakdown of the order of 10"^ s. Looms (1961) was the first to develop gas surface-discharge single-channel spark gaps intended for the operation at dc voltages. Pulsed multichannel spark gaps were designed by Dashuk and his co-workers (Dashuk, 1976; Dashuk and Chistov, 1979). This work was fixrther developed by Hasson and von Bergmann (1976), Johnson et al (1982), and Von Bergmann (1990). The most important property of this type of spark gap is that it is capable of providing multichannel switching and thus enabling low L and R of the spark during switching. This is because with strip cathode and anode both there are many effective triple junctions at the cathode. From these junctions, at a voltage rise rate dVldt > 10'^ V/s, many surface discharges start. The time of discharge channel growth and gap closure is div, where d is the gap spacing and v is the velocity of motion of the discharge plasma over the dielectric, which increases with dVldt. This time should be long enough in order that many discharges be initiated at the cathode TJ's. By varying d and dVldt^ it is possible to attain a situation where N channels appear practically simultaneously. Spark gaps of this type can operate both in the self-triggering mode and in the mode of triggering by an external pulse. The circuit of a self-triggered spark gap is shown in Fig. 11.1. During the discharge, the dielectric behaves as a chain of capacitors with volumetric and surface specific capacitances C\ and Ci. The ratio of these capacitances determines the rate of development of the discharge (Mesyats, 1974). Figure 11.2 presents different triggering schemes for surface discharge spark gaps. The spark gap shown in Fig. 11.2, a is self-triggered, while those in the other figures operate from a trigger pulse. In Fig. 11.2, b, the trigger electrode is put on the surface of the dielectric; in Fig. 11.2, c it is built in the dielectric, and in Fig. 112, d it is located some distance from the dielectric surface. Figure 11.3 shows the

SOLID-STA TE AND LIQUID SPARK GAPS

205

pattern of a triggered multichannel discharge at different voltages between cathode and anode for the case of a built-in trigger electrode (Fig. 11.2, c). A

C2 II

" D

II

II

^1

II r—IL

ir^ ^ 1

Cx^

(c

^n

Figure ILL Arrangement of the electrodes and dielectric in a nontriggered surface spark gap: A and C - electrodes, S - substrate, D - dielectric, Cx - specific volumetric capacitance, C2 specific surface capacitance of the dielectric

{a)

^'v^^V^v.^^^V.VV^'vVv^WVV.'^'v'v'^V'^Tr^

\\\A\\

m

(c)

miî

^^^'^^^^^.^^','

(12.12)

h where Ao is some constant, which determines the pulse waveform. For a nonuniform line with wave impedance Z o ( x ) = i?ioad

Aol

(12.13)

where x is the running length of the line counted from the switch and / is the total line length, we obtain a rectangular pulse of amplitude ^F(/p) across the load of resistance i?ioad. Nonuniform lines are convenient to design in strip version. When a nonuniform symmetric strip line with the wave impedance varied from 2.8 to 4.1 Q was used in a 1-kA current generator, the 15% overshoot of the pulse was eliminated (Mesyats, 1974). The influence of the nonlinear resistance of a spark on the discharge of a capacitor into a load was analyzed by Weizel (1953).

3.

SPARK PEAKERS

A peaker is a device intended for shortening the pulse rise time. Generally, a peaker (P) is connected in series with lines (Li and L2) (Fig. 12.5). A pulse Vi(t) with a rather long rise time tî arrives at the peaker through the line Li and a pulse V2{t) with a short rise time tri arrives at the load through the line L2. The principle of operation of the peaker relies on that within a time / > tri, its resistance is much greater and then becomes

GENERATORS WITH GAS-DISCHARGE SWITCHES

223

much lower than the wave impedance of the line. It can readily be seen that a spark gap possesses this property if its breakdown delay time ^d>/rl,

(12.14)

while ts I atm, we have Fdc = const and t^ « t j p , where /si is the switching time at atmospheric pressure. In view of the above considerations, Eq. (12.17) becomes ^r2« — + ^rl

1-

(12.19)

2K

From (12.19) it follows that if we increase pd so that the bracketed term tends to zero, we get t^2 * hxlpAnother possible way of increasing the ratio trxlUi is to use several peakers connected by segments of cable. This is the so-called sequence peaking (Mesyats, 1963). When three peakers were used, the rise time of a 30-kV pulse decreased from 0.8-10"^ to 10"^ s. With peakers operated in this mode, microsecond pulsed charging of a coaxial line was used in fact for the first time. In this charging scheme, the first peaker is the main switch. This scheme is currently the basic one in creating nanosecond high-power generators. For the first time, a peaker was used by Hertz in 1917 in his experiments with short waves. He utilized a series connection of a transmission line and a two-electrode spark gap filled with transformer oil. In 1926, Burawoy developed and built a generator with a peaking spark gap in oil to produce voltage pulses with a rise time of several nanoseconds and amplitude of about 150 kV. A description of these experiments was given by Binder (1928). The first generator with a gas peaker was developed by Fletcher (1949). Figure 12.7 shows a circuit where a high-pressure spark gap is used for peaking a pulse. The initial pulse is generated by the coaxial cable Li, which is charged through a resistor i?i from a source with a voltage of +20 kV. To reduce the rise time of the primary pulse, the trigger spark gap is broken down under an overvoltage created on the operation of a threeelectrode switch. + 20kV

5kV

Figure 12.7. Schematic of a nanosecond pulse generator using a compressed-gas peaker in the primary charging device: 1 - mercury lamp; 2 - trigger spark gap; 3 - peaker; 4 - output pulse

226

Chapter 12

A peaking spark gap separated from the trigger gap by the cable L2 is used to increase of the steepness of the pulse. The primary pulse arrives, through the separating line, at a spark gap with a rather small electrode separation, which, under the action of this pulse, is broken down at a high overvoltage. To attain a required delay time, the peaking gap is filled with nitrogen at a pressure of about 100 atm. This generator produced pulses of amplitude 10 kV with a rise time of 0.3-10"^ s. A peaker operating in atmospheric air with short-rise-time primary pulses was used in a generator described by Vorob'ev and Mesyats (1963). The primary pulse rise time was 5 ns. For the primary switch, a switch with three spark gaps was used and an adjusting capacitor was connected in parallel with the energy storage line. Two-electrode gas-discharge peakers have a narrow range of operating voltages. To remedy this flaw, it was proposed (Mesyats, 1974) to use for the peaker a great number of series-connected small gas gaps (microgaps of width -0.1 mm). As the gaps are very small, an output pulse of short rise time can be obtained even at atmospheric pressure, and the value of t^ necessary for condition (12.14) to be satisfied is chosen by varying the number of gaps and the ground capacitance of the electrodes. For this type of peaker, a wide range of operating voltages can be realized without rearrangement of the gaps. With the number of gaps N=25 and the width of each gap equal to 200 |im for the range of pulse amplitudes from 15 to 40 kV, a pulse rise time of 0.7 ns was obtained (Mesyats, 1974) (Fig. 12.8).

Figure 12.8. Design elements of the peaker: 7 - washer; 2 - fixing dielectric washer; 3 dielectric cylinder, and 4 - metal screen

A wide range of operating voltages of a peaker can also be attained with a discharge over the surface of a dielectric in vacuum at a nonuniform field in the cathode region. As shown above, if the field at the cathode is

GENERATORS WITH GAS-DISCHARGE SWITCHES

111

nonuniform and there is a significant normal field component, the dielectric surface discharge in vacuum features the time t^ weakly dependent on voltage and highly stable from discharge to discharge and a short switching time (< 10"^ s). Besides, if the difference in diameters between the cathode and the dielectric is great, the pulsed breakdown voltage is much lower than the dc breakdown voltage because of the highly nonuniform field distribution over the dielectric surface under the action of pulses (see Chapter 3). It was proposed (Bugaev and Mesyats, 1964) to harness these properties of a discharge over a dielectric in vacuum in developing nanosecond peakers with a wide range of operating voltages that have highly stable time characteristics and small dimensions due to the high dielectric strength of vacuum. Figure 12.9 presents the arrangement of a vacuum peaker (Mesyats, 1974). Used for the dielectric was a steatite ceramic disk of thickness 1 mm and diameter 11 mm; the diameter of the cathode was 5 mm. The vacuum in the peaker was 10"^ mm Hg. The peaker operated without rearrangement in the range of operating voltages from 5 to 40 kV with the rise times of the primary and the secondary pulse equal to 20 and 0.5 ns, respectively. The range of operating voltages of the peaker can easily be varied by varying the dimensions of the ceramics. When changing the pulse polarity, it is necessary to interchange the input and the output of the peaker.

Figure 12.9. The main elements of a vacuum peaker: 1 - cathode; 2 -anode; 3 - dielectric; 4 screen protecting the envelope from electrode metal vapors, and 5 - envelope

For the production of nanosecond high-current pulses, water-insulated lines are used as energy storage and transmission lines. In this case, to do away with the bushing isolator between the line and the peaker, the peaker is immersed in water.

228

Chapter 12

REFERENCES Binder, L., 1928, Die Wanderwellenvorgdnge auf Experimenteller Grundlage. Springer, Berlin. Bugaev, S. P. and Mesyats, G. A., 1966, A Spark Peaker. USSR Inventor's Certificate No. 186 033 (October, 1964). Fletcher, R. C, 1949, Production and Measurement of Ultrahigh Speed Impulses, Rev. Sci. Instrum.lO'Ml. Griinberg, R., 1965, Gesetzmapigkeiten von Funkenentladungen im Nanosekundenbereich, Z. fur Naturforsch. A. 20:202-212. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1996, J. C. Martin on Pulsed Power. Plenum Press, New York. Mesyats, G. A., 1963, Theory of the Peaking Spark Gap, Izv. Vyssh. Uchehn. Zaved, Fiz. 1:137-141. Mesyats, G. A., 1974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Rompe, R. and Weizel, W., 1944, Uber das Toeplersche Funkengesetz, Z fur Physik. 122:636. Vorob'ev, G. A. and Mesyats, G. A., 1963, Techniques of the Formation of Nanosecond High-Voltage Pulses (in Russian). Gosatomizdat, Moscow. Weizel, W., 1953, Berechnung des Ablaufs von Funken mit Widerstand und Selbstinduktion im Stromkreis, Z. fur Physik. 135:639-657.

Chapter 13 MARX GENERATORS

1.

NANOSECOND MARX GENERATORS

We spoke of the Marx voltage multiplication circuit in Chapter 1. Recall that in this circuit a number of capacitors are charged in parallel to a voltage FQ. Then the capacitors are connected in series by means of closing switches and are discharged into a load at a voltage NVQ, where N is the number of capacitors (see Fig. 1.2). In circuits of this type, gas-filled spark gaps are used, as a rule, as switches. These circuits have found very wide application in pulsed power technology. In the technology of generation of high-power nanosecond pulses, Marx generators (MG's) are used in two cases. First, they are used as charging devices for the energy storage lines of generators. In this case, they operate on the microsecond time scale. An MG-charged energy storage line is discharged to generate a nanosecond pulse. The voltage of generators of this type reaches ten megavolts. Second, when properly configured, an MG is capable of generating pulses of duration 10"^ or even 10"^ s directly across the load. The peak voltage, as a rule, is not over 1 MV. In this section, we shall deal with the first and second types of Marx generator. To initiate a discharge in a Marx generator, an additional electrode is mounted in the first spark gap or the gap and the cathode are illuminated with ionizing radiation. All other spark gaps are broken down sequentially due to an overvoltage across the discharge gap. It should be noted that the breakdown and the discharge sustainment in the spark gaps are possible in the presence of stray capacitances. Stray capacitances should sustain the discharge before the breakdown of the last spark gap into the load. The

230

Chapter 13

problems concerned with the design calculations of charging and discharge circuits and the determination of the pulse parameters for Marx circuits were discussed by Smimov and Terentiev (1964). The equivalent circuit diagram of the discharge circuit of a nanosecond pulse generator is similar to that given in Fig. 12.1. Here, Co = C/N, is the MG capacitance; instead of VQ it is necessary to take «Fo, where C and Vo are, respectively, the capacitance and voltage of a stage of the MG; L is the inductance of the discharge circuit, i?s is the resistance of the spark gaps; K is a perfect switch, and N is the number of stages. Depending on the conditions (the pressure in the spark gaps, the parameters of the circuit, the operating voltage, and the type of the load), the value of one or another parameter of the circuit can be neglected. We assume that the spark gaps are broken down under near-dc conditions. Then the process in the discharge circuit can be analyzed assuming that the spark resistance varies by the Rompe-Weizel formula. For the pulse FWHM with ^loadCo/O < 20, it can be obtained that /p«2.2e + 1.3/?,oadCo,

(13.1)

where Q^lpd^laVQ , If ifioadCo/O » 10, the spark will have almost no influence on /p. Thus, the pulse amplitude and duration depend not only on the parameters i?ioad and C of the discharge circuit, but also on the value of 0, which is determined by the gas properties and pressure and by the electric field in the discharge gap. The smaller 6, the larger the amplitude of the pulse and the shorter its duration. For a fixed voltage VQ « pd, we have 0 x/7"^ Hence, the higher the gas pressure, the smaller the value of 0. For air at atmospheric pressure and J = 1, we have 0 « 2 ns, i.e., according to (13.1), the pulse duration, even if the circuit has no inductance and resistance, cannot be shorter than 4 ns. Hence, the necessary condition for the production of pulses of nanosecond duration is that the spark gap should be immersed in compressed gas. At a high gas pressure, the value of 0 becomes so small that the spark gap can be considered a perfect switch. For the circuit shown in Fig. 12.1, the pulse rise time between 10% and 90% of the amplitude will be given by U = 2,2L/Rioa& Hence, to produce a pulse of rise time about 10~^ s, it is necessary that the inductance of the discharge circuit, Z, be not over 10"^/?ioad. For i?ioad = 100 Q, it is necessary to have Z < 10"^ H. The inductance of the discharge circuit, Z, is determined in the main by the dimensions of the generator. For a given pulse amplitude, these dimensions are determined by the dielectric strength of the medium surrounding the generator. To increase the dielectric strength of the medium, it is necessary to place the generator as a whole in

MARX GENERA TORS

231

compressed gas since in this case the value of 9 and the inductance L of the discharge circuit of the generator simuhaneously decrease. Some versions of generators of nanosecond high-voltage pulses, designed based on the Marx circuit are known. A first generator of this type with a voltage of up to 400 kV was built by Schering and Raske (1935). To reduce the switching time, the spark gaps were placed in a chamber with carbon dioxide under a pressure of 13 atm. The generator produced voltage pulses with a rise time of 10"^ s. In another version of the generator (Mesyats, 1960), to reduce the inductance of the discharge circuit, six coaxial lines were used as energy storage devices. This generator was capable of producing rectangular pulses of voltage 100 kV and rise time 10"^ s. In the experiment described by Broadbent (1960), to shorten the triggering delay time of an MG, trigger electrodes were mounted in its discharge gaps. It is well known that the stability of operation of spark gaps depends on the intensity of ultraviolet irradiation of the cathode. To make the operation of the spark gaps of an MG more stable. Smith (1958) proposed to shunt the first spark gap by a capacitor whose capacitance was comparable to that of one stage of the generator. In this case, intense illumination from a high-power spark formed in the first gap considerably shortened and stabilized the breakdown of all subsequent gaps. Charbonnier et al (1967) described a Marx generator in which 160 stages with the capacitors of an individual stage having a low self-inductance were used for the production of 2-MV pulses of duration 50-10"^ s. To reduce the dimensions and to shorten the time delay to breakdown of the gaps, the generator units were placed in compressed gas. A small-sized nanosecond high-voltage pulse generator was developed (Gygi and Schneider, 1964) in which the discharge circuit had a low inductance because the system as a whole was immersed in compressed gas. The generator consisted of ten stages connected in a Marx circuit and was used to power a spark chamber. At the output of the generator, a pulse of duration --5 ns and amplitude 200 kV was obtained. The delay between the application of the trigger pulse and the onset of the output voltage rise was --10 ns with a jitter no more than 1 ns. In contrast to the conventional MG circuit, coupling capacitors were connected between the individual stages of the generator and this considerably speeded up the process of breakdown of the spark gaps. The use of coupling capacitors allowed, if the first gap was broken down, a 100% overvolting of the second gap irrespective of the number of stages. To eliminate statistical fluctuations of the breakdown delay time, an auxiliary corona discharge was used. This discharge was initiated at needles placed opposite the discharge gaps and provided permanent presence of free electrons at the cathode. The system as a whole,

232

Chapter 13

together with the spark gaps and charging resistors, was immersed in nitrogen at a pressure of 7 atm. Keller and Walschon (1966) developed a 100-kV pulse generator. To stabilize the breakdown of the gaps, an optical path was used that was formed by the chamber walls coated with a reflecting material. The nitrogen pressure in the chamber was 3 atm. The rise time of the pulsed voltage across a resistive load was 3 ns.

1 Rx SGi

SGi5

SG

Figure 13.1. Schematic diagram of a Marx generator with controllable pulse duration and peak voltage: 1 - ring insulators (organic glass); Ri, Ri - charging resistors; SG1-SG15 module spark gaps; SGp - peaking spark gap; Si, S2 - bellows of the cathode-moving hydraulic drive; Q - capacitive voltage divider; C - cathode holder; A - anode unit; R^^ diode electron-current shunt; SGch - chopping spark gap; C\-C\s - module capacitors; T1-T3 - triggers; SGtr - trigger spark gap; VQ - charge voltage; Id - diode current; V^ - diode voltage

A 500-keV nanosecond electron accelerator was developed (El'chaninov et al, 1974) based on a ceramic capacitor MG that produced pulses of controllable duration and amplitude. Besides, it showed low-jitter operation (Fig. 13.1). Each of the 15 stages of the generator represented a unified section consisting of six capacitors C\ connected in parallel, spark gaps SGi, and charging resistors R\ and R2. The stages were stacked with the help of organic-glass ring insulators 1 to form a column. The section high-voltage insulator was assembled from alternating metal and polyethylene rings; the potential was distributed over them with the help of resistors. The second and third stages of the generator were equipped with devices intended for illumination of the spark gaps. This stabilized the triggering of the spark gaps and extended the range of their operating voltages. Illumination was

MARX GENERATORS

233

carried out with the ultraviolet radiation of a ferroelectric surface discharge; each illuminating device was triggered from the previous stage. The Marx generator was driven by a pulse generator with a thyratron at a jitter no more than 5 ns. To control the pulse duration within the limits 3-50 ns, a chopping spark gap SGch with smooth adjustment of the gap spacing was connected to the generator output. The generator was placed in a steel tube filled with nitrogen at a pressure of 10 atm. The graphite cathode produced a beam with current density uniformly distributed over a large area. The MG voltage could be controlled within 20% by varying the charge voltage, and by varying the pressure in the MG column it was possible to vary the output voltage, not changing the width of the spark gaps, in the range 80-450 kV.

2.

CHARGING OF A CAPACITIVE ENERGY STORE FROM A MARX GENERATOR

The idea of pulsed charging of the capacitive energy store (capacitor or line) of a generator with the use of a Marx generator proposed by Mesyats (1962) was of fundamental importance in the production of high-power nanosecond pulses. Vorob'ev and Mesyats (1963) described a Marx generator that charged, through an additional spark gap, a coaxial line segment filled with transformer oil. The circuit diagram of the MG with a compensating capacitor (Q) is given in Fig. 13.2. Originally, this capacitor was intended to compensate the influence of the self-inductance of the Marx generator on the pulse rise time. A theory that interprets the operation of this type of generator in various modes is given by Vorob'ev and Mesyats (1963).

{a)

Vo R3 0—ÂM^

-^load

(b) Cid!=zCo/N

1

=i=C2

Figure 13.2. Circuit diagram of a Marx generator with a compensating capacitance {a) and its discharge circuit {b)

Chapter 13

234

The MG's using an additional capacitive energy store have found wide appUcation. Vorob'ev et al (1963) described a generator producing a 150-kV pulse of rise time 5 ns across a resistive load. The design of the coaxial capacitor was similar to that described by Vorob'ev and Mesyats (1963). A description of a voltage generator capable of producing 500-kV pulses with a rise time of 1.5 ns was given by Vorob'ev and Rudenko (1965). The compensating capacitor was insulated with glycerin (s = 40). Due to the increase in dielectric strength of the insulator at short times of voltage action, the capacitor and the discharge chamber, which was structurally united with the capacitor, could be considerably reduced in dimensions. The design of the generator is shown schematically in Fig. 13.3. The low-inductance capacitor 5 is a coaxial line segment consisting of two cylinders with the space between them filled with glycerin. The capacitance of capacitor 3 was 1 nF and the capacitance of the Marx generator used as a high voltage source was 12.5 nF at a voltage of 150 kV. The inner cylinder of the capacitor also served as the case of the discharge chamber 4 filled with nitrogen at a pressure of 16 atm in which a spark gap switch was placed. The distance between the electrodes of the spark gap could be adjusted without depressurization of the chamber.

Figure 13.3. A 500-kV nanosecond pulse generator

The transmission line 5 of length 4 m with a wave impedance of 100 Q was made as a brass tube 8 cm in diameter with an inner conductor 8 mm in diameter, filled with transformer oil. Capacitor 1 was connected to the MG output through an additional inductor 2. This provided a more efficient multiplication of voltage across the capacitor; however, the amplitude of the first wave was not twice, but only by a factor of 1.7 greater than the operating voltage of the generator. At the open end of the transmission line, the voltage doubled and, as a result, it was a factor 3.4 greater than the voltage developed by the Marx generator. Voltage pulses of amplitude 1 MV and rise time about 5 ns were produced (Vorob'ev et al, 1968) by discharging a low-inductance capacitor charged to about 250 kV into a

MARX GENERATORS

235

transformer consisting of uniform line segments with an increasing wave impedance. MG's of this type were used to power the first Soviet streamer chambers. The optimum conditions for energy transfer from the capacitors of an MG to an energy storage line was given by Graybill and Nablo (1967), Link (1967), Martin (1969), and Bernstein and Smith (1973).

3.

TYPES OF MICROSECOND MARX GENERATOR

The occurrence of new fields of application of pulsed accelerators of electrons and ions, such as inertial confinement fusion, high-power gas lasers, and sources of soft and hard x radiation, called for high-power generators rated at megaampere and higher currents and voltages of up to ten megavolts. Marx generators have found wide use in these fields. To reduce the overall dimensions of these devices, when they are insulated with compressed gas or dielectric liquid, close-type MG's became widespread in recent years. A generator of this type is placed in a metal tank, and this increases the capacitance of the stages relative to the grounded walls of the tank. To increase the power of an MG and decrease its inductance, several sections are connected in parallel. To make the operation of these sections this connection reliable, new circuits have been designed that use capacitive and other type coupling elements, three-electrode spark gaps in each stage, and special high-impedance trigger sections. It is well known (Kremnev and Mesyats, 1987) that simultaneous operation of several MG's is possible if they are switched into the load within a time during which an increase in voltage across the load yet does not reduce the voltage across the spark gaps of the output stages; that is, the spread in operation times of the generators should be much less than the rise time of the voltage across the load, which is several microseconds for the generators used for charging capacitive energy stores and not over 0.1 \is for the generators operating into a resistive load. Hence, for stable simultaneous operation of several generators, it is necessary that the generators operate with the same delay time and about 10 ns jitter. If in the switches have air gaps of width about 1 cm under a pressure of \-2 atm, it is possible to attain jitters less than 10 ns under the conditions of a uniform field of about 100 kV/cm with preliminary illumination of the gaps. Stable simultaneous operation of several MG sections is attained, first of all, by eliminating the possibility of the self-operation of a section in the case where the voltage between the electrodes of the trigger spark gap is much lower than the dc breakdown voltage. This implies that the factor of safety

236

Chapter 13

ks =^dc/ôper. where Fdc is the dc breakdown voltage and Foper is the gap operating voltage, is greater than unity. At the same time, it is necessary to have electric fields of the mentioned strength in the spark gaps. All this resulted in the creation of special versions of Marx generator and Marx-like systems (Fitch, 1971). The need in MG's of higher and higher power resulted in the zigzag configuration of energy storage capacitors. It has been revealed that adjacent capacitors of even and odd stages have stray capacitive couplings among themselves, which speed up the operation of the spark gaps of the first stages. Using this phenomenon, an MG with additional capacitive or resistive couplings through one or several stages has been developed. An essentially new point here is the theoretical opportunity of producing more than a double overvoltage across the two-electrode gaps of the MG and fast and reliable operation of the MG into a load. It has appeared inexpedient to increase the power of single MG's because of the high self-inductance of the discharge circuit, the high inductance and active resistance of the operating gaps, the rather unreliable operation of this type of MG under the conditions of emergency breakdowns, and the difficulties involved in the standardization of the design elements. The development of high-power generators has gone on a way of parallel connection of a great number of MG's of comparatively low power (Bernstein and Smith, 1973; Kremnev and Mesyats, 1987; Prestwich and Johnson, 1969). In this case, the failure of one of the capacitors causes lesser disturbances in the operation of the system. Besides, the techniques of manufacturing and assembling of an MG, the replacement of defective units, and the combining of the generator output parameters become simpler. For the continuous operation of many MG sections, the triggering of individual sections, their operation into a common load, the influence of stray couplings between elements on the operation of the spark gaps, and some accompanying phenomena are of principal importance. For triggering a great number of simultaneously operating MG's, rather low-power trigger MG's are used (Fitch, 1971). In simultaneously triggered MG's, the spark gaps are made three-electrode; a pulse from the trigger MG is applied to the trigger electrode of each of them. Making a parallel connection of MG's more reliable, this, however, complicates the circuit as a whole and calls for modeling tests. With increasing number of stages, the losses increase and the influence of the stray parameters or the chopping spark gap on the overvolting during the operation of the MG and, consequently, on its triggering becomes substantial (Bastrikov et al, 1981). This complicates the realization of one or another idea in a multisection MG placed in a metal tank. The main design features and schematic circuits of the most high-power, megajoule MG's are described below.

MARX GENERATORS

237

Prestwich and Johnson (1969) described the circuit of the MG's used in the Hermes I and Hermes II accelerators. In these generators, the energy storage capacitors were charged on two sides from sources of dc voltage, + Fo and -Fo, through charging resistors. As a high-voltage pulse was applied to the trigger electrode of each spark gap in the first (bottom) row, the capacitors of this row were connected in series. The voltage at the output of the row was equal to NVQ, where N is the number of capacitors in the row (number of stages). The Hermes I machine was capable of storing 0.1 MJ of energy for the MG output voltage equal to 4 MV. For the Hermes II accelerator, an MG was developed which was structurally similar to the previous one with the only difference that each stage contained two parallel-connected 0.5-|LIF, 100-kV capacitors. To increase of the breakdown voltage, the lengths of the spacers were changed. The MG consisted of 186 capacitors, arranged in 31 rows, and 93 spark gaps. It was placed in a steel tank of diameter -6 m and length -12 m, filled with transformer oil. The minimum distance from the MG to the tank wall was about 1.2 m. The generator was capable of storing 1 MJ of energy with the capacitors charged to 10^ kV. The MG capacitance with the capacitors connected in series was 5.38 nF. The total inductance and the series resistance were equal to 80 jiH and 20 Q, respectively; the charging resistance of each section was 1.5 kQ. The generator could charge a long line of capacitance 5.6 nF to a voltage of 16.1 MV within 1.5 |is; however, its operating parameters were the following: charge voltage 73 kV and stored energy 0.5 MJ. For this MG, the generator capacitance was estimated to be 45 pF, the capacitance of capacitors in a stage 190 pF, and the ground capacitance of a stage < 10 pF. Both MG's, judging by the diagram of the breakdown of the spark gaps given by Prestwich and Johnson (1969), were triggered within ~2 |is. With these triggering delay times, there was no need to illuminate the spark gaps or specially strengthen the field in them. Therefore, the pressure in the spark gaps was not over several atmospheres, and the electrode geometry had no peculiarities. Since in all cases the insulator was transformer oil, there was no need to speed up the process of charging of the line. Bernstein and Smith (1973) described the Aurora system capable of storing 5 MJ of energy. Four MG's connected in parallel served as primary energy stores. Each MG consisted of 95 stages, each stage containing four parallel-series-connected 1.85-|LIF, 60-kV capacitors. The capacitance of each MG was 78 nF for the output voltage equal to 11.4 MV; its inductance was 12 |aH. For triggering the spark gaps of these MG's, a special MG with an output voltage of 600 kV was used. In the high-power MG's, the first three stages became series-connected as trigger pulses were arrived simultaneously at the trigger electrodes of their spark gaps. With a small

238

Chapter 13

stray capacitance between adjacent rows and a rather large interelectrode capacitance, the initial overvoltage across the unbroken gaps was rather low at small N, It is difficult to take into account the influence of "ground" capacitances of stages. All this results in the need to include additional resistive couplings in the circuit and to replace the corresponding twoelectrode spark gaps by three-electrode ones. Thus, we obtain a hybrid MG circuit with resistive couplings. The presence of couplings of this type allows one to extend the range of controllable operation to reduce the rms time spread in triggering of all MG's to approximately 10 ns with the triggering delay time of each MG equal to 1 |is and to reduce the jitter even in no-load operation. The charging of all capacitors of the MG demanded 2 min. To exclude erroneous start of the Aurora system as a whole with incompletely charged capacitors, the output of the MG to the double lines was shunted with resistors, which were disconnected on complete charging of the capacitors. The diagram of connection of the gaps in the MG circuit was not given by Prestwich and Johnson (1969). Relevant data were reported in detail for the MG's used in the PBFA II ion accelerator (Schneider and Lockwood, 1985; Woolston and Ives, 1985). In total, the PBFA II accelerator consisted of 36 Marx generators, each capable of storing 370 kJ of energy. Each of the 60 1.37-|aF capacitors of the MG was charged on two sides to 95 kV. The output voltage of the MG was 17 MV (Turman et al, 1985). The mass of one generator was 7.2 t, its overall dimensions were: length 2.1 m, width 1.8 m, and height 4.2 m. Five columns of capacitors on one side of the assembly were coupled to form five columns on the opposite side. Two adjacent columns on the different sides of the assembly formed a discrete row. Between these columns, three-electrode spark gaps operating by the principle of field distortion were connected. Their trigger electrodes had holes. Adjacent columns on one side were connected by flat aluminum busbars. The 30 spark gaps of the MG operated in SF6 under an optimum pressure of 0.2 MPa. The final version of the trigger circuit of the MG provided an average triggering delay time of -200 ns with 4-ns jitter for an individual generator. Much attention was given to the trigger circuit of a single MG for the PBFA II accelerator (Schneider and Lockwood, 1985). The zigzag configuration that had been used earlier (Bernstein and Smith, 1973) was retained. In the previous versions (Bernstein and Smith, 1973; Prestwich and Johnson, 1969), insufficient attention had been given to the jitter of the operation of an MG. Since in PBFA II thirty six MG's operated independently, each into its own module, it was required to reduce the rms jitter of the triggering delay time of one MG to 4 ns. This was achieved by means of numerical modeling and comparison of the predictions with

MARX GENERATORS

239

experimental data obtained with the use of light and magnetic gages (Lockwood, et al, 1985). The trigger pulse of amplitude 500 kV and rise time 80 ns was applied, through resistors, simultaneously to the trigger electrodes of all spark gaps of the first row. This pulse was generated by a six-stage trigger MG with twelve 0.15-|iF capacitors charged on two sides to 50 kV. The experiments showed, first, that the jitter of the operation of the main MG decreased with increasing charge voltage or decreasing the gas pressure in the discharge gaps, and the optimum pressure was determined. Second, it was found that the main contribution to the jitter was given by the triggering of the gaps of the first two rows, and that the jitter decreased when additional resistive couplings were introduced between the trigger electrodes of the first and second rows. A similar principle of powering one module from one Marx generator was developed for the Angara-5 system (Bolshakov et al, 1982) earlier than the publication by Woolston and Ives (1985) had appeared. This system consisted of individual modules arranged in radii around a reactor chamber in which a target was placed. Each module represented a pulsed electron accelerator producing electron beams of energy 2 MeV and current 0.8 MA with a pulse duration of 85 ns. In each module, the primary energy store was a Marx generator capable of storing 200 kJ of energy. The MG of a module consisted of three parallel branches (sections), each containing 14 stages. For the spark gaps of the MG, three-electrode spark gaps with field distortion, immersed in gas, were used. To reduce the inductance of the discharge circuit, the spark gaps were arranged on the outer perimeter of the generator. To attain low-jitter operation of the MG sections, longitudinal and transverse resistive couplings were used in them. The generator was erected in a compartment of the common tank of diameter 3 m, filled with transformer oil. With the energy storage capacitance of the generator equal to 78.6 nF, the output voltage of the MG was 2.3 MV. The average triggering delay time of the generator reached 600±30 ns with a 100-150 ns spread in triggering of individual branches. This rather large spread seems to be due to the absence of illumination of the trigger electrodes of the spark gaps (Sterligov

etal,\916).

4.

MULTISECTION MARX GENERATORS

Koval'chuk and his co-workers, when developing the Gamma, GIT-4, and GIT-12 machines at IHCE, have created multimodule Marx generators capable of storing large amounts of energy. These generators contain a great number of parallel-connected sections being also Marx generators, each

240

Chapter 13

storing a much lower energy with the same voltage as the main MG (Kremnev and Mesyats, 1987; Bastrikov etal., 1989; Koval'chuk et al, 1989). Let us consider the operation of this type of MG with the Gamma microsecond electron accelerator as an example (Koval'chuk et al, 1989). For generators of this type, a wide range of powers and energies can be achieved by parallel-series connection of identical sections and use of various types of capacitors. It has been shown (Vorob'yushko et al, 1977; Babykin and Bartov, 1972) that simultaneous operation of MG sections is possible if they are switched into a load when the voltage across the load yet does not reduce the voltage across the spark gaps of the output stages, i.e., the spread in triggering delay times of the sections must be much shorter than the rise time of the voltage across the load. In every specific case, the rise time is determined by the characteristics of the generator and load, making some microseconds for generators used to charge capacitive energy stores and less than 0.1 \is for those operating into a resistive load. Hence, for stable simultaneous operation of generators, the spread in their triggering delay times must be no more than 10 ns. If the discharge gaps are about 1 cm wide and operate in air at a pressure of 0.1-0.2 MPa and if they are preirradiated and the (uniform) electric field in them is about 100 kV/cm, it is possible to attain a less than 10-ns jitter of their triggering delay time (Kremnev and Mesyats, 1987). For stable continuous operation of the sections, it is necessary, first of all, to eliminate the possibility of their selfoperation; that is, the voltage V^G between the electrodes of the spark gaps must be much lower than the dc breakdown voltage Fdc, and then we have for the factor of safety ks = ^dc/^so > 1. At the same time, it is necessary that the field in the spark gaps be as strong as mentioned. Figure 13.4 shows the complete circuit of a section of an MG with threeelectrode spark gaps and capacitive coupling of the middle electrode with the previous stages (Bastrikov et al, 1981). The designations in this figure are as follows: Ccoupb C, Ci, C2, C3, and C4 are, respectively, the capacitances of coupling capacitors (259 pF), energy storage capacitors (0.4 |LIF), equivalent capacitances between the energy storage capacitors {C\ = C2 = 40 pF), capacitances between the screen and the case (46 pF), and capacitances between the screens (30 pF). Besides, L, Li, L2, and LQ are, respectively, the inductance of the capacitors (150 nH), the inductance of the leads {L\ =1.2 = 150 nH), and the stray inductance (0.45 |iH). In the main spark gaps with identical gaps, Gi and G2, the voltage is initially distributed fiftyfifty between them. The trigger spark gap, for the extension of the triggering range and shortening the jitter, is made three-gap and in the charging mode, the potentials at electrodes 7-4, in the direction from the ground, are, respectively, zero, Fo/4, Fo/2, and FQ. The gaps Go and SGQ of the trigger spark gap are equal to a half of the gap Gi or G2 of the spark gaps of the

MARX GENERATORS

241

middle stages. The additional discharge switch ô serves for preliminary illumination of the trigger spark gap. The capacitors of the MG are charged from a high-voltage source of dc voltage +VQ through the voltage divider R^, cables Lo ... L2, and charging resistors R\. •OFr

R1 "AMAA-

^2

AAAAA ^shl

"T~ C3

RI

'~T~ C3 ^ /v.

-'Coupl2

^3

• T o oscil.

r4»fvw\^ -'coupl 1

G2

G2

C L

M in ^0 %cI\Q^ SGo

G2

CL

iL2TG,TiiT^ T121 TiiT'^ 1^2!

'JO

C2 \^r

TooJEll^ -&

Lo

CL

w w w

^

»

-VWA-

-AM/V^

^4

^1

Cl

•*•

-AVW

Figure 13.4. Circuit diagram of the GM of the Gamma accelerator: R^ - voltage divider (50 Q); Rshu ^sh2, ^sh3 - shunting resistors; L2 - Fo/4 line; SGtr - trigger spark gap; Ctr = 750 pF - trigger capacitance; R = 1 MQ; /^s = 10 kQ; Rio^d ~ load resistance; Iioad - load inductance (other symbols are described in the text)

The resistors i?2 (510 Q) and i?3 (1 kQ) serve to decouple the circuits on triggering and R^ (51 Q) serves to protect the cable Lo (line with voltage VQ) against the voltage wave reflected from the load of the MG. By means of the trigger spark gap SGtr, pulses of amplitude - VJl and 10%-90% rise time /r ^ 30 ns for triggering and illumination of the spark gap ô are formed in the cables Li and L3 (line with voltage Fo/2 and trigger line). As the trigger pulse arrives at the gaps G2 and SGQ of the trigger spark gap, the voltage across these gaps can increase three times compared to its initial value. The overvoltage across the gap G2 increases more rapidly than across the gap SGQ. This just determines the sequence in which the gaps in the first (trigger) spark gap are broken down: G2, SGQ , and Go. After the operation of the first spark gap, the voltage across the gap Gi of the second spark gap can be tripled compared to its initial value. For the gap Gi of the second spark gap broken down, the voltage across the capacitor Ccoupii is determined by the formula

Chapter 13

242

Vc^.,n(0 = Vo 0.5-

1.5

(13.2)

( 1 - C O S CO/)

C'coupll/C' + l 0.5

where co = ((Ccoupii / C +1) / [Ccoupii (^ + A + ^ ) ] } ^ obtained in view of the initial conditions Kc(0) = -FQ , VQ^^^^ (0) = VQ/I . From (13.2) it follows that for Ccoupii VQ {a) and v^ VQ (b). The photographs were taken at a peak voltage of 600 kV, a current of 5 A, a pulse duration of 25 ns, and a pulse repetition rate of 100 Hz Table 14.1. Parameters of some pulsed accelerators of the SfNUS series Accelerator Electron Beam current, Pulse duration, version energy, keV kA ns SINUS-4 400 8 25 700 SINUS-5 7 10 SINUS-6 400 5 25 SINUS-7 20 40 2000

Pulse repetition rate, Hz 100 100 1000 100

Tesla transformers are also widely used in compact nanosecond highvoltage pulse generators intended for the production of electron beams and pulsed X rays (Tsukerman et al, 1971). High-efficiency devices of this type are systems of the Radan series (Shpak et al, 1993) in which a coaxial line filled with transformer oil is charged from a built-in Tesla transformer (Fig. 14.4). Switching of the current in the primary circuit of the transformer is performed with the help of thyristors at a voltage equal to the voltage of the supply line. The switch on the high-voltage side is a dismountable highpressure spark gap, which operates in the environment of nitrogen at 40 atm. The general view of a Radan accelerator is given in Fig. 14.5. The Radan accelerators are widely used for pumping gas and semiconductor lasers, for the production of x rays and microwaves of wavelength 2-10 mm and pulse power 10-60 MW, for sterilization of medical devices, and for other purposes. Martin and Smith (1968) proposed to produce voltage pulses of up to 1 MV with the use of a pulse autotransformer with metal foil windings. The characteristic feature of this type of transformer is that it is insulated with paper impregnated with high-s dielectric (water). This has the result that the

Chapter 14

256

electric field at the foil edge levels off. The configuration of one of the windings of such a transformer is shown in Fig. 14.6. Contacts D and C are the terminals of the primary winding and A and B are the ends of the secondary one. Before the foil is turned in a spiral, it is coated with insulating polyethylene or Dacron tape and the cutouts are filled with adsorbing paper whose thickness is chosen equal to the thickness of the foil. Then the foil tape with the imposed insulation is wound on a cylinder. Figure 1.7 shows a circuit diagram and the equivalent circuit of an autotransformer. The primary voltage can be applied not necessarily to the bottom turns, but also to the central ones. 320 mm

5-50 îs

-220 V 50/60 Hz Figure 14.4. Block diagram of a Radan-type accelerator: 1,2- primary and secondary windings; 3, 4 - outer and inner windings of the Tesla transformer; 5 - gas-gap switch; 6 load; 7,8- capacitive voltage divider; A1-A4 - timers; B1-B4 - pulse dividers; D - driver

Figure 14.5. General view of a Radan-type system. Voltage 30-300 kV, line wave impedance 45 Q, pulse duration 4 ns, pulse rise time 1 ns, maximum pulse repetition rate 25 Hz, mass 28 kg, average required power 250 W

PULSE TRANSFORMERS

257 C

D

Figure 14.6. Configuration of a foil winding with an applied insulation: 1 - insulating layer; 2 - foil ribbon

Several pulsed electron accelerators were developed in which a pulseforming line was powered from an autotransformer. Bugaev et al (1979) reported on the development of the SESfUS-l accelerator that produced an electron beam of energy 500 keV, current 10 kA, and pulse duration 25 ns. The pulse-forming line was charged by a pulse autotransformer with an open ferromagnetic core. The pulse-forming element was a coaxial line of wave impedance 8 Q filled with glycerin. The accelerator is schematically shown in Fig. 14.7. A metal tube 2 incorporates a pulse transformer 4, an energy storage element 5 made as a coaxial line segment, chamber 6 with high-pressure spark gaps, and an acceleration tube. Originally, energy is stored in a charging capacitor 1 which is located outside the tube and is connected to the transformer winding by a strip line. The capacitor 1 is switched into the transformer winding by an air spark gap 3. In the pulse transformer, an open armored core made of electrotechnical steel is used because the magnetic flux has no time to be distributed throughout the core. The absence of a closed core facilitates the service of the transformer having a coaxial configuration. The winding is designed like that of an autotransformer and has the shape of a wedge (narrowing from the beginning to the end). The turns are interlaid with polyethylene film. The necessity of fast charging of the energy storage line (0.5 |is) with the high charging capacitance places rigid requirements on the inductance of the charging circuit. This problem is solved by using a transformer of small dimensions with the least possible spacing between the turns and by making the inductance of the transformer primary circuit as low as possible. With this purpose, the energy supply from the primary capacitive energy store to the transformer is realized with the help of a lowimpedance strip line, which passes the shortest way inside the transformer core. The top part of tube 2, where the transformer is located, is filled with transformer oil. In the bottom part of the tube, a coaxial energy storage line 5 with glycerin as dielectric is located. For shortening the rise time of the pulse across the load, a spark gap 7 is used which operates in the environment of nitrogen compressed to 12 atm, and a necessary pulse duration is specified by a chopping spark gap 5, since with no chopping spark gap, because of the incomplete match of the line to the load, afterpulses appear.

Chapter 14

258 0 -15 kV

WWWXl 300 mm Figure 14.7. Schematic drawing of an accelerator: 1 - charging capacitor, 2 - tube, 3 - spark gap, 4 - pulse transformer, 5 - energy storage unit, 6 - spark gap chamber, 7 - peaking spark gap, 8- chopping spark gap, 9 - cathode, JO- anode

II

10

5

9

8

7

12

Figure 14.8. Schematic diagram of the Sinus-2 accelerator: 1 - energy input from primary storage capacitors, 2 - secondary winding, 3 - autotransformer core, 4 and 5 - double pulseforming line, 6 - electron beam extraction foil, 7 - explosive-emission cathode, 8 - charging inductor, 9 and 10 - capacitive voltage dividers, 11 - gas switch, 12 - window for injection of electrons into the gas gap

PULSE TRANSFORMERS

259

An autotransformer was also incorporated in the design of the SINUS-2 accelerator that produced electron beams of energy 1 MeV, current 30 kA, and pulse duration 40 ns (Bugaev et al, 191 A) (Fig. 14.8). Foil autotransformers are successfully used in charging high-power water energy stores. The advantages of foil transformers for the above purpose are realized at best in the accelerator described by Fedorov et al (1978). The use of high-strength film insulation impregnated with conducting water solution, the realization of parallel operation of transformers, and the increase in turn voltage by connecting the primary energy store to a section of the transformer primary turn enabled the authors of the cited work to transform 20 kJ of energy from a 50 kV voltage level to 1 MV within 10"^ s.

3.

LINE PULSE TRANSFORMERS

For the production of megavolt pulses of microsecond duration with an energy of up to 10^ J and more, linear pulse transformers (LPT's) are used (Mesyats, 1979). As mentioned in Chapter 1, an LPT consists of A^ singleturn transformers with a common secondary winding. The secondary winding is a metal rod on which toroidal inductors with the primary winding are put on. A capacitor or line is discharged into all primary windings simultaneously through a triggered fast spark gap switch. The equivalent circuit of an LPT and the mechanism of voltage multiplication were considered above (see Chap. 3). Mesyats (1979) described the Modul pulse generator designed for the production of hot plasmas by the method of MHD implosions, developed at IHCE. This machine, with 100 kJ of stored energy, generated pulses of current up to 2 MA, duration 10"^ s, and voltage 2 MV. The generator consisted of a charging device, water energy storage and transmission lines, and appropriate switches. The charging device in this system was a linear pulse transformer (Fig. 14.9). The pulse transformer 2 had a low internal inductance since the secondary winding is made as one turn 2a, Owing to the low intemal inductance, LPT's can be used for fast charging of high-voltage energy stores with high-energy storage capabilities, including water stores. The LPT was designed as a set of twelve identical sections. Each section consisted of two transformers with single-turn primary and secondary windings. The secondary windings were connected in series. The primary circuit of the transformer consisted of two oppositely charged capacitors 3 (3 10"^ F, 40-10"^ H, 50-10^ V), six parallel-connected transmission cables, and two gas switches 4, The primary turn was formed by the cores of the transmission cables. The transformation factor of the LPT, reduced to the charge voltage of the capacitor, was equal to 48. The cores of the magnetic

260

Chapter 14

circuits were made of electrotechnical tape covered with lacquer and glued with epoxy. This made the cores mechanically strong and simplified their processing. The final internal and external diameters of the cores were, respectively, 250 and 515 mm; the filling factor was 0.8, and the weight of one core was 75 kg. Two cores mounted in a case with a gap of 3-4 mm between them formed one magnetic circuit of cross-sectional area 230 cm^. For the reduction of the cross section of magnetic circuits, provision was made for pulsed magnetic reversal (5,11), To connect the capacitors C\ to the LPT primary winding, triggered spark gaps were used which, in the voltage range 25-45 kV, operated with a jitter less than 10 ns. The secondary turn of the LPT was formed by the case and the central core 2a made of a tube of diameter 80 mm. To insulate the tube from the magnetic circuit, polyethylene film 10 impregnated with glycerin was applied on the tube. The internal space of the transformer was also filled with glycerin. The choice of glycerin as dielectric instead of water was dictated by the presence of steel magnetic circuits. In testing the film-glycerin insulation with single pulses of peak voltage 1.5-10^ V and duration 1.8-10"^ the insulation was broken down at a field of 1.5-10^ V/cm; at 1.2-10^ V/cm breakdown occurred after 10-15 pulses. With the maximum design parameters, the field inside the transformer was 0.5-10^ V/cm. 5500 mm

2000 mm

2000 mm

Figure 14.9. Schematic diagram of the Modul system: 1 - trigger generator; 2 - line pulse transformer; 5 - 4 8 capacitors; 4 - spark gaps; 5 - remagnetization capacitor; 6-6 water pulse-forming lines; 7 - peaking spark gaps; 8 - transmission line; 9 - load; 10 - glycerinimpregnated film insulation; 11 - remagnetization inductor; 12 - insulators; 13 transmission line

PULSE TRANSFORMERS

261

The use of an LPT for charging an energy store can be illustrated by the SNOP-2, SNOP-3, and MIG systems developed and built at IHCE (El'chaninov and Mesyats, 1987; Kovsharov et al, 1987; Luchinsky et al, 1997). The SNOP-3 generator (Fig. 14.10) (Kovshsarov et al, 1987), intended for studying the dynamics of imploding wire arrays, produces a power of 1 TW and provides in a 30-nH inductive load a current of 2.2 MA with a rise rate of 4-10^^ A/s. The generator consists of a primary energy store (capacitor bank), a line pulse transformer, an intermediate capacitive energy store, a pulse-forming line, and a transmission line. The switching between these elements is accomplished by triggered and nontriggered water spark gaps. The quest for short charging times for low-resistance waterinsulated lines forces one to use transformers with a minimum stray inductance. 11 12

CiUfTCi

1

Figure 14.10. Schematic diagram of the SNOP-3 generator: 7 - 2 4 inductors; 2 - inner conductor; 3 - film-glycerin insulation; 4 - bushing insulator; C\ - 48 capacitors; S 49 spark gap switches; 5 - L and C2 - separating inductor and the capacitor of the demagnetization circuit; 6 - intermediate capacitive energy store; 7 - support insulators; 8 water insulation; 9 - triggered multichannel spark gap; 10 - pulse-forming line; 11 nontriggered multichannel switch; 12 - transmission line; IS - capacitive voltage pickups; 14- current pickup; 15 -load unit; 16 -vacuum insulator

In the SNOP-3 machine, an LPT is used for charging an intermediate capacitive energy store of resistance 1.3 Q and electric length 75 ns. The voltage increases to a maximum of 2 MV within 1.3 jis. The energy store 6 (see Fig. 14.10), switch P, and pulse-forming line 10 form an LC circuit with the time of voltage rise to a maximum equal to 300 ns. The energy transfer from the store to the pulse-forming line occurs in the resonance manner: two runs of an electromagnetic wave from the switch to the end of the store and back (-300 ns) correspond to its four runs from one end of the line to another ('-^300 ns). The pulse-forming line is discharged into a transmission

262

Chapter 14

line 12 of the same wave impedance through a nontriggered multichannel switch 77. At the end of the transmission line, there is a load unit 75. Further development of the ideology of the Modul and SNOP systems was realized in the MIG multi-purpose machine (Luchinsky et al, 1997). This system is intended for the generation of pulses of peak voltage up to 6 MV and current up to 2.5 MA with a power of 2.5 TW. The load resistance ranges from a few ohms to several hundreds of ohms since the load is generally a z-pinch or an electron beam. In this machine, to produce a voltage of 6 MV across a load, plasma and exploding-wire opening switches are used. The Hermes III accelerator (Corley et al, 1987; Johnson et al, 1987; Pate et aL, 1987) built at SNL is the most powerfiil LPT-based system in the world. It is capable of generating a beam of current 800 kA and pulse duration 40 ns at an accelerating voltage of 20 MV and is intended for experimentation under the conditions of high-doze irradiation. This machine is capable of producing doze rates of 5-10^^ R/s in a cylindrical volume of base area 500 cm^ and height 15 cm. The main distinguishing feature of the accelerator is the use of a magnetically insulated vacuum coaxial line to sum up the voltages of 20 inductor sections of the LPT. The magnetically insulated line is formed by the cathode holder and the internal cylindrical surfaces of the sections enclosing the holder. An electromagnetic pulse is supplied to the line through the ring slots cut in the internal surfaces of the inductor sections. The latter contain transmission lines and magnetic cores providing highvoltage insulation due to inductance. With this system design and the 20-MV accelerating voltage, there are difficulties, first, with the insulation of the energy storage sections and, second, with the reduction of the leakage currents resulting from the electron emission from the cathode holder. The first problem is solved by using metglas magnetic cores, providing an inductive isolation of the sections from the total voltage. The second difficulty is overcome by that the cathode holder serves simultaneously as an element of the magnetically insulated vacuum line that operates in a selfconsistent mode and provides the transportation of the "electron layer", formed by leakage electrons in the diode. It has made it possible to create an accelerator with small losses. The Hermes III accelerator (Ramirez et al, 1987) contains ten Marx generators, twenty intermediate energy stores, twenty laser-triggered multielectrode gas switches, eighty water pulse-forming and transmission lines, and twenty LPT's (inductively insulated storage ring sections) that switch energy into the voltage summation system (magnetically insulated vacuum coaxial line) that delivers energy to an electron diode (radiation converter). The energy storage system consists of a primary store and an

PULSE TRANSFORMERS

263

intermediate store. The primary store incorporates ten 156-kJ, 2.4-MV Marx generators. The generators are placed in two tanks, five in each, on two sides of the accelerator. The intermediate store consists of twenty 19-rLF cylindrical water capacitors. Under optimal conditions, each capacitor is charged to 2.2 MV within 950 ns. As the voltage peaks, the gas switches switch energy from the intermediate store into the pulse-forming lines. Twenty spark gaps filled with SF6 are responsible for synchronous operation of the all units of the accelerator. The switches are immersed in transformer oil. They are similar in design to the switches used in the PBFA II. They also have two sections: one section is laser-triggered and the other, where the voltage it is distributed over ten gaps, is nontriggered. The jitter of the operation of the lasertriggered spark gaps is not over 2 ns. Such a switch ensures reliable operation of the system up to 2.5 MV. To trigger the spark gaps, a pulsed KrF laser {X « 248 nm) with pulse duration of 20 ns and energy of 900 mJ is used. The optical system, which contains 20 fiber channels that bring the radiation to the switches, controls, with the help of mirrors, the pulse delay time within 5 ns. 200 mm

Figure 14.11. Schematic and circuit diagrams of a stage of the LTD-100 transformer

Chapter 14

264

Kovarchuk et al (1997) of IHCE developed a series of pulse generators with LTD-type line transformers. Figure 14.11 presents the schematic and simplified electric circuit diagrams of a capacitor-based stage of the LTD100 transformer with the parameters: 100 kV, 40 nF, 25 nH, and 270 mQ. The stage contains eighteen capacitors subdivided into nine identical pairs (2); the capacitors of each pair are oppositely charged to ±100 kV. The circuit of a pair contains a series spark gap 1 that connects the capacitors of the pair to load 5. High-voltage insulation is provided by polyethylene insulators 3 and transformer oil filling the internal space of the stage. The core of the stage is wound of steel tape. It consists of six rings of total cross section 53 cm^. The stage is intended for the operation into a load of resistance R = {LIC)^'^ -^ 0.4 Q.

Starting resistors

Charging voltage leads (±)

Starting voltage lead

Figure 14.12. Side view of the LTD-100 stage

Figure 14.12 gives a side view of the module. It has the shape of a disk of diameter 1350 mm and height 200 mm; nine pairs of capacitors are arranged evenly in a circle. The charging resistors are ~1 kQ liquid (water solution of CUSO4) resistors; the triggering resistors of the same resistance are made of conducting rubber. Five cables are connected to the module: two cables for the charge voltage, two cables for the current biasing the cores, and one

PULSE TRANSFORMERS

265

triggering cable. The bleed-in and effluent of dry air from the spark gaps is performed through a common sleeve. In the short-circuit mode with the inductance of the coaxial output equal to 3 nH, the time of conversion of the energy stored in the capacitors into the energy of a magnetic field is 125 ns at a peak current of 380 kA. By mere addition of transformer stages of this type, it is possible to design pulse generators with parameters ranging over wide limits.

4.

TRANSFORMERS USING LONG LINES

In the technology of nanosecond high-power pulses, besides the above transformers with lumped parameters, transformers based on long lines (see Chapter 2) are also used. Figure 14.13 presents a high-voltage pulse generator proposed by Lewis (1955) and developed by Pavlovsky and Sklizkov (1962). The generator consisted of three basic elements: a pulseforming line (PFL), a spark gap, and a transforming line (TL). The pulseforming line consists of five cable pieces, each 25 m long, connected in parallel, and was charged to 70 kV. As the spark gap operated, a rectangular pulse of duration 0.25 ^s, rise time over 5 ns, and amplitude 35 kV was generated across the PFL. The transforming line also consisted of five cable pieces. The input resistance of the TL was equal to the wave impedance of the PFL. At the output of the TL, all cables were connected in series. The electric length of the TL was chosen equal to the pulse duration. The cable pieces in the TL were formed into coils that were offset by no less than 10-20 cm from each other and from the surrounding massive metal units. The coils were placed on a bakelite tube 30 cm in diameter. The highvoltage ends were carefully insulated and, together with the load, immersed in oil to prevent a crown. A spark gap of coaxial geometry operating at a pressure of several atmospheres was used. When matched to the load, the generator produced a rectangular pulse of amplitude 160 kV and duration 0.25 i^s. For a load with /?ioad = 2 kQ, a pulse of amplitude 300 kV and rise time 50 ns was obtained. For the production of high-voltage (up to 300 kV) pulses of duration 250 ns with a rise time of 20 ns, a two-stage pulse-forming line and a transformer based on cable pieces can be used (Nasibov et al, 1965). Nasibov (1965) described a transformer circuit based on pieces of coaxial lines wound on a ferromagnetic core. The windings consist of three pieces of coaxial cable. The beginnings and the ends of the cable piece braids are connected in parallel and form the primary winding of the transformer. The cores of the cable pieces are connected in series and form the secondary winding. The transformation factor is equal to the number of cable pieces.

266

Chapter 14

To increase the inductance of the winding, the cables are wound on a ferromagnetic core. For the case of short pulses, the best choice of the core material is ferrite. Q

300kV

111 rWi

Rectifier

Figure 14.13. Schematic diagram of a 300-kV nanosecond pulse generator S

1

2

Figure 14.14. Cunênt pulse transformer with a coaxial cable wound in spiral: 1,2 - inner and outer conductors of the cable; 3 -collecting bars; 4 -cut in the cable enveiope

PULSE TRANSFORMERS

267

Designs of the step-down air transformer are known in which coaxial cable turns are used as windings. A similar principle is used in the transformers intended for the production of pulsed voltage. In these transformers, the cable core and conducting envelope are utilized as windings, which improves the frequency characteristic of the transformer (Gaaze and Shneerson, 1965). A step-up current transformer with a coaxial cable spiral winding was described by Latushkin and Yudin (1967) (Fig. 14.14). On each turn of the spiral, a small portion of the conducting envelope of the cable is cut off The cuts are located one above the other, and their edges are connected with busbars to the load. The cable is connected through a switch to a capacitor bank. When the capacitors discharge, a current flows through the cable core, envelope ends, busbars, and load. In the turn envelope, an emf is induced, and, therefore, the total current of all coils passes through the load.

REFERENCES Abramyan, E. A., Alterkop, B. A., and Kuleshov, G. D., 1984, Intense Electron Beams: The Physics, Technology and Applications (in Russian). Energoatomizdat, Moscow. Bugaev, S. P., El'chaninov, A. S., Zagulov, F. Ya., Kovarchuk, B. M., and Mesyats, G. A., 1970, A High-Current Pulsed Electron Accelerator, Prib. Tekh Eksp. 6:15-17. Bugaev, S. P., El'chaninov, A. S., Zagulov, F. Ya., Koval'chuk, B. M., Mesyats, G. A., and Potalitsyn, Yu. F., 1974, A High-Power Electron-Beam Pulse Generator. In High-Power Nanosecond Pulsed Sources of Accelerated Electrons (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 113-119. Corley, J. P., Johnson, D. L., Weber, B. V., et al, 1987, Development and Testing of the "Hermes III" Pulse Forming Transmission Lines. In Proc, VI IEEE Pulse Power Conf., Arlington, VA, pp. 486-489. El'chaninov A. S., Zagulov F. Ya., and Koval'chuk B. M., 1974, A short-electron-beam generator with a high-voltage source built in a line. In High-Power Nanosecond Pulsed Sources of Accelerated Electrons (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 119-123. El'chaninov, A. S. and Mesyats, G. A., 1987, Transformer Power Supply Circuits for HighPower Nanosecond Pulse Generators. In Physics and Technology ofPulsed Power Systems (in Russian, E. P. Velikhov, ed.), Energoatomizdat, Moscow, pp. 179-188. El'chaninov, A. S., Zagulov, F. Ya., Korovin, S. D., and Mesyats, G. A., 1979, Electron Beam Accelerator with High Pulse Recurrence Frequency. In Proc. Ill Intern. Conf on High Power Electron and Ion Beam Research and Technology, Novosibirsk, USSR, pp. 191-197. El'chaninov, A. S., Zagulov, F. Ya., Korovin, S. D., Landl', V. F., Lopatin, V. V., and Mesyats, G. A., 1983, High-Pulse-Repetition-Rate, High-Current Electron Beam Accelerators. In High-Current Pulsed Electron Beams in Technology (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 5-21.

268

Chapter 14

Fedorov, V. M., Scheglov, M. A., and Semenov, E. P., 1978, A Compact 1-MV Transformer. In Proc. All-Union Workshop on Engineering Problems of Thermonuclear Reactors (in Russian), Res. Inst, of Electrophysical Apparatus, Leningrad, p. 62. Gaaze, V. B. and Shneerson, G. A., 1965, A High-Voltage Cable Transformer for the Production of High Pulsed Currents, Prib. Tekh Eksp. 6:105-110. Johnson, D. L., Ramirez, J. J., Huddle, C. W., et ai, 1987, "Hermes III" Prototype Cavity Tests. In Proc. VIIEEE Pulse Power Conf, Arlington, VA, pp. 482-485. Koval'chuk, B. M., Vizir, V. A., Kim, A. A., Kumpyak, E. V., Loginov, S. V., Bastrikov, A. N., Chervyakov, V. V., Tsoi, N. V., Monjaux, P., and Choi, P., 1997, A Fast Primary Energy Store Based on a Line Pulse Transformer, Izv. Vyssh. Uchebn. Zaved, Fiz. 12:25-37. Kovshsarov, N. F., Luchinsky, A. V., Mesyats, G. A., Ratakhin N. A., Sorokin, S. A., and Feduschak, V. F., 1987, "SNOP-3", a Pulse Generator, Prib. Tekh. Eksp. 6:84-89. Latushkin, S. T. and Yudin, L. I., 1967, A Short Current Pulse Generator, Ibid. 4:110-114. Lewis, I. A. D., 1955, Some Transmission Line Devices for Use with Millimicrosecond Pulses, Electr. Eng. 27:332. Luchinsky, A. V., Ratakhin, N. A., Feduschak, V. F., and Shepelev, A. N., 1997, A Transformer-Type Multipurpose Pulse Generator, Izv. Vyssh. Uchebn. Zaved., Fiz. 12:67-75. Martin, J. C. and Smith, I. D., 1968, U.S. Patent No. 1 114 713. Mesyats, G. A., 1979, Pulsed High-Current Electron Technology, Proc. 2nd IEEE Intern. Pulsed Power Conf., Lubbock, TX, pp. 9-16. Mesyats, G. A., Khmyrov, V. V., and Osipov, V. V., 1969, A 500-kV Nanosecond Rectangular Pulse Generator, Prib. Tekh. Eksp. 2:102-104. Nasibov, A. S., 1965, A Pulse Transformer with Coaxial-Cable Windings, Elektrichestvo. 2. Nasibov, A. S., Lomakin, V. L., and Bagramov, V. G., 1965, A Short, High-Voltage Pulse Generator, PnT). Tekh. Eksp. 5:133-136. Pate, R. C , Patterson, J. C , Dowdican, M. C , et al, 1987, Self-Magnetically Insulated Transmission Lines (MITL) Systems Design for the 20-Stage "Hermes III" Accelerator, Proc. VI IEEE Pulse Power Conf., Arlington, VA, pp. 478-481. Pavlovsky, A. I. and Sklizkov, G. V., 1962, Production of Rectangular High Voltage Pulses, Prib. Tekh. Eksp. 2:98. Ramirez, J. J., Prestwich, K. R., Burgess, E. L., et al, 1987, The Hermes III Program, Proc. VI IEEE Pulse Power Conf., Arlington, VA, pp. 294-299. Shpak, V. G., Shunailov, S. A., Yalandin, M. I., and Dyad'kov, A. A., 1993, RAD AN SEF303A, a Compact High-Current Pulse Generator, Prib. Tekh. Eksp. 1:149-155. Tsukerman V. A., Tarasova L. V., and Lobov S. I., 1971, New X-Ray Sources, Usp. Fiz. TVawA:. 103:319-337.

PART 6. GENERATORS WITH PLASMA OPENING SWITCHES

Chapter 15 PULSE GENERATORS WITH ELECTRICALLY EXPLODED CONDUCTORS

1.

INTRODUCTION

The generators of high-power nanosecond pulses described in the previous sections are based on capacitive energy storage (CES) followed by voltage multiplication with the help of Marx generators or transformers. In devices of this type, the extraction of energy occurs on the microseconds time scale. To attain nanosecond times, it is necessary to use intermediate energy stores (capacitors or lines) and one or several peaking switches. This makes the devices with CES, especially megajoule systems, very bulky and costly. Now the designs of CES devices feature high perfection, especially those where many Marx generators operate in parallel. However, even in these systems, the energy density is not above 5 kJ/m^ at an output voltage of 3 MV. The energy density is roughly in inverse proportion to the output voltage V: for V ^ lO*^ V it is > 0.5 kJ/m-^ (Aurora). The low energy density results in a significant inductance of the CES discharge circuit that limits the output power to Pmax = 1 - 3 TW and the average power rise rate to about 3 TW/|is. In other words, CES devices provide the rise time of power at the load tr ^ 0.5-1 |Lis. However, the expanding research and engineering applications demand powers above 10^^ W with tr < 10"^ s. In some cases, for example, in systems intended for the production of high-power hard x rays and microwave radiation, inductive energy stores are employed in which the current is cut off by electrical explosion of conductors (EEC). This method has long been known (Early and Martin, 1965; Maisonnier et al, 1966). However, it came in nanosecond pulse technology only in the 1970s when it became clear that to increase the

272

Chapter 15

resistance rise rate in an opening switch, dRIdt, it is necessary to use not a foil, but a set of parallel-connected conductors (Kovarchuk et al, 191 A). In this case, the generator operates as follows (Fig. 15.1): as the switch S closes, the current flows from the energy store of capacitance C charged to a voltage VQ through the inductor L and exploded conductors EC. The load R is connected through the spark gap SG. If the cross section of a conductor is small, it is heated by the current it carries; its resistance increases and causes an increase in the rate of energy absorption by the conductor. As the energy becomes high enough, the conductor fuses and explodes. As this takes place, a jump is observed in the voltage waveform (Fig. 15.2); the fused conductor is heated up to some point in time t\ at which it starts exploding, i.e., quickly expanding with dispersion and partial evaporation of the metal. As this takes place, the conductor resistance increases by several orders of magnitude, the current abruptly decreases, and a voltage pulse is generated across the circuit inductor. If the electric strength of the EEC products is higher than the pulse peak voltage, the current is completely cut off (time ti in Fig. 15.2). This is followed by a no-current interval (^2 " ^3) whose duration is determined by the voltage remaining across the capacitor bank and by the velocity of expansion of the EEC products. However, if the spark gap SG (Fig. 15.1) is tuned so that it is broken down by the voltage generated on explosion, the inductor current / will be switched into the load and the voltage across the load may become several times greater than the charge voltage of the capacitor bank. The circuit shown in Fig. 15.1 is referred to as one-stage since it uses only one opening switch. If one more inductive energy store and an EEC switch are used as a load for the first stage, the circuit is referred to as two-stage. Generators with circuits consisting of thee and more stages are feasible. The studies performed have shown that EEC opening switches are capable of reducing the power rise time by an order of magnitude and increasing the power (mainly due to an increase in voltage) by an order of magnitude as compared to the direct discharge of a CES into a load. In this case, the energy density in the source increases due to the decrease in CES output voltage and absence of pulse-forming lines.

Figure 15,1. Circuit diagram of a pulse generator with an EEC opening switch

Figure 15.2. EEC current (top) and voltage (bottom) waveforms

PULSE GENERA TORS WITH EEC'S

2.

273

CHOICE OF CONDUCTORS FOR CURRENT INTERRUPTION

It is well known that if a high current pulse (with the current density reaching 10^-10^ A/cm^), generally produced by discharging a capacitor (Fig. 15.1), is passed through a thin metal conductor, there occurs an electrical explosion of the conductor. As this takes place, the liquid metal, because of its inertia, is overheated throughout its volume or in some regions and evaporates as intensely as if exploded. During evaporation, the metal conductivity of the conductor quickly decreases, resulting in current cutoff in the discharge circuit and a voltage pulse across the circuit inductor L whose amplitude is given by (15.1) at where / is the current in the circuit. If the voltage VL does not result in breakdown of the gap in which the exploding conductor is located, there comes a no-current interval (NCI). As the metal vapors expand, the pressure in the channel falls and, when the voltage remaining across the capacitor becomes equal to the breakdown voltage of the metal vapors, an arc discharge is initiated. If the voltage arising across the circuit inductor upon current cutoff is higher than the breakdown voltage, the conductor is shunted by the discharge even earlier than the explosion is complete. For fixed discharge circuit and conductor parameters, an increase in conductor length increases the NCI duration, while its decrease results in shunting of the conductor by the arc discharge. The conductor length at which there occurs complete current cutoff with a zero NCI is called the critical length. When using EEC to interrupt a current, the choice of the conductor material, shape, and dimensions and the parameters of the discharge circuit should ensure prescribed parameters of the pulse to be generated across the load. Though the mechanism of EEC remains obscure in many respects and there is no mathematical model for the calculation of its characteristics, the available experimental data allow one to choose the conductor material, cross-sectional area, and shape and to estimate its length necessary for a current pulse of specified amplitude be generated across the load. First, we restrict the spectrum of suitable metals by their boiling temperature T\y and work function. If Tb of the conductor metal is high enough, a shunting discharge develops over the conductor surface due to thermoemission even before the explosion, and the circuit is not broken. As revealed in experiment, an explosion followed by a no-current interval cannot be realized under normal conditions for tungsten, molybdenum, VL=L^,

274

Chapter 15

tantalum, and zirconium (Sobolev, 1947; Kvartskhava et al, 1956). Therefore, the metals whose work function is lower than the sublimation energy are not suitable for opening switches. To attain high efficiency of the energy transfer from a primary to an inductive energy store, obviously low-resistivity materials should be used. To transfer energy from an inductive energy store to a load, it is necessary to heat an exploded conductor (EC) to Tb and evaporate it. Since the energy losses for the heating and evaporation of the EC reduce the efficiency of the whole of the system, it is desirable to have a material with a low specific heat of evaporation. If we take into account that the temperature factors of resistance of high-conductivity materials are approximately identical, the product of resistivity x by sublimation energy Ss can be taken as a criterion in judging if the material is suitable for an opening switch (Kotov et al, 1974). Table 15.1 lists the characteristics of the metals showing the lowest values of the product of x by Sg. It can be seen that Ag, Au, Al, Zn, and Cu have the most suitable characteristics. Since gold is expensive and its characteristics are worse than those of silver, four metals remain that should be checked up experimentally. It should be noted that Maisonnier et al (1966) and Janes and Koritz (1959), who used more intricate comparison methods, arrived at the conclusion that the above metals, except zinc, should have the best opening characteristics. Table 15.1. Metal

X-IO^ Q-m

8s-10-^ J-m-3

X' Ss QJm-2

Silver

0.166

27.6

457

Gold

0.24

19.5

470

Aluminum

0.32

23

736

Zinc Copper

0.61

12.5

762

0.178 1.13

47.5 10.2

845

Tin Lead

2.08

11.2

2330

Platinum 1.10 58.5 Note: X is the resistivity at 18^C and Ss is the sublimation energy.

1150 6440

Experiments with exploding Ag, Cu, and Al wires (Mesyats, 1974) have shown that silver has better opening characteristics then copper and aluminum. Thus, under identical experimental conditions, for Ag and Cu wires the peak interrupted current, /max, appears to be approximately the same, while for Al wires it is a factor -^1.3 lower. Besides, a gap with an aluminum wire has a lower electric strength than a gap with a copper or silver wire. Therefore, an exploded Al wire is shunted by the arc discharge

PULSE GENERATORS WITH EECS

275

within a shorter time than copper and silver wires, resulting in a lower peak voltage. Silver wires, compared to copper ones, owing to the lower specific heat of evaporation of silver, provide generation of a pulse of higher amplitude and longer duration, the gap electric strength being the same. Silver, however, is much more expensive than copper; therefore, copper conductors are more usable. Let us pass to the choice of the shape and dimensions of exploded conductors. If for two differently shaped conductors identical in crosssectional area, the energy density immediately prior to the explosion is the same, the initial velocity of propagation of the evaporation wave will also be the same (Bennett, 1967). For this case, it can be shown that the shape of the conductor cross-section affects the rate of current interruption.

\A/N/NAAAAAAAAAA/WNAA/%AA/NA<W\/\^v\/Wvs»

(6)

^^0m^0^^0^0^0î0^J^^mm^

Figure 15.3. Voltage waveforms for copper conductors of the same cross-sectional area in air connected in a circuit with C = 2.6 jiF, VQ = 37 kV, L - 2.2 |iiH: a foil of cross-section 0.0147x4 mm and length 580 mm (a); a wire of diameter 0.28 mm and length 190 mm (b), and 12 parallel wires of diameter 0.08 mm and length 350 mm. The voltage scale is the same for all traces. The calibrationfrequencyis 12.5 MHz

An opening switch made of parallel thin wires provides a shorter opening time and a considerably higher power (Fig. 15.3) than a single cylindrical or foil conductor of the same cross-section does. It is should be noted that the chosen conductor lengths ensured the highest voltage (power), and the energy absorbed by the opening switches was approximately the same. Therefore, in subsequent experiments and developments, opening switches made of parallel thin wires were used. It should be noted that in switching currents of --10^ A, foil opening switches may appear to be more technological (Bakulin et al, 1976). The overall dimensions of a switch can be reduced by arranging the conductors in a zigzag (Kotov et al, 1976).

276

3.

Chapter 15

THE MHD METHOD IN DESIGNING CIRCUITS WITH EEC SWITCHES

In magnetohydrodynamic (MHD) calculations, the coordinate-dependent current density, the electric and magnetic field strengths, the density, temperature, pressure, and mass velocity of the material, and the radiation field in the material (if this field is significant) are determined at each point in time. Simultaneously, the calculation gives the time dependences of currents and voltages for every element of the electric circuit. As a rule, calculations of this type are based on solving numerically one-dimensional MHD equations in the one-temperature approximation taking into account electronic heat conductivity. The radiation transfer to the material is described in the spectral diffiision approximation. The system of equations in Lagrangian coordinates for the case of cylindrical symmetry is given by }Loiov etal (1987). In calculations of this type, it is of critical importance that the properties of the material, equations of state, relations of the electric and heat conductivities on the state of the material, and spectral coefficients of absorption of radiation be described adequately. The description of the properties of a material over a wide range of states, including the metal-toplasma transition region, is an independent and rather intricate physical problem. In calculations of an EEC, various methods for such a description are used. For example, Bakulin et al (1976), used the equations of state derived based on the Thomas-Fermi model (Kalitkin and Kuzmina, 1978) for the high-temperature region (7 > 1 eV). To specify the coefficients of electrical and heat conductivities, interpolation formulas constructed with the use of a semiclassical theory of transfer were applied. The spectral radiation field over which the absorption coefficients were averaged was determined by solving the equations of spectral diffusion of radiation (Kotov and Luchinsky, 1987). The absorption coefficients were set either by tables, obtained fi-om detailed quantum-mechanical calculations, or by analytic formulas (Zel'dovich and Raizer, 1963). The procedure of averaging was carried out in a certain number of time steps. The values of hydrodynamic quantities at the boundary of the mixed phase region calculated from thermodynamic relations as functions of the relative density of the material are presented in Fig. 15.4. The critical point is characterized by 8 = 0.322 and 8T = 5.28 kJ/g. Within the mixed phase region, the hydrodynamic quantities were estimated by interpolation with respect to the concentration of one of the phases between the values of these quantities at the boundary. To find the dependence of the electrical conductivity on the state of the material, a calculation-experimental method was applied in which the electrical conductivity was chosen so that the

111

PULSE GENERATORS WITH EEC'S

calculations would describe with a reasonable accuracy a number of "reference" experiments on the explosion of conductors that had been carried out under conditions considerably different from each other. For fixed values of ST below the critical value, the resistivity abruptly increases with decreasing 6 near the 6 values corresponding to the boundary of the mixed phase region and has a maximum at a density below the critical density. This circumstance plays an important role and largely determines the increase in metal resistance during an electrical explosion and the switching capabilities of electrically exploded conductors.

Figure 15.4. Time variations of pressure /?, specific internal energy 8, and specific thermal energy Sj at the boundary of the phase mix region for copper

60

600

50

500

40

400

§30 -

/ == 61 cm /

/ /

^ 300

20

200

10

100 - /

0

0

/V H !l

/ /

V .fl

'

/ = 27cm|

/ J^^^^^^^^

- n\

V 1

1

1

'

1

3 2 t [\xs\

A

0

I

I

1 2 t [^s]

I

3

Figure 15.5. Voltage and current waveforms for single wires of different length exploded in air at VQ= 140 kV, Co = 1.5 ^F, Z = 3 îH, r = 0.014 cm

278

Chapter 15

The calculation method described was checked by comparing the calculation results with the data of numerous experiments among which there were two-stage explosions of copper and aluminum conductors in air, water, oil, and epoxy compound (Kotov and Luchinsky, 1987). In all cases, the difference between the calculated and experimentally determined peak currents and voltages was not over 10%. The calculations described rather adequately the dependences of the current and voltage on time and on the characteristics of the wires and electric circuits. Some calculation results and experimental data are compared in Fig. 15.5. The solid and dashed lines represent, respectively, the measured and calculated current /(/) and voltage V{t). With this method, calculations of the pulsed currents and voltages generated by systems of the IGUR type (Kovalev et al, 1981) were carried out, the parameters of the systems were chosen, the operation of the circuits was analyzed, and the modes of operation were selected.

4.

THE SIMILARITY METHOD IN STUDYING GENERATORS WITH EEC SWITCHES

The MHD method allows one to calculate all characteristics of a circuit with an EEC opening switch operating into a load. At the same time, these calculations are rather cumbersome and call for special computer facilities. The alternative is similarity theory that enables one, with a minimum of information on the mechanism of a phenomenon, to reduce the number of variables, to establish the form of the dependence of the sought-for quantities on similarity criteria, and to extend the dependences obtained to the whole class of similar phenomena. Calculations of EEC with the use of similarity criteria allows an engineer to optimize a circuit for a chosen parameter with an accuracy sufficient for designing and to predict the basic characteristics of the circuit, such as the amplitude and duration of current and voltage pulses, the energy transferred to the load, the time to explosion, etc. (Kotov et al, 1974; Kotov and Luchinsky, 1987). The factors that substantially affect the behavior of an LC circuit with an EEC switch (without a load), are the capacitance C and charge voltage Fo of the capacitor bank, the inductance of the discharge circuit, L, the diameter d, length /, and number n of the parallel wires used, and some characteristic values of resistivity Xo? specific energy So, and rate of destruction ô of the conductor material. It is supposed that VQ is a function of only SQ. According to the similarity theory, the eight dimensional factors, which are described with the help of five independent dimensions (the dimensions of length and diameter in the given description of the phenomenon are considered independent) (Kline, 1965), can be combined in three

PULSE GENERATORS WITHEECS

279

dimensionless complexes. When doing this, it is desirable that the complexes be physically meaningful. We write these complexes as

n =—l2L_ ,

n2 =

CVo'

n^dêoyfl/C

, n3 = ^0

VZc

(15.2)

where 111 describes the attenuation of oscillations in the circuit, i.e., characterizes the ratio of the active resistance of the conductors to the wave impedance of the circuit Z = VZC; 112 describes the specific action of the circuit current for conductors of the chosen section (the product of 111 by the ratio of the stored energy to 8o), and Yl^ describes the ratio of the time constant of the circuit to that of the explosion of the conductors. If we investigate one metal, the constants %, So, and VQ that describe the metal in (15.2) can be omitted, and then we obtain three dimensional parameters: X=

I nd^Z

1 Qmm

8=

cvl_

mm^ -fit

V--

yflC

^s . (15.3) mm

n^d^Z For convenience, we assume that the initial factors have the following dimensions: / and d [mm], C [|iF], L [|LIH], FQ [kV], and 4LC [|IS]. The investigations performed by Kotov and Sedoi (1976) have shown that all characteristics of an LC circuit with EEC can be modeled by the parameters (15.3) with an error no more than 20% over a wide range of initial values of the circuit characteristics: Fo = 1-500 kV, n = 1-80,

C = 0.1-2000 |aF, d = 0.04-1 mm,

L = 0.4-50 |LIH, / = 4-2600 mm.

The parameters were varied within the following limits: ^ = (0.07-2>104Q-^-mm-^ 8 = (0.18-20)40^ J/(mm^.Q), v= 10-190 |as/mm, thus covering the entire spectrum of the operation characteristics of EEC opening switches. Prior to the onset of an explosion, the characteristics depend only on X and 8 (Azarkevich, 1973). For example, the normalized circuit current is given by hZ

> ^ m = ^ = ^(B-10-^;il/^)\

(15.4)

Fo (where /a is the peak current) and the normalized time it takes for the current to reach a maximum is

280

Chapter 15

VZc

= B(lO-'eX'^y

(15.5)

In (15.4), A = 0.9 and a = -0.25 for copper conductors and A = 0.78 and a = -0.31 for aluminum conductors. In (15.5), B = 0.9 and p = -0.31 for copper conductors and B = 0.9 and P = -0.3 for aluminum conductors. Similar expressions have been obtained for the energy absorbed by a conductor to the moment the current reaches a maximum and for silver conductors. If a characteristic also describes the stage of explosion, for example, the peak voltage across the conductor. Fa, it depends on all the three parameters that enter in (15.3). It was revealed (Kotov et al, 1974) that the highest rise rates of resistance of an exploded conductor are reached if the conductor length is close to its critical value, /cr, that provides, with other things being equal, a no-current interval of zero duration. To simplify the expressions for the characteristics under investigation, the dependence of the parameter A.cr on s and v was found for / = /cr (Fig. 15.6) and all other dependences were determined for the critical length. For example, the normalized peak voltage (overvoltage) K = VÎVQ was obtained for A.cr as a function of 8, v, energy absorbed by the conductor explosion delay time, voltage pulse duration, etc. (Fig. 15.7) (Sedoi, 1976; Kolganov et al, 1976). Analysis of these dependences allowed the conclusion that silver conductors have characteristics very similar to the characteristics of copper conductor, while aluminum conductors, for the production of the same power, demand a lower inductance of the circuit and should have larger cross sections and lengths in comparison with copper, i.e., in technological and constructive requirements they are exceeded only by copper conductors. Therefore, the latter were used in the subsequent research and development work. 20

pJJr 2

'

1

1.0 1.5 t [us]

2.0

Figure 16.5. The Gamma electron accelerator with an MPOS: a - schematic diagram of the accelerator (7 - Marx generator, 2 - diode, 3 - plasma guns); b - current and voltage waveforms for the diode not filled with plasma; c - current and voltage waveforms with the diode filled with plasma

The circuit of such a generator is shown schematically in Fig. 16.6. With the MPOS closed, a capacitor bank or a Marx generator is discharged into a line, which stores an energy L\{^J'Î2. As the current reaches I = Vo^lC/L , where L = Liine + ^MG (^line and LUG being the respective inductances of the line and MG) the energy stored in the line will be a maximum. If at this moment the current is cut off by the opening switch, a pulse will appear across the load ZioadThe Marina machine, a nanosecond high-power pulse generator, incorporated a vacuum energy storage line, an MPOS, and a load with a line segment built in between the two last components (see Fig. 16.6) (Koval'chuk and Mesyats, 1985; Mesyats et al., 1987). The Marx generator had the following parameters: voltage Vo up to 960 kV, capacitance C = 0.4-10"^ F, and inductance Lg = 0.8-10"^ H. The vacuum line was 4 m long. Its wave impedance was 60 Q and the inductance Lune, including the inductance of the bushing insulator, was 1.3-10^^ H. An inductor (closed vacuum line segment) of inductance Lioad = 0.2-10"^ H, an explosiveemission vacuum diode producing an electron beam, or an opening switch were used as a load. The opening switch contained eight plasma injectors.

PULSE GENERATORS WITH PLASMA OPENING SWITCHES

295

An investigation of the operation of the opening switch as the load of the generator showed that its resistance reached 16 Q at a rise rate of 10^ Q/s. The switch was in the open state for 10"^ s. The voltage across the switch increased within 25 ns to 2.5 MV, which was a factor of 3.4 greater than FQ. •^line? ^

II I

Cii:

Figure 16.6. Schematic diagram of a pulse generator with a vacuum line and a POS {a) and its equivalent circuit {b)

A developed version of a generator with an MPOS and an MIVL is the GIT-4 system (Koval'chuk and Mesyats, 1990). It comprises four multimodule Marx generators with vacuum bushing insulators through which the generators are connected to a common MIVL (Fig. 16.7, a). The plasma opening switch and the load are mounted at the far end of the vacuum energy store relative to the generator. Used as plasma sources are coaxial plasma guns or surface plasma sources. The discharge current in the plasma sources is oscillatory or aperiodic with the rise time to a maximum equal to --1 |is and the amplitude ranging between 10 and 15 kA. The shift of the onset of current passage in the guns relative to the main current is provided by a timing circuit. The total energy storage capability of the Marx generators is 2.16 MJ, their inductance is LUG = 0.1 jxH and capacitance CMG = 4.8 |iF. The equivalent circuit of the GIT-4 generator is given in Fig. 16.7, Z>. Here, CMG and LMG are the MG capacitance with its capacitors connected in series and the MG inductance, respectively, and Ly is the inductance of the vacuum insulator and MIVL up to the opening switch; the element Z replaces the opening switch - load system. To perform a z-pinch experiment, the generator was operated with radial MPOS's (Fig. 16.8). Sixty four guns of the capillary type were mounted in the outer cylinder of an MIVL. The central conductor was shaped as a cylinder; the outer one was composed of rods of diameter 10 mm. The central conductor was shorted to the end face of the coaxial line through an indium gasket. The switched current was measured by an integrating coil placed at the end face of the system.

296

Chapter 16

ia)

(b)

Figure 16.7. Schematic diagram of the GIT-4 system {a) and its equivalent circuit {b)\ 1 Marx generators, 2 - coaxial vacuum line, 3 - connection of the unit incorporating an MPOS and a load. Each Marx generator contains 36 sections

{b)

3MA 3MV

I

I

I

I

I

I

I

I

I

I

I I

100 ns 3TW

64 plasma guns 32 plasma guns

Figure 16.8. The POS in the GIT-4 system {a) and the output parameters of GIT-4 in idle run at the end of the vacuum line load (JUG = 600 kV, h=2 MA, Pz = 3.4 TW) (h)

With the diameters of the outer and the central conductor equal to 560 and 480 mm, respectively, the current was 2.8 MA at a generator voltage of 720 kV. The switched current was 2.4 MA. The current rise rate within a period of 100 ns between zero and 2.1 MA was 2.1 10^^ A/s. As the generator voltage was increased from 480 to 720 kV, the peak current increased from 1.8 to 2.8 MA. The magnetic field intensity at the cathode at a peak current was 1.85-10^ A/m. To enhance the magnetic field at the cathode, the conductors of the opening switch were reduced in diameter. With the generator idling, the central conductor terminated in a hemisphere (the dashed line in Fig. 16.8, a). The z-pinch load was simulated by a solid metal cylinder placed at the center. The switched current was measured by a Rogowski coil and magnetic loops. In the short-circuit mode at a generator voltage of 720 kV, the maximum cutoff current was 2.6 MA and the switched current amplitude and rise rate


297

were, respectively, 2.3 MA and 2.5-10^^ A/s. As the voltage of the generator was increased from 480 to 720 kV, the current increased from 1.67 to 2.6 MA. The intensity of the magnetic field at the cathode at maximum currents was -2.6-10^ A/m. In the idling mode, the equivalent resistance of the switch-load system was about 1 Q. At a generator voltage of 480 kV, the cutoff current was 1.74 MA, the voltage across the opening switch was 1.4 MV, and the power was 2 TW. At a generator voltage of 600 kV, the cutoff current was 2 MA, the voltage across the opening switch was 1.7 MV, and the output power was 3.4 TW (Fig. 16.8, b). On the GIT-4 system, the operation of a two-stage circuit, i.e., a circuit with two POS's was tested. The geometry of the vacuum part of the experimental arrangement is presented in Fig. 16.9. The cathode of the first stage, POSl, was 280 mm in diameter. The anode was made as a squirrel cage of diameter 350 mm. Sixty four guns were arranged in a circle of diameter 480 mm. The second stage, P0S2, was a coaxial line segment with a diameter ratio of 210/40 (mm). Thirty two plasma guns were located on the anode. 1+r

32 plasma guns •

# / 3

TST

P0S2

i lET

64 plasma guns -

/

\

P h POSl

ja

Figure 16,9. Schematic diagram of the GIT-4 generator with two plasma opening switches

With the voltage of the Marx generator equal to 480 kV the current in POSl reached 1.7 MA within 1.2 |is. As P0S2 opened, a voltage pulse of amplitude 1 MV was generated. This made it possible to obtain a 0.6-MA current in P0S2 within 100 ns. To measure the voltage generated on operation of P0S2, a short-circuited coaxial vacuum line segment of length 3 m was used, and the current was measured by integrating Rogowski coils. The voltage increased thirteen times compared to that produced by the Marx generator. Downstream of P0S2, the pulse FWHM was 20 ns. Thus, microsecond plasma opening switches have made it possible to considerably simplify and reduce the price of the pulse generators operating

298

Chapter 16

in the megajoule, megaampere, and megavolt ranges. Experimental studies of generators with MPOS's were also performed by Commisso et al (1992), Goodrich and Hinshelwood (1993), Sincemy et al (1995), and Weber et al (1992). We shall speak of some of them below, when discussing megajoule systems with MPOS's. Here, we consider one more research system, the HAWK machine (Commisso et al, 1992). It included an oil-insulated Marx generator (1 |LIF, 640 kV, 225 kJ) terminated in an MIVL. The current amplitude and rise time were, respectively, 720 kA and 1.2 îs. The anode of the MPOS consisted of twelve rods located on the surface of a cylinder of radius 7.5 cm. A variety of configurations of the inner electrode (cathode) could be used. In the majority of experiments, plasma sources with a dielectric surface breakdown were employed. Besides, the system contained twelve coaxial guns (Commisso et al, 1992) each made as a cut of a coaxial cable. In some experiments, four gas valves were used that operated 400-500 |Lis before the start of the system. The gas discharge was initiated by discharging a capacitor. The working gases were H2, Ar, and He. The results obtained were similar to those obtained with conventional plasma sources. The plasma density in the POS was -10^^ cm"^. Experimental studies of the operation of POS's and MIVL's in the conduction and current cutoff phases are described by Ottinger et al (1984), Mosher et al (1987), Golovanov et al (1988), Weber et al (1990), and Bystritskii e/a/. (1992).

3.

NANOSECOND MEGAJOULE PULSE GENERATORS WITH MPOS'S

In Section 2 of Chapter 16 we already spoke of some pulse generators with MPOS's that were used basically for studying the physical processes occurring in plasma opening switches. In this section, we consider nanosecond pulse generators with MPOS's that serve to meet special goals such as to study the properties of z-pinches, to produce high-power x-ray pulses, to irradiate materials in various technological processes, etc. The GIT series of generators has been developed at IHCE. We spoke of one of them, the GIT-4 machine (see Section 2 of Chapter 16) (Koval'chuk and Mesyats, 1990). Now we consider the GIT-16 machine (Bugaev et al, 1997). This electrophysics system is a current pulse generator with an intermediate inductive energy store and an MPOS-based opening switch. The system is intended for experimentation with high-temperature plasmas generated by gas puff and wire array implosions. It has a modular configuration. The modules are arranged in a circle of diameter 22 m (Fig. 16.10).


299

Figure 16.10. General view of the GIT-12 facility

The use of a system composed of eight modules (GIT-8, 50% of the energy storage capability) in experiments with a POS and a z-pinch load since 1992 showed that damping resistors must be connected in the circuit of each module to protect the energy storage capacitors against the backward voltage wave. As this was done, experiments could be performed with currents of -4 MA (70 kV charge voltage of MG) at an acceptable level of failures of the capacitors in the course of operation. In 1996, four modules were added (GIT-12), and now the system is capable of storing 5 MJ of energy with the current in the circuit increasing to --6 MA within -1.7 |is. The main parameters of intermediate versions of the system are given in Table 16.1. Table 16.1. Parameters of GIT-12 depending on the number of modules Configuration Parameters With no damping resistor With damping resistors GIT-12 GIT-8 GIT-8 1.74 1.69 1.67 Current rise time ^max* M-s Charge voltage, kV Stored energy, MJ POS current at / = /max* MA POS current at t = O.S^niax, MA

50.0 1.73 4.43 4.20

50 1.73 3.04 2.93

70 3.38 4,26 4.10

50 2.59 4.4 4.2^

70 5 6.2 5.94

Each module (Fig. 16.11) consists of a primary energy store (set of Marx generators), a vacuum bushing insulator (5, and a vacuum transmission line 7.

Chapter 16

300

The primary energy store is an assembly of nine parallel sections 2 connected as a 12-stage Marx generator and placed in a metal tank L The damping resistor 5 is made of stainless steel foil that forms a bifilar winding insulated with electrotechnical cardboard and transformer oil. The capacitance of the primary energy store of each module is 1.2 |LIF and its inductance is --440 nH. The inductance of the bushing insulator, damping resistor, and 4-m transmission line is, respectively, -200, 250, and 179 nH. The active resistance of the damping resistor is 0.42 Q. 2

3

Oi-

âHeRHHHHF^ ^

^ _ l J i J _ b a Ulzd l = g l=LJ L±=j bd=J L^LJ I —JQ—

Figure 16.11. Schematic diagram of the GIT module: 1 - tank with transformer oil; 2 - Marx generators; i , 4 - systems for starting and timing of the Marx generators; 5 - resistor; 6 bushing insulator; 7 - vacuum line

The transmission lines 1 converge from the twelve modules to the central unit (Fig. 16.12) that is a vacuum coaxial line segment of length 0.6 m with the shell diameter equal to 1.6 m. The main collector 2 is 1.5 m in diameter. It leans on the short-circuited vacuum line 3 whose wave impedance is 60 Q and electric length 6.7 ns. On the top flange of the shell, which is 30 mm apart from the inner high-voltage electrode, the POS unit is located. The POS's subject to investigation were axially symmetric systems with the anode-to-cathode diameter ratio Did = 380/320 (mm). The anode was solid or transparent as a squirrel cage, made of thirty two rods of diameter 10 mm. The cathode was solid, with a spherical adapter to a short-circuited load with Did = 70/40 {mm). To create an initial conducting medium, plasma was injected in the POS region within a time t^ =(2-10) |is prior to the operation of the Marx generators. Used as plasma injectors were highly reliable, long-lifetime guns. The discharge current in each gun was oscillatory (with a period of 4.8 |Lis and a damping decrement of 1.6); the amplitude of the first current maximum was -9 kA.


301

The GIT-12 megajoule system is one of the world's largest pulse generators in which the idea of direct pumping of an inductive energy store from Marx generators and energy delivery to a load with the help of a microsecond POS is realized. In the course of z-pinch experiments, the basic mechanisms of the operation of microsecond POS's with currents on the level of several megaamperes have been revealed and the factors interfering the improvement of switching characteristics have been determined. It has been shown that during the conduction stage the current channel propagates in the MPOS zone in the direction from the generator to the load. In this case, if the plasma density in the switch zone is too large, some part of this plasma is drawn into the load region, breaking the match of the generator to the load and can promote the occurrence of backward breakdown of the MPOS. Optimization of the MPOS-load adapter has made it possible to increase the z-pinch current and the x-radiation power not increasing the plasma density and current in the MPOS. Experiments with a combined MPOS have shown the possibility of going to larger currents, with the total amount of the injected plasma preserved, due to a proper distribution of the plasma density over the MPOS region.

Figure 16.12. Central unit of the GIT-12: 1 - coaxial vacuum transmission line, 2 - main collector, i - base vacuum line

One more electrophysics system with an MPOS is the DECADE machine (Sincemy et al^ 1995). This is a multimodule system operating into x-ray explosive-emission diodes. It produces 20 krad of x radiation in a pulse at a distance of 13 cm from the diodes over an area of 1 m^ at a pulse duration of 40 ns and a voltage of 1.8 MV. Within the framework of this program, the DRMl and then DM1 and DM2 modules have been built. The DM2 system operates with a magnetically triggered plasma opening switch.

302

Chapter 16

The DM1 module consists of an oil Marx generator capable of storing 570 kJ of energy, an intermediate energy storage capacitor, a water line, a vacuum line with an MPOS, and a diode. As the MPOS is short-circuited, the current increases to 1.8 MA within 300 ns. The Marx generator consists of six modules, each containing twelve stages (85 kV per stage). The output voltage of the Marx generator is 1 MV at a capacitance of 1.1 |iF. The intermediate energy storage capacitor has a capacitance of 400 nF. It is discharged through six parallel triggered gas (SF6) gaps that operate with a jitter < 5 ns. The plasma sources are coaxial cable guns that produce a plasma density of-10^^ cm"^. The radius of the inner electrode (cathode) is 4.4 cm. The anode consists of two parts closed through the plasma. The anode on the generator side ("upstream anode") is a cylinder of radius 9 cm. The anode on the side load ("downstream anode") is made as a ring with an internal diameter of 16.5 cm. For the MPOS of standard configuration, the maximum voltage is 1.2 MV at a conduction time of --300 ns. For the "plasma anode", a maximum voltage 2.3 MV has been achieved for the longest investigated conduction time equal to 550 ns. The ACE-4 megajoule system, developed by the Maxwell company, contains a Marx generator, an oil line, a vacuum line, a coaxial or radial (disk) MPOS, and an electron diode (Thompson et al., 1994). The opening switch is subdivided into two identical POS's with their cathodes facing each other. Experiments have shown that the opening times of the top and the bottom POS differ insignificantly. The principal parameters of some operation modes of the ACE-4 system are given in Table 16.2. Table 16.2. ô,kV POS type 4 MA ^, l^s Fpos, MV Radial 8 1.3 0.3 3.7 0.87 Coaxial, i?c "= 9 cm 520 1.0 2.1 1.05 Coaxial, Rc = 6 cm 360 1.2 Here, to is the time to the current cutoff in the MPOS, RQ is the radius of the MIVL cathode, VQ is the output voltage of the Marx generator, and Is is the MPOS current.

The ACE-4 system is capable of storing 4 MJ of energy (Thompson et al, 1994). The Marx generator consists of twenty four generators placed in four oil tanks. In the case of a radial MPOS, the plasma sources were placed on two disks of internal and external radii 40 and 60 cm, respectively, located outside the MPOS. Plasma entered the MPOS region through a transparent anode. The data given in Table 16.3 refer to the case where the load was an electron diode with an impedance of 0.25 Q. The inner electrode of the coaxial MPOS has a negative polarity. The anode consists of sixteen longitudinal rods. Around of the anode, fifteen plasma sources are located. The load was an inductor of inductance 200 nH.


303

According to interference measurements, the electron density in the MPOS was 10^^ cm"-^. Along with the conventional MPOS's considered above, there exist magnetically triggered POS's that can operate both on the nanosecond and the microsecond scale. In conventional plasma opening switches, the triggering delay time can be varied by selecting the operation mode of the plasma sources, by varying the delay between the injection of plasma and the onset of current passage through the POS, etc. The technology of magnetic POS's, according to the intention of their developers (SNL), should simplify the control of the opening time due to the application of external magnetic fields (Mendel etal, 1992; Savage etal, 1992, 1994, 1997). The elements of a POS of this type operate in the following sequence: 1. An external magnetic field is created in the POS by a "slow" coil. 2. The plasma source fills the anode-cathode gap with plasma. 3. An additional plasma source creates plasma in the trigger POS. 4. The current of the generator flows successively through the trigger POS, cathode, and main POS. 5. As the trigger POS opens, the current is switched into a coil producing a fast magnetic field, which is directed opposite to the external magnetic field. 6. The change in magnetic field configuration initiates the opening process in the main POS. Thus, at the first stage, the problem becomes simpler: the opening process is realized not in the main POS, but in the trigger one, at a substantially lower voltage. However, first, it is necessary to choose initial conditions for the trigger MPOS. Second, for the operation of the magnetic POS to be efficient, it is required that the trigger switch in the POS remained open until all processes in the main POS are complete.

4.

OTHER TYPES OF GENERATOR WITH MPOS'S

A nvmiber of systems with MPOS's operating in the pulse repetition mode were developed at I. V. Kurchatov Institute of Atomic Energy (Barinov et al, 1997). They were used in electron accelerators and x-ray pulse generators and had the following: voltage up to 1 MV, current up to 100 kA, average power up to 20 kW, pulse repetition rate 1-4 Hz, pulse duration --lO"^ s, and efficiency 20-30%. The MPOS technology was combined with the operation of a line transformer (Bastrikov et al, 1999). The major factor that limits the efficiency of the current switching fi-om inductive energy stores with the help of microsecond POS's is their rather low resistance in the open state. It

304

Chapter 16

reaches, as a rule, ~2 Q at a current of ~1 MA. The low resistance limits the rate of energy extraction from the energy store and increases the time of current switching into the load. The use of a line transformer as a generator in a circuit with seriesconnected opening switches makes it possible to solve the problem of increasing the current rise rate in an inductive load. In this circuit, in several stages of the transformer a plasma opening switch is connected in the primary circuit. As the POS operates, a voltage pulse appears at the output of the primary circuit. The amplitude of this pulse is determined by the POS resistance and by the current in the primary circuit at the instant the POS operates. Summation of the voltages of several circuits makes it possible to increase the output voltage of the generator. To realize the scheme proposed, it is necessary that at the stage of charging the load be isolated from the generator circuit with the help of a spark gap. The feasibility of the circuit with a nontriggered spark gap operated due to a surface discharge over a dielectric, which was connected upstream of the load was checked in experiments on the GIT-4 machine (Koval'chuk and Mesyats, 1990). As a result, a spark gap with the required switching characteristic has been developed. The GIT-4 consists of three sections, each containing five steps of a line transformer. Between the sections, opening switches with sixteen plasma gun injectors are connected. The vacuum part of the primary circuit of each section is formed by coaxial conductors with a diameter ratio of 200/160 (mm). The distance between the end of one and the beginning of the other electrode of the vacuum coaxial line of the transformer primary circuit is 40 mm. The electrodes of a vacuum coaxial line with a diameter ratio of 155/130 (mm) form an additional inductor of the lead to the load. Originally, the primary circuits of the transformer sections are short-circuited by the plasma opening switches connected in a break of the outer electrode of the transformer vacuum coaxial line. The cathodes of the opening switches are fixed on the electrodes. To prevent the current passage in the load before the operation of the opening switches, a nontriggered spark gap with a surface discharge over a dielectric is used. The spark gap is connected in a break of the central electrode of the load. It should be broken down upon operation of the opening switches. The charge voltage was 90 kV. The opening switches and the switching spark gap operated with a delay of 0.8 |is. The generator current at this moment was ---760 kA. The residual current in the opening switches was -100 kA and the load current was -400 kA. The peak voltage maximum the MPOS was -1.4 MV, the voltage across the load reached 2.6 MV, and the peak power delivered to the load was 430 GW. The corresponding values for the transformer consisting of fifteen steps with one opening switch at the

PULSE GENERA TORS WITH PLASMA OPENING SWITCHES

305

output were 1.5 MV and 160 GW. Thus, the circuit proposed allows one to increase the output voltage by a factor of 1.7 and the power by a factor of 2.7. An even greater gain in voltage can be obtained by decreasing the inductance L^ between the central conductor of the transformer and the plasma opening switch. If Ls is reduced to 50 or 30 nH, the voltage across the load will increase to 3 or 3.5 MV, respectively.

REFERENCES Abdullin, E. N., Bazhenov, G. P., Kim, A. A., KovaFchuk, B. M., and Kokshenev, V. A., 1986, A POS with Microsecond Times of Energy Delivery to an Inductive Energy Store, Fiz.Plazmy. 12:1260-1264. Barinov, N. U., Belenky, G. S., Dolgachev, G. I., Zakatov, L. P., Nitishinsky, G. I., and Ushakov, A. G., 1997, Repetitive Plasma Opening Switches and Their Use in the Technology of High-Power Accelerators,/zv. Vyssh. Uchebn. Zaved,Fiz. 12:47-55. Bastrikov, A. N., Zherlitsyn, A. A., Kim, A. A., Koval'chuk, B. M., Loginov, S. V., and Yakovlev, V. P., 1999, Increasing the Power of a Line Transformer with a SeriesConnected POS, Ibid 9-14. Bugaev, S. P., Volkov, A. M., Kim, A. A., Kiselev, V. N., Koval'chuk, B. M., Kovsharov, N. F., Kokshenev, V. A., Kurmaev, N. E., Loginov, S. V., Mesyats, G. A., Fursov, F. I., Khuzeev, A. P., 1997, GIT-16, a Megajoule Pulse Generator with a Plasma Switch for Z-Pinch Loads, Ibid. 38-46. Bystritskii, V. M., Mesyats, G. A., Kim, A. A., Koval'chuk, B. M., Krasik, Ya. E., 1992, Microsecond Plasma Opening Switches, Fiz. Elem. Chastits At. Yadra. 23:20-57. Commisso, R. J., Goodrich, P. J., Grossman, J. M., Hinshelwood, D. D., Ottinger, P. F., and Weber, B. V., 1992, Characterization of a Microsecond-Conductive-Time Plasma Opening Switch, Phys. Fluids. B4 (Pt 2):2368-2376. Golovanov, Yu. P., Dolgachev, G. I., Zakatov, L. P., and Skoryupin, V. A., 1988, Use of Plasma Opening Switches in Inductive Energy Stores for the Creation of Terawatt Generators with High Energy Capabilities, Fiz. Plazmy. 14:880-885. Goodrich, P. J. and Hinshelwood, D. D., 1993, High Power Opening Switch Operation on "HAWK". InProc. IXIEEE Intern. Pulsed Power Conf, Albuquerque, TX, pp. 511-515. Guenther, A., Kristiansen, M., and Martin, T., eds., 1987, Opening Switches. Plenum Press, New York. Koval'chuk, B. M. and Mesyats, G. A., 1985, Nanosecond Pulse Generator with a Vacuum Line and a Plasma Opening Switch, Dokl. ANSSSR. 284:857-859. Koval'chuk, B. M. and Mesyats, G. A., 1990, Superpower Pulsed Systems with Plasma Opening Switches. In Proc. VIII Intern. Conf. on High-Power Particle Beam Research and Technology, Novosibirsk, USSR. Vol. 1, pp. 92-103. Meger, R. A., Commisso, R. J., Cooperstein, G., and Goldstein, S. A., 1983, Vacuum Inductive Store / Pulse Compression Experiments on a High Power Accelerator using Plasma Opening Switches, Appl. Phys. Lett. 42:943-945. Mendel, C. W., Goldstein, S. A., and Miller, P. A., 1976, The Plasma Erosion Switch. In Proc. I IEEE Pulsed Power Conf, Lubbock, TX, pp. (1C2) 1-6. Mendel, C. W., Goldstein, S. A., and Miller, P. A., 1977, A Fast Opening Switch for Use in REB Diode Experiments, J. Appl. Phys. 48:1004-1006.

306

Chapter 16

Mendel, C. W., Jr., Savage, M. E., Zagar, D. M., Simpson, W. W., Crasser, T. W., and Quintenz, J. P., 1992, Experiments on a Current-Toggled Plasma-Opening Switch, Ihid. 71:3731-3746. Mesyats, G. A., Bugaev, S. P., Kim, A. A., Kovarchuk, B. M., and Kokshenev, V. A., 1987, Microsecond Plasma Opening Switches, IEEE Trans. Plasma Sci. 15:649-653. Mkheidze, G. P., Plyutto, A. A., and Korop, E. D., 1971, Acceleration of Ions during the Passage of a Current through Plasma, Zh Tekh. Fiz. 41:952-963. Mosher, D., Grossmann, J. M., Ottinger, P. F., and Colombant, D. G., 1987, A Self-Similar Model for Conduction in the Plasma Erosion Opening Switch, IEEE Trans. Plasma Sci. 15:695-703. Ottinger, P. F., Goldstein, S. A., and Meger, R. A., 1984, Theoretical Modeling of the Plasma Erosion Opening Switch for Inductive Storage Applications, J. Appl. Phys. 56:774-784. Savage, M. E., Hong, E. R., Simpson, W. W., and Usher, M. A., 1994, Plasma Opening Switch Experiments at Sandia National Laboratories. In Proc. X Intern. Conf. on HighPower Particle Beams, San Diego, CA, pp. 41-44. Savage, M. E., Simpson, W. W., Cooper, G. W., and Usher, M. A., 1992, Long Conduction Time Plasma Opening Switch Experiments at Sandia National Laboratories. In Proc. IX Intern. Conf. on High-Power Particle Beams, Washington, DC, pp. 621-626. Savage, M. E., Simpson, W. W., Mendel, C. W., et a/., 1997. In Proc. Intern. POS Workshop, (April 1997), Gramat, France. Sincemy, P., Ashby, S., Childers, K., Goyer, J., Kortbawi, D., Roth, I., Stallings, C , Denpsey, J., 1995, Performance of Decade Module No 1 (DM1) and the Status of the Decade Machine. In Proc. X IEEE Intern. Pulsed Power Conference, Albuquerque, TX, pp. 405-416. Stringfield, R., Schneider, R., Genuario, R. D., Roth, I., Childers, K., Stallings, C , and Dakin, D., 1981, Plasma Erosion Switches with Imploding Plasma Loads on a Multiterawatt Pulsed Power Generator, J. Appl. Phys. 52:1278-1284. Suladze, K. V., Tskhadaya, B. A., and Plyutto, A. A., 1969, Features of the Formation of Intense Electron Beams in Confined Plasmas, Pis'ma Zh. Eksp. Teor. Fiz. 10:282-285. Thompson, J., Coleman, P., Gilbert, C , Husovsky, D., Miller, A. R., Rauch, J., Rix, W., Robertson, K., and Waisman, E., 1994, ACE 4 Inductive Energy Storage Power Conditioning Performance. In Proc. X Intern. Conf on High-Power Particle Beams, San Diego, CA, pp. 12-16. Weber, B. V., Boiler, J. R., Commisso, R. J., Goodrich, P. J., Grossman, J. M., Hinshelwood, D. D., Kellogg, J. C , Ottinger, P. F., and Cooperstein, G., 1992, Microsecond-ConductionTime POS Experiments. In Proc. IX Intern. Conf. on High-Power Particle Beams, Washington, DC, pp. 375-384. Weber, B. V., Commisso, R. J., Cooperstein, G., Goodrich, P. J., Grossman, J. M., Hinshelwood, D. D., Kellog, J. C , Mosher, D., Neri, J. M., and Ottinger, P. F., 1990, Plasma Erosion Opening Switch Operation in the 50 ns - 1 \is Conduction Time Range. In Proc. VIII Intern. Conf on High-Power Particle Beam Research and Technology, Novosibirsk, USSR, pp. 406-413. Weber, B. V., Commisso, R. J., Cooperstein, G., Grossman, J. M., Hinshelwood, D. D., Mosher, D., Neri, J. M., Ottinger, P. F., and Stephanakis, S. J., 1987, Plasma Erosion Opening Switch Research at NRL. In IEEE Trans. Plasma Sci. 15:635-648.

Chapter 17 ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

1.

INTRODUCTION

In this chapter, we consider high-pressure discharge devices (the right branch of Paschen's curve) with full triggering. This implies that these devices are able not only to pass a current due to the application of a trigger pulse, as spark gaps or thyratrons, but also to stop passing the current when the trigger pulse is complete or an additional blocking pulse is applied. In this respect, they have properties similar to those of electron tubes or triggered semiconductor devices. A feature of the switches to be considered here is that the physical processes occurring in them have been rather well investigated in the physics of gas discharges (see Section 5 of Chapter 4). In this respect, they have an advantage over EEC switches and POS's. However, these devices are not capable to switch powers of 10^^ W and greater as the mentioned switches do. At the best, the pulse power is 10^^ W. However, an important advantage of these devices is that they can operate in the repetitive pulse mode, and in a burst mode the pulse repetition rate can reach 10^ Hz. The central place in this chapter is occupied by injection thyratrons (IT's). Their operation is quite understandable. Imagine a conventional thyratron that, as the heat circuit of the cathode is rapidly broken, will cease to pass a current. However, this process will be long because the cathode cooling is a sluggish process. In IT's, instead of the electron emission from a hot cathode, direct injection of electrons into gas is used. For the first time, this type of discharge was realized by the team of Mesyats at IHCE (Koval'chuk et al, 1971a, 1976; Mesyats et al, 1972). However, originally

308

Chapter 17

the effect of injection of electrons into high-pressure (> 1 atm) gas in the presence of an electric field was utilized in high-power gas lasers. A fundamental property of IT's (Koval'chuk et al., 1976) is rapidly rising plasma resistance in the gas discharge colunrn as a result of recombination of charge carriers and attachment of electrons to gas molecules. This occurs when the injection of an electron beam into the gas is rapidly terminated. This effect can be harnessed for current interruption in generators with inductive energy storage. Besides, an IT can serve merely as a switch to interrupt kiloampere currents. An IT can also be operated in the closing mode, as a conventional thyratron. In the closing and opening mode, an IT can serve as a repetitively pulsed device. A serious disadvantage of IT's is the radiation background that is created by an electron beam with an electrons energy > 100 keV (electrons with lower energies cannot be injected into the gas volume of an IT because of the presence of the metal foil separating the vacuum and gas chambers). Another disadvantage is that these devices are bulky because of the presence of the electron accelerator. The third one is the short lifetime of IT's resulting from the fact that the foil is broken after a certain number of pulses. We do not consider the triggered devices that operate in modes corresponding to the distant left branch of the Paschen curve, such as tacitrons and crossatrons. They are seldom used in the technology of highpower nanosecond pulses as basic devices but can play an auxiliary role in the first stages of compression of high-power pulses.

2.

TRIGGERING OF AN INJECTION THYRATRON

The problem of full triggering can be solved by using a non-selfsustained discharge and injecting pre-accelerated electrons into the gas-filled gap. The device called an injection thyratron consists of two chambers (Fig. 17.1): gas chamber 1-2 and vacuum chamber 2-3, separated by a thin metal foil 2. Cathode 3 emits electrons, which are accelerated and then pass through foil 2 into the gas chamber. The accelerated electrons ionize the gas, and, if voltage is applied to the gas gap, a current will flow in the circuit. Under certain conditions, it is possible to interrupt this current by terminating the injection of electrons (Koval'chuk et al, 1971a). Thus, we have a fully triggered device. The effect of full triggering by the discharge current was demonstrated in early injection electronics experiments (Koval'chuk e/(^/., 1971b; Mesyats e/a/., 1972).

ELECTRON-TRIGGERED GAS-DISCHARGE SWITCHES

309

R

t

t

t

Figure 17.1. Sketch of an injection thyratron and its connection circuit (Ca - storage capacitance of the accelerator; C,R- capacitance and resistance of the pulse generator)

To analyze the operation of an IT, we transform the system of equations (4.29H4.36) to obtain ^ = V|/-P«2-TiiV^,, at j = enve,

(17.1) (17.2)

where rie is the electron density in the gas, m"^; N is the electronegative gas molecule density, m"^; r| is the probability of attachment of one electron to an electronegative gas molecule in 1 s; p is the recombination coefficient, m^/s; \|/ is the number of electrons generated by the beam electrons in 1 m^ in 1 s; Ve is the drift velocity of electrons, m/s; e is the electron charge, C, and j is the electron current density, A/m^. Let us consider a mode with V «: V^c (F being the voltage across the gap and Fdc the dc breakdown voltage). This allows us to neglect the term describing impact ionization in equation (17.1). Hereinafter, we assume that the voltage across the gas gap varies in time. To simplify the analysis, we put y = const, p = const, and r| = const. For the closing mode, the exact solution of (17.1), in view of the above assumptions, has the form |vj7 y p = 0.2Q

20 ^

20 t [ns]

10

10 0 -10 -20

I

1

100

i\

1

200\

300

1

400

t [nsf^^

Figure 18.9. Current waveforms recorded in switching with a high-resistance load (^load = 21 Q) {a) and in the short-circuit mode (b). L - laser light pulse waveform

338

Chapter 18

REFERENCES Andreev, D. V., Dumanevich, A. N., and Evseev, Yu. A., 1983, Preobrazovatel'naya Tekh. 9:5. Belov, A. F., Voronkov, V. B., Grekhov, I. V., et a/., 1970, Ihid, 5:15. Brylevsky, V. I., Grekhov, I. V., Kardo-Sysoev, A. F., and Chashnikov, I. G., 1982b, A HighPower, High-Voltage Fast Switch, Prib. Tekh. Eksp. 3:96-98. Brylevsky, V. L, Kardo-Sysoev, A. F., Levinshtein, M. E., and Chashnikov, I. G., 1982a, Mechanism of the Localization of Current in Turning on Submicrosecond Modular Thyristors, Pis 'ma Zh, Tekh. Fiz. 8:1288-1292. Driscoll, J. C, 1976, High Current, Fast Turn-on Pulse Generation Using Thyristors. In Energy Storage^ Compression, and Switching: Proc 1st Intern. Conference on Energy Storage, Compression and Switching {Nov. 5-7,1974) (W. H. Bostick, ed.). Plenum Press, New York-London, pp. 433-440. Grekhov, I. V. Levinshtein, M. E., and Sergeev, V. G., 1970, Investigateon of the Extension of the On State along Sip-n-p-n Structure, Fiz. Tekh. Poluprovodn. 4:2149-2156. Grekhov, I. V., 1987, Pulsed Power Switching by Semiconductor Devices. In Physics and Technology of Pulsed Power Systems (in Russian, E. P. Velikhov, ed.), Energoatomizdat, Moscow, pp. 237-253. Page, D. J., 1976, Some Advances in High Power, High dildt. Semiconductor Switches. In Energy Storage, Compression, and Switching: Proc. 1st Intern. Conference on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W. H. Bostick, ed.). Plenum Press, New York-London, pp. 415-421. Pittman, P. F. and Page, D. J., 1976, Solid State High Power Pulse Switching. In Proc. I IEEE Intern. Pulsed Power Conf, Lubbock, TX, pp. (IA3)1-12. Voile, V. M., Voronkov, V. B., Grekhov, I. V., Levinshtein, M. E., Sergeev, V. G., and Chashnikov, I. G., 1981, A Nanosecond High-Power Thyristor Switch Triggered by a Light Pulse, Zh. Tekh Fiz. 51:373-379. Zucker, O. S. F., Long, J. R., Smith, V. L., Page, D. J., and Hower, P. L., 1976a, Experimental Demonstration of High-Power Fast-Rise-Time Switching in Silicon Junction Semiconductors, ^jC|p/. Phys. Lett. 29:261-263. Zucker, O. S., Long, J. R., Smith, V. L., Page, D. J., Roberts, J. S., 1976b, Nanosecond Switching of High Power Laser Activated Silicon Switches. In Energy Storage, Compression, and Switching: Proc. of the 1st Intern. Conference on Energy Storage, Compression and Switching (Nov. 5-7, 1974) (W. H. Bostick, ed.). Plenum Press, New York-London, pp. 538-552.

Chapter 19 SEMICONDUCTOR OPENING SWITCHES

1.


There are two principal approaches used in the production of nanosecond high-power pulses that differ from one another by the method of energy storage. The first method is based on the accumulation of the energy of an electric field in fast capacitive stores, such as low-inductance capacitors and pulse-forming lines, followed by energy delivery to a load through switching devices - nanosecond high-current closing switches. By the second method, energy is accumulated in the magnetic field of an inductive current-carrying circuit and delivered to a load with the help of opening switches. The latter method holds promise for pulsed power technology since the energy density stored in inductive stores is about two orders of magnitude greater than that stored in capacitive ones. On the other hand, fast interruption of high pulsed currents is a much more technically complicated problem than the problem of closing. This problem is most critical in the production of nanosecond high-power pulses where the switch must hold off megavolt voltages and be capable of interrupting currents of tens or even hundreds of kiloamperes within a few or tens of nanoseconds. These requirements are satisfied by three main types of nanosecond opening switch: plasma opening switches with nanosecond and microsecond triggering, opening switches based on electrically exploded wires, and injection thyratrons. However, these switches either are essentially incapable of operating repetitively (exploded wires) or have low pulse repetition rates and limited lifetimes because of electrode erosion (see Chapters 16 through 18). The creation of essentially new pulsed power systems that would be technologically applicable calls for new principles of switching. In this

340

Chapter 19

respect, the schemes with inductive energy stores and solid-state semiconductor opening switches hold the greatest promise for pulsed power devices with high specific characteristics and long lifetimes. The main problem is to develop repetitive high-power solid-state opening switches which could interrupt kiloampere currents within nanosecond times and hold off voltages of the order of 10^ V. The well-known principles of nanosecond current interruption in solids are based either on injection of charge carriers into the base of a p^-n-ri^ structure followed by extraction of the built-up charge by the reverse current (Tuchkevich and Grekhov, 1988) or on electron-beam initiation of high conduction in the inherent semiconductor (Schoenbach et al, 1989) with the ionization source quickly turned off The obvious engineering difficulties involved in the second method that are associated with the need of using charged particle accelerators to control the operation of the opening switch, along with the low parameters of switched currents (hundreds of amperes) and hold-off voltages (a few kilovolts), make this method impracticable in pulsed power technology. The method of injection of charge carriers was proposed to cut off the reverse current in semiconductor diodes in the 1950s when much work was done on the creation of fast pulsed diodes. Diodes with the effect of abrupt current cutoff were named charge storage diodes (CSD's) (Eremin et al, 1966). A CSD depends for its operation on the built-in braking electric field that exists in the base of a diffuse diode due to the donor concentration gradient. At the stage of charge buildup by the forward current, the built-in electric field directed from the n base into the p region hinders the propagation of the injected holes into the base bulk and holds the charge near the p-n junction. Owing to this, during the passage of the reverse current, almost the whole of the accumulated charge has time to go away from the diode base at the stage of high reverse conduction. The small charge remaining in the base by the moment a space charge has formed at the p-n jimction has the result that the reverse current is cut off within 10"^-10"^^ s. The operation of a diode in the charge storage mode is possible only at a low level of injection of charge carriers and a high level of doping of the base with a donor impurity. When going to a high-current mode of operation (high and superhigh level of injection) or reducing the level of doping of the n base with the aim to increase the reverse voltage of the diode, the built-in electric field disappears and current cutoff fails to occur. In view of this, the operating currents and reverse voltages characteristic of CSD's with a builtin field lie in the ranges 10-100 mA and 10-50 V, respectively. Grekhov et al (1983) proposed and realized a high-current operation mode for a p'^-n-n'^ structure with a cutoff current density of up to 200 A/cm^, a current cutoff time of about 2 ns, and an operating voltage of

SEMICONDUCTOR OPENING SWITCHES

341

1 kV. These diodes received the name fast-recovery drift diodes (FRDD's). The principle of operation of an FRDD is as follows: Owing to the short duration of the forward current pulse (hundreds of nanoseconds), a thin layer of injected plasma is formed in the base near the p-n junction in which most of the accumulated charge is localized. During the passage of the reverse trigger current, the plasma layer near the p-n junction resolves and, simultaneously, holes go out fi-om the rest part of the base. The structure parameters (base length and doping level) and the triggering mode (current density and duration) must be chosen such that the drift current density reaches a maximum for a given level of doping of the base as the nonequilibrium charge carriers are completely removed fi'om the structure. If this condition is fiilfilled, the process of reverse current cutoff involves the removal of equilibrium carriers from the base with the highest possible saturation rate (-10^ cm/s). In view of this, an FRDD has a limitation on the current density that can be carried by the structure. To obtain an about 1-2-kV reverse voltage across the structure, the donor impurity concentration in the base should be not over 10^"* cm"^, which corresponds to a maximum current density of 160-200 A/cm^ in the opening phase. However, the operating current and voltage of the switch can be increased by increasing the structure area and by making a set of series-connected structures. Of fimdamental importance to the progress in nanosecond pulsed power technology has been the discovery of the so-called SOS (semiconductor opening switch) effect at lEP (Kotov et al, 1993a). It turned out that harnessing this effect makes it possible to interrupt currents of density up to 10"^ A/cm^ within nanosecond and subnanosecond times at voltages of up to 10^ V. The principle of operation of a semiconductor opening switch is as follows: The triggering circuit, whose diagram is given in Fig. 19.1, includes a semiconductor diode. Generally, such a diode is a set of series-connected p-n junctions produced by diffusion of donors and acceptors into «-type low-doped silicon (Fig. 19.2). The triggering circuit is designed so that the current passing through the diode is oscillatory in character: during the positive and the negative trigger half-wave, the diode conducts in the forward and in the reverse direction, respectively (Fig. 19.3). The mechanism of current interruption in SOS's is essentially different from that in switches with lower current densities, such as FRDD's. First, in an SOS, the low-conductivity region where a strong field is localized appears not in the diode base, as this is the case of an FRDD, but in the highly doped (with the dopant concentration of the order of 10^^ cm"^ or higher) p region where the saturation current density is several kiloamperes per square centimeter. Therefore, SOS's are essentially high-current devices.

Chapter 19

342

which operate at reverse current densities of the order of 10^-10"^ A/cm^. Second, in the phase of current decay, plasma remains in the diode in appreciable amounts; therefore, the onset of current decay has no relation to the principle of equality of the charge introduced into the structure during the positive trigger half-wave to the charge removed from the structure during the negative half-wave, which is of fundamental importance, for instance, for fast-recovery drift diodes. Detailed information on the mechanism of operation of semiconductor opening switches is given elsewhere (Bonch-Bruevich and Kalashnikov, 1977; Madelung, 1982; Darznek et al, 1996, 1997,2000; Rukin, 1999). S

$ D

•^load

Figure 19.1. Experimental arrangement: C and V - capacitance and output voltage of the primary generator; L - its circuit inductance; D - semiconductor opening switch; iîoad - load

100 200 Coordinate [jim] Figure 19.2. Schematic of doping of a semiconductor diode. Solid curve - distribution of donors; dashed curve - distribution of acceptors. The arrows at the abscissa axis points to the position of the p-n junction

SEMICONDUCTOR OPENING SWITCHES hn •k

/

343

> / ^ rNy^

I* '' /

+

u),

\

K- .

\

n '

\

f

V] i

FsD,

'

^""S

/ Wvl

'

Figure 19.3. Conventionalized oscillograms of the current flowing through the opening switch and of the voltage across the load, /so and FSD ~ current and voltage of the semiconductor diode; /p - pulse duration

The best performance of FRDD's was achieved in the experiment performed by Efanov et al (1997) where pulses of peak voltage 80 kV, current 800 A, and pulse repetition rate 1 kHz were produced with the help of series-connected FRDD's. Grekhov (1997) describes a generator with a semiconductor opening switch whose operation is based on the inverse recovery of the diode. The diode depends for its operation on the removal of the excessive plasma from the base in the phase of high reverse conductance. Based on this diode, a generator with a voltage of 30 kV, a current of 600 A, and a pulse repetition rate of 1 kHz has been developed.

2.

OPERATION OF SOS DIODES

Thus, FRDD-based pulse generators are capable of producing pulsed voltages of tens of kilovolts and currents of up to 10^ A. To produce pulses with higher parameters, SOS diodes are used. The SOS effect was discovered by Rukin and co-workers (Kotov et ai, 1993 a) in semiconductor diodes intended for rectification of alternating current at a certain combination of current density and triggering time. On the other hand, there are various classes of rectifying diodes that are different in recovery rates and in the character of voltage recovery upon diode reversal. By the reversal characteristics, diodes with conventional, "hard" recovery and modem, improved, diodes with "soft" recovery are distinguished.

344

Chapter 19

Technologically, soft and hard diodes are different in original dopant profile in the structure, m p-n junction depth Xp, in base length, and in resistivity of the original base-forming ^-silicon. Figure 19.4 presents a typical p^-p- n-n" structure of a diode. A conventional (hard) diode has a p region formed by diffijsion of aluminum for a depth Xp - 100 |im. To produce a soft diode, one of the following technological means (or their combination) is used: decreasing Xp with a simultaneous increase in the abruptness of the p-n junction by forming an epitaxial p^ region with a high gradient of acceptor concentration near the p-n junction (Duane and Ron, 1988; Potapchuk and Meshkov, 1996) and increasing the base length and conductivity of the original silicon (Assalit et al, 1979; Chu et al, 1980). The above means have the result that as the current reverses its direction, on the one hand, the p-n junction very quickly becomesfi-eeof excessive plasma and, on the other hand, the plasma remaining in the diode in large amounts makes the decay of the reverse current longer, thus providing soft recovery of voltage. 1020 I

[__^

1

tv '\ '

3

10" I

10'5IL 1014 1 1

\

P

P

\

/

"^

\

10'3| x:p= 80-120

1

n

Xp2--160-200

[|im] •

Figure 19.4. The typical p^-p -n-n"" structure of a rectifier diode: 1 - epitaxy (soft diode); 2 - conventional diffusion (hard diode); 3 - deep diffusion (superhard SOS diode)

To investigate the effect of the structure parameters on the process of current interruption in the SOS effect mode, experimental opening switches were developed that differed fi-om one another by the original resistance of the silicon, base length, structure area, and p-n junction depth. Each of the opening switches contained twenty series-connected diodes tightened with dielectric dowels. Each diode was a copper cooler on which four seriesconnected structures were soldered. An increase in hardness of an opening switch was achieved when the p-n junction depthXp was increasedfi-om100 to 200 |Lim. The dependence


345

of the overvoltage across an opening switch in idle run on Xp was investigated by Darznek et al (1999). For Xp over 160 |im, the overvoltage factor reached six. According to the existing classification, these diodes can be referred to as diodes with "superhard" recovery. Figure 19.4 shows the structure of a SOS diode in comparison with the structures of soft and hard diodes. An SOS diode, due to a small base length, is capable of passing, at the stage of triggering, and then interrupting high currents (as Xp was increased, the thickness of the silicon plate remained unchanged and equal to 310-320 |am). Shorter times of current interruption provide a higher overvoltage factor with a higher efficiency of energy switching, and the design of a SOS diode, with its developed surface of the coolers, offers the possibility to increase the dissipated power. For series-connected semiconductor devices, a practically important problem is to provide a uniform voltage distribution over the structures, which is necessary for the device to operate reliably and without emergencies. For this purpose, either resistive voltage dividers are used to compensate the technological spread in structure characteristics that appears in their production or the structures are selected before assembling by their capacitance-voltage and current-voltage characteristics. A very important feature of the SOS effect is that in the phase of current interruption the voltage is in uniformly distributed in an unattended manner over a great number of series-connected structures (diodes). This makes it possible to create megavolt opening switches by connecting in series a number of diodes without use of external voltage dividers. Thus, each branch of the opening switch of the Sibir system (Kotov et al, 1995) contained 1056 seriesconnected structures (eight diodes each containing 132 structures) and operated at a voltage of up to 1.1 MV. This property of the SOS effect, along with the high density of the interrupted current, has made it possible to attain gigawatt powers in nanosecond pulses produced by semiconductor devices. Investigations of the voltage distribution over the series structures of an opening switch operating in the SOS-effect mode were performed by Ponomarev et al (2001). The test diode contained ten series-connected structures. To simulate the technological spread in parameters, the value of Xp was varied from structure to structure with a step of 2 |im in the range from 170 to 188 îm. It was found that the formation of the strong field region (SFR) in structures with smaller Xp began earlier than in those with larger Xp, The largest time difference, 2.5 ns, was observed for the structures with most different Xp (170 and 188 |im) (Fig. 19.5). For the same structures, the difference in w, and, hence, in structure voltage, was a maximum. The mechanism of the earlier operation of the smaller-x^ structures is as follows:

346

Chapter 19

At the forward triggering stage, when there occurs charge buildup in the p region, the excessive plasma density is higher in the smaller-Xp structures the same charge is distributed over a thinner p layer. Accordingly, in the smaller-Xp structures, the recombination processes are more intense and the built-up charge, which can later be removed from the structure by the reverse current, is smaller. During the reverse triggering phase, with the same law of variation of the current density in time (series-connected structures), the smaller built-up charge in the smaller-x^ structures has the result that the saturation of the charge carrier velocities in the p region and the SFR formation come into play earlier than in the larger-jc^ structures. {a)

(b)

Figure 19,5. Time dependences of the SFR width w ( / , 2), rate of width variation v (3, 4\ difference Aw (5), and deviation 5 (6) in the phase of current interruption for structures with Xp = 170 \im. (curves 7, 3) and 188 îm (curves 2, 4)

By the onset of the SFR formation in the structure with Xp = 188 |Lim (curve 2 in Fig. 19.5) the width of the SFR in the structure with x^ = 170 \xm (curve 1 in Fig. 19.5) reached 11.5 |im. At this point in time, the voltage distribution over the structures was most nonuniform and its largest deviation 6 from the average value was observed for the structure with Xp=\lQ |im, reaching 56% for 5 estimated as 5 = |)^-Fav |-100%/Fav ?


347

where Fav is the arithmetic average of the voltage per structure (curve 6 in Fig. 19.5). Darznek et al (2000) have demonstrated that the velocities of expansion of the SFR are higher in the larger-x^ structures due to the lower excessive plasma density in the/? region. As can be seen in Fig. 19.5 (curves 3 and 4\ in all cases the SFR expansion velocity in the structure with x^ = 188 |im was greater than that in the structure with Xp = 170 |im. As a result, both the difference between the SFR widths, Aw, and the voltage deviation from its average value, 5, decrease during the process of current interruption. When the voltage across the structures reached a maximum (maximum value of w), the difference in SFR widths was not over 5 |Lim (curve 5 in Fig. 19.5) and 6 decreased to 4% (curve 6 in Fig. 19.5). Thus, it has been shown that in the SOS effect mode, in the phase of current interruption and voltage rise across series-connected structures a mechanism operates by which the voltage distribution over the structures in which the depth of the p-n junction is different levels off This mechanism is associated with the fact that the SFR in large-Xp structures starts forming later in the phase of current interruption, but it expands with a higher velocity than in smaller-x^ structures. Investigations of the influence of the dopant profile of a structure on the process of current interruption under the SOS effect for both long and short triggering times have formed the basis for the creation of a new class of semiconductor devices - SOS diodes, whose distinguishing design feature is the large depth of diffiision of aluminum into the structure (Darznek et al, 1999). For nanosecond devices, Xp is 160-180 |im, while for devices with short-term triggering and subnanosecond current interruption times it reaches 200-220 jim. The typical design of a SOS diode is shown in Fig. 19.6. The switch involves a series of elementary diodes tightened with dielectric dowels between two output electrode plates. Each elementary diode consists of a cooler with four series structures soldered on it. A protective coating resistant to transformer oil is applied on the side surface of the structures. Before assembling the diodes, the contact surfaces were flattened and grinded. The assembly has a thermal expansion compensator consisting of two metal bushes with a rubber washer between them. On one of the electrodes, there is a screw to control the force in tightening the diodes. The assembled SOS diodes were tested on specially developed stands. An experiment has shown that the switched current through a SOS diode of area 1 cm^ was 5.5 kA and the time measured between 10% and 90% of the peak current was 4.5 ns. The switching rate was 1200 kA/|is, which is about three orders of magnitude greater than the current rise rate in conventional fast thyristors.

348

Chapter 19

Figure 19.6. Typical design of a SOS diode consisting of series-connected structures with coolers: 1 - insulator rod, 2 - cathode plate, 3 - tightening screw, 4 - coolers with solderedon semiconductor structures, 5 - anode plate

Table 19.1 lists the characteristics of the SOS diodes developed at lEP. The most powerful device whose structure area is 4 cm^ operates at a voltage of 200 kV and interrupts a current of 32 kA, which corresponds to an interruption power of 6 GW. A device has been created which is capable of operating in a continuous mode at a high pulse repetition rate. This device has a developed system of coolers and, with an interrupted current of 1-2 kA and a voltage of 100-120 kV, operates at a pulse repetition rate of 2 kHz. There also exist devices that harness the effect of subnanosecond current interruption; they are intended to produce pulses of duration a few nanoseconds. With a short triggering time, they interrupt currents of up to 2 kA within 500-800 ps. Table 19.1. Parameters of the SOS diodes developed at lEP Parameter Value Operating voltage

60-400 kV

Number of series structures

80-320

Structure area

0.25-4 cm2

Forward current density

0.4-2 kA/cm2

Interrupted current density

2-10kA/cm2

Forward triggering time

40-600 ns

Reverse triggering time

15-150 ns

Current interruption time Power dissipated in transformer oil (continuous operation)

0.5-10 ns

Length/mass

50-220 mm/0.05-0.6 kg

50-500 W


349

Investigations and use of the SOS diodes as units of various pulse generators have demonstrated their exceptionally high reliability and ability to withstand many-valued overloads in current and voltage. Since 1995, when first pilot SOS diodes were made, up to 2002 there was no one failure of these devices. Stand tests carried out to specially disable such a device have shown that an increase in trigger current density (and in dlldt) by an order of magnitude (from 5 to 50 kA/cm^) increases the energy losses in the triggering phase and reduces the efficiency of operation of the opening switch. In this case, the structures operate as a resistor that limits the trigger current, since at these high current densities the modulation of the base is accompanied by the appearance of high forward voltages. Attempts to disable a SOS diode by applying a high operating voltage (a device with an operating voltage of 120 kV was incorporated in a generator with an output voltage of 450 kV) have shown that in the phase of current interruption the SOS diode operated as a voltage limiter (the pulse amplitude was not over 150 kV), consuming energy from the trigger capacitor. Simulations performed for this operating mode have demonstrated an abrupt intensification of the processes of avalanche multiplication of carriers in the electric field region and a corresponding decrease in structure resistance in the current interruption phase. Obviously, this ability of SOS diodes to withstand overloads is due to the specific operation of a semiconductor structure that is filled with plasma in the SOS mode. Investigations have also revealed another feature of SOS diodes: the current interruption characteristics are improved when the semiconductor structure is heated. In contrast to conventional power devices (diodes and thyristors) whose structure under reverse voltage is free of excessive plasma and an increase in temperature results in breakdown of the structure due to an increase in reverse current and its localization at irregularities, the base of a SOS diode remains filled with excessive plasma during the current interruption and generation of a reverse voltage pulse. In an experiment with an overheated SOS diode, it has been established that as the structure temperature increases in the course of operation until the onset of melting of the high-temperature solder, the charge extracted at the stage of reverse triggering increases by about 10-15%. The increase in extracted charge increases the interrupted current amplitude and decreases the interruption time. This effect is related to the increase in lifetime of minority carriers with temperature and with the corresponding decrease in charge losses due to recombination. The operating parameters of SOS diodes, such as current density, peak voltage, and pulse repetition rate, should be matched to the required efficiency of energy switching into a load and to the temperature regime of the device operation. The main energy losses (80-90%) in a SOS diode take

350

Chapter 19

place in the phase of current interruption. Therefore, for the same triggering mode, variations in load parameters vary the current interruption characteristic, the peak voltage across the switch, and the amount of energy released in the switch. This leads to problems with the determination of the admissible pulse repetition rate. For the above reasons, we give recommended values of the current density and trigger pulse duration in Table 19.1 where, instead of the pulse repetition rate, the admissible power losses are given which correspond to the temperature difference between the cooler and the surrounding transformer oil lying in the range 50-80°C (0.25-0.4 W/cm^). The typical pulse repetition rates for the switch operation under invariable heat removal conditions range between 200 and 2000 Hz. When a device operates in the burst mode for which the thermal regime is nearly adiabatic, the pulse repetition rate is, as a rule, limited by the repetitive operation capabilities of the power supply generator, since the intrinsic limiting pulse repetition rate of a SOS diode, which is determined by the duration of the triggering process, is over 1 MHz. The operating voltage of the devices, given in Table 19.1, makes up 80% of the voltage at which a SOS diode starts operating in the voltage limitation mode. When SOS diodes are incorporated in a generator, their parallel-series connection is admissible to attain required parameters of the opening switch.

3.

SOS-DIODE-BASED NANOSECOND PULSE DEVICES

The method of increasing the power of capacitive generators with the help of an intermediate energy store and an opening switch has been known long ago. This method is based on the fact that the inductance of the discharge circuit, which is a passive element of a capacitive generator and prevents rapid energy extraction from the capacitors into the load, becomes an active element when an opening switch is used and operates as an inductive energy store. In this case, an increase in pulse power is achieved since the energy delivery from such a system to a load takes a short time. In pioneering experiments on harnessing the SOS effect for the production of pulse power (Kotov et al, 1993a), the power enhancement mode was realized for a Marx generator with an opening switch based on high-voltage rectifier diodes. The Marx generator had a capacitance of 0.13 |LiF and an idle-run voltage of 150 kV. The SOS opening switch was assembled from 64 rectifier diodes (16 parallel branches each containing four series-connected diodes). The forward and reverse trigger currents of the switch were 25 and 20 kA, respectively. The reverse current triggering time was 300-400 ns. Under these conditions, as the current was cut off.


351

voltage pulses of amplitude up to 400 kV and FWHM 40-60 ns were produced across a 100-Q load. In another version, the opening switch had 20 parallel branches consisting of diodes of the same type. With the Marx idle run voltage equal to 150 kV, pulses of amplitude 420 kV were produced across a 150-Q load. For a load of resistance 5.5 Q, the pulse amplitude was 160 kV with the current rise time equal to 32 ns. In this experiment, record values of the switched power and dlldt in a load have been achieved with semiconductor opening switches, which were, respectively 5 GW and lO^Â/s. For a minimum inductance of the discharge circuit (without an additional inductor) and with the Marx generator operated into the same load (5.5 Q) without an opening switch, the load current rise time was 180 ns with the peak current equal to 25 kA. Thus, the use of a rectifying-diodebased semiconductor opening switch has made it possible to increase dlldt in a load about seven times. Nanosecond pulse generators and accelerators with semiconductor opening switches based on commercial rectifying semiconductor diodes operating in the SOS-effect mode are described in (Kotov et al, 1993a; Kotov et al, 1993b). Marx-based capacitive generators and single- and double-circuit triggering schemes were used as power supplies. The generators had an output voltage ranged from 150 to 450 kV and differed from one another in stored energy by three orders of magnitude. One of them is a compact generator designed as a portable unit of mass 10 kg and length 600 mm. The Marx generator contains four modules with inductive decoupling, which are pulse-charged from a thyristor charging device to a voltage of 18 kV in 20 |LIS. The output parameters of the generator are as follows: capacitance 0.85 nF, voltage 70 kV, and stored energy 2 J. The inductance of the intermediate energy store in the one-circuit triggering scheme of the opening switch is 2.5 \xi\. As the Marx generator is turned on, the pulsed forward triggering of the SOS lasts 150 ns; the duration of the reverse trigger pulse is 80 ns. The current interruption occurs within 10 ns, resulting in the formation of a voltage pulse of amplitude 160 kV and FWHM 10-12 ns across a 180-Q load. The interrupted current is about 1 kA. The SOS opening switch is assembled of 88 rectifier diodes: four parallel branches each containing 22 series-connected diodes. The maximum current density in the structure during forward triggering and prior to current interruption is, respectively, 15 and 12.5 kA/cm^. The generator is designed in an oil-free version; the elements of the input unit are insulated from the case with a removable screen consisting of several layers of Dacron film. The device operates with a pulse repetition rate of 50 Hz.

Chapter 19

352 - | , +Triggering (+) §08

ia)

f^HbTT

\-o o-|[o o-||-o o-|f Marx generator (-) (b)

k r'^"

•

td

>

I 0.2 0.4

1

280 >230

1.23 1.35 1.36 1.30 0.50 0.45 0.55 1012

10^

AB(T)

"H 3.1 1.4 1.05 3.4 3.1 1.5 0.58 0.63

The main difference of amorphous alloys from permalloys is that the resistivity of the former is approximately three times higher, while the coercive force is about three times smaller. This difference affects in the main the specific energy lost for magnetic reversal. Amorphous alloys show smaller specific losses for hysteresis due to the narrow static hysteresis loop for magnetic reversal times over 30 |as and due to the elevated resistance to eddy currents for magnetic reversal times less than 300 ns. For magnetic reversal times ranging from 0.3 to 30 |is, the specific losses in permalloys and amorphous alloys are almost the same.

Chapter 20

360

2.

GENERATION OF NANOSECOND HIGH-POWER PULSES

A first generator of nanosecond high-power pulses using ferromagnetic elements with fast magnetic reversal is described by Mesyats (1960). In this generator, sharp pulses of duration 10"^ s and amplitude up to 30 kV were obtained with the use of a fast nonlinear inductance coil (Fig. 20.2, a). The capacitor Ci, charged through the resistor Ri and thyratron 7, was discharged into the coil L, The coil inductance was proportional to the permeability of the ferromagnetic material, |LI. The typical dependence of |x on the magnetization current / is given in Fig. 20.2, b. The permeability and, hence, the inductance peaked at a current /max- This behavior of the inductance provided conditions for the production of a short pulse. {a)

R,

(b)

0 Im

I

Figure 20.2. Production of nanosecond pulses with the help of a thyratron and a ferromagnetic coil: a circuit diagram of the generator (a), the current dependence of permeability ji (b), and the production of a nanosecond pulse by discharging a capacitor (c)

If the capacitor discharge through the thyratron was periodic, two pulses were generated: negative and positive. With an aperiodic discharge (7?2 > lyjLIC), the thyratron passed a unipolar current pulse; therefore, a short voltage pulse (Fig. 20.2, c) appeared across the inductance coil. To increase of the steepness of the pulse trailing edge, the inductance coil L was shunted by the spark gap P with the damping resistor R^, This made possible a sharp pulse of voltage up to 10 kV and duration 5 ns. Further development of this technique gave rise to a considerable increase in power. The output pulse power of generators now reaches several terawatts. Owing to these high powers and nanosecond pulse durations attained with magnetic generators, new applications of these systems have been brought into practice. While earlier magnetic pulse generators were used in the main in radiolocation and in automated and computer facilities, the new types of generator are mainly intended for use in physical experiments. One new field of application has arisen in cormection with improved electron accelerators as an alternative to generators based on spark gaps and

GENERA TORS IN CIRCUITS WITH MA GNETIC ELEMENTS

361

thyratrons. Magnetic generators offer the possibility to produce chargedparticle beams of nanosecond duration with pulse repetition rates as high as several kilohertz (Meshkov, 1990). Structurally, all nanosecond magnetic pulse generators are practically identical irrespective of the output power and purposes. Let us consider a magnetothyristor generator (Meshkov et al, 1984) as an example. Figure 20.3 presents a simplified circuit diagram of one of the four parallelconnected and synchronously operated modules of the generator. The circuit consists of three main parts: a primary pulse generator, magnetic compression sections, and a pulse-forming device. Besides, the generator may contain additional units such as load-matching devices and pulse peakers and transformers. Among other units necessary for the operation of this type of generator are power supplies with filters, start-up systems, power supplies and decoupling elements of the bias circuits, cooling systems, etc.

Chi

ib) input

^

Xn =FC6

Chs

4=^7 1.5 n 1.5 ^

u

-n? i-

Output

Figure 20.3. Circuit diagram of a nanosecond high-power pulse generator (one of the four parallel-connected modules): 1 - primary pulse generator, 2 - energy compression sections with a transformer, 3 - pulse-forming device (a); one of the 22 parallel-connected circuits of the pulse-forming device: Li - 1-m long rf cable, L2 - 25-ns, 37-Q line, L3 - two parallelconnected sections of the output rf cable (b)

The transmission line Li only connects the units. The capacitor C7 serves as a capacitive energy store and, together with choke C/zg and line L2, produces a quasirectangular pulse in the load line L3. The saturation mode for the core of Chs is chosen such that the current of the discharge of C? into L2 and L3 has the waveform of the first period of the squared-sine function (so-called squared-sine waveform) of duration 100 ns. In the line L3, this discharge pulse is summed up with an identical one reflected from the open end of the line L2. If the length of L2 is chosen properly, a pulse with a flat top is generated across the load. The output pulse has a duration of 100 ns

362

Chapter 20

and an energy of 0.5 J, which makes 0.65 of the energy received from the power supply. At a frequency of 5 kHz, the net average output power of four modules is 10 kW. Energy losses take place in the sections and in the transformer. For stabilization of the temperature regime, the generator is immersed in circulating transformer oil, and the thyristors give up heat to water-cooled radiators. Other types of magnetic generator are described in the review by Meshkov (1990). A breakthrough on the way of increasing of pulsed power was the use of magnetic switches with metglas (strip of amorphous magnetic material) coils. We now consider the operation of the Comet system designed at SNL (Neau et al, 1984) as an example. This was a generator with two stages of magnetic compression. For the primary store, a Marx generator capable of storing 370 kJ of energy at a charge voltage of 95 kV was used. The Marx generator charged, through a gas gap switch, a coaxial water line that charged, through the first magnetic switch, the second energy storage line. This storage line was then discharged, through the second magnetic switch, into a transmission line terminated in a 1.9-Q (copper sulfate solution) load. In the final version, 42% of the stored energy was delivered to a load, 80% were transferred through magnetic switches, and the remaining losses took place in the Marx generator and in the gas gap. Eventually, a pulse of power 3.7 TW, voltage 2.7 MV, and FWHM 35 ns was produced across the load. Magnetic elements can efficiently operate in pulse peaking and chopping circuits. On the nanosecond scale, it is necessary to take into account the dissipation processes involved in magnetic reversal of the magnetic element. Let us consider the transformation of a wave described by V\{t) = Vof(ct), where c is a proportionality factor, with a monotonicly rising front and a flat top that propagates from an infinitely long line Li with wave impedance ZQ into an identical line L2, the lines being connected through a nonlinear inductance coil (Fig. 20.4) (Mesyats and Baksht, 1965). The wave incident on the nonlinear inductance coil, Vi(t% and the wave passed through the coil, V2(t), are related as Vi (0 = V2 (t) +1 (d\\f/dt).

(20.5)

The flux linkage \|/ is determined by the parameters of the nonlinear inductance coil: \|/ = L/ + [iowsM(t),

(20.6)

where L is the inductance of the choke as / -> 00, the so-called "selfinductance of the choke; w and s are, respectively, the number of turns and the cross-sectional area of the choke core; the magnetization of the core, M(0, is related to the magnetic field strength //=/?/by Eq. (20.4).

GENERA TORS IN CIRCUITS WITH MAGNETIC ELEMENTS Vi(t)

B

363

V2(t)

2x

'y^

Q

Figure 20.4. Circuit for wave transformation in a long line with a series-connected nonlinear inductor

(b)

0.8

mo = 0.7 ,-0.3

0.4

/ v / \ j

\^-l

20

40

Figure 20.5. Refracted wave amplitude as a function of normalized time for WQ = 0.5 and various values ofb (a) and for Z? = 10 and various values of WQ (b)

The shape of the refracted wave (Fig. 20.5), constructed with (20.5) and (20.6), indicates that the time of appearance of the wave in the line Li depends on 6 = [loMsSwXp / 2Zo, where X = aVlô ? and can be controlled by varying mo = M-JM^ (Mn being the initial magnetization of ferrite). Alongside with in-series connection of a nonlinear choke, its connection in parallel with a long line can also be used. Such a circuit can serve to differentiate a pulse (Baksht and Mesyats, 1964) and allows one to vary the pulse duration. Hence, the most important characteristic of the circuit is the time during which the impedance of the choke will be far in excess of the wave impedance of the line. A nonlinear inductance coil is most effective in circuits in which a prepulse with a rather tapered leading edge is generated by some additional device, such as, most frequently, a gas-discharge switch. Most widespread is the circuit, first described by Il'in and Shenderovich (1965), where a nonlinear inductance coil and a uniform line are connected in series. In this circuit, the pulse produced by the primary pulse generator comes in the first line and then passes, through a ferrite element, into the second line. With a voltage of 20 kV and a primary pulse rise time of 20 ns, a proper choice of the dimensions of the ferrite ring and magnetization make it possible to produce a secondary pulse rise time of about 1 ns. Other circuits that are

364

Chapter 20

used to produce nanosecond high-power pulses with the help of nonlinear inductance coils are described elsewhere (Kerns, 1950; Wilhelm and Zwicker, 1965; Kunze et aL, 1966; Mesyats, 1965; Nasibov et al, 1965). In the nanosecond pulse power technology, chokes with saturated cores are used not only for the correction of the pulse shape, but also in cases where, within a certain time upon application of voltage, an abrupt change in circuit impedance is required. A typical device using a nonlinear inductor is a spark gap overvolted with the help of so-called "ferrite-based decoupling". This type of device was first proposed by Kerns (Kerns, 1950). Several versions of this type of spark gap were developed later (Wilhelm and Zwicker, 1965; Kunze etal, 1966). For nanosecond circuits, the need often arises to pass pulses of only one polarity through some device. This problem can be solved with the help of a nonlinear inductor connected in series with a uniform line (Mesyats, 1965).

3.

MAGNETIC GENERATORS USING SOS DIODES

Once experimental and theoretical investigations of the SOS effect had been performed and powerfiil generators and accelerators using semiconductor opening switches pumped by generators with spark gaps had been developed, it became obvious that qualitatively new nanosecond pulse power devices must use an all-solid-state power switching system with magnetic switches. The circuit ideology of this approach is illustrated by the block diagram shown in Fig. 20.6. The thyristor charging device (TCD) executes dosed energy takeoff from the supply line. From the TCD, the energy comes in a magnetic compressor (MC) at a voltage of 1-2 kV within 10-100 |as. The MC compresses the energy within about 300-600 ns and increases the voltage to hundreds of kilovolts. The SOS appears as a final power amplifier, shortening the pulse duration to 10-100 ns and increasing the voltage 2-3 times. The TCD contains a primary capacitive energy store, a thyristor switch, and charging and energy recuperation circuits and operates in the singlepulse mode, such that a unit portion of energy is taken from the supply line which is necessary to produce a single pulse at the output of the entire system. The criterion for choosing the pulse duration for the energy transfer from TCD to MC is self-contradictory. On the one hand, to simplify the MC, in particular, to reduce the volume of the cores and the number of energy compression stages, it is necessary to shorten the duration of the pulses formed in the TCD. On the other hand, to reduce the time of energy extraction from the TCD to several microseconds calls for a great number of simultaneously operating fast thyristors, complicating the system of primary

GENERATORS IN CIRCUITS WITH MAGNETIC ELEMENTS

365

energy switching and making it less reliable. In this connection, the optimum time of energy extraction from TCD ranges from 10 to 100 [as for the pulse energy ranging from a few joules to hundreds of joules. 1-2kB 10--100 |is TCD

— •

100-400 kB 300 -600 ns MC

— •

200--1000 kB 10 -100 ns SOS

— •

Load

Figure 20.6. Block diagram of a generator with an all-solid-state energy switching system

The pulse parameters at the output of the MC are determined by the operating conditions of the semiconductor opening switch and by the pulse parameters to be obtained at the load. The pulse amplitude at the MC output is determined as Vuc = iîoad/ôv, where KQ^ is the overvoltage factor at the instant the current is interrupted by the opening switch and Fioad is the desired amplitude of the pulse across the load. The time of energy extraction from the MC determines the duration of the forward triggering of the opening switch: tuc = t^ • The use of the magnetic energy compression section was dictated by the need to match the parameters of the TDC output pulse to the parameters of the pulse that pumps the opening switch. To obtain nanosecond pulses of amplitude about 1 MV at the output of the system as a whole, the magnetic compressor should form pulses of duration several hundreds of nanoseconds with a peak voltage of several himdreds of kilovolts. Thus, with an input pulse of amplitude 1-2 kV and duration 10-100 |LIS, the MC should ensure about 100-fold energy compression in time and an increase in voltage by a factor of 100-400. Figure 20.7 presents a circuit diagram of the magnetic compressor proposed by Rukin (1997) in which energy compression in time is realized with a simultaneous increase in output voltage. The principal difference of this compressor circuit from conventional ones is that the capacitive energy store of each energy compression section has a middle point or it is composed of two series-connected capacitors of the same capacitance. In this case, the output of each previous energy compression section is connected to the central point of the capacitor of the next section, and the bottom capacitors of each section are shunted by magnetic switches. Upon energy compression, the voltage across each section doubles. The output voltage of the MC, without regard of active energy losses, is 2" times greater than the input voltage {n being the number of capacitor sections).

366

Chapter 20

to SOS

TCD

MC

Figure 20.7. Circuit diagram of a magnetic compressor doubling the voltage across each section

Such an MC does not require additional circuits for magnetic reversal of the magnetic switch cores, since in this type of circuit this process occurs automatically because of different directions of the charging and discharge currents in each switch (in Fig. 20.7, the charging and discharge currents are shown by dotted and solid arrows, respectively). One more distinctive feature of the circuit is that in each capacitor section there occurs a double compression of energy due to the recharging of the bottom capacitors. Therefore, to compress an energy in time by two orders of magnitude, it suffices to have two sections with a compression factor Kc -^ 3-4 provided by each magnetic switch. Another important problem concerned with the energy transfer from an MC to a semiconductor opening switch is associated with the circuit embodying double-loop triggering of the opening switch in the mode of amplification of the reverse current. This solution was proposed independently by Kotov et al (1993) and Grekhov et al (1994). The matching circuit is given in Fig. 20.8. Between the magnetic compressor output and the opening switch, a reverse triggering capacitor Qev and a reverse triggering magnetic switch (or a pulse transformer) are connected. After saturation of the forward triggering switch MS^, which is the output switch of the magnetic compressor, energy is transferred from the last section of the compressor to the capacitor. In this case, the current /"^ charging the capacitor Qev is simultaneously the forward triggering current for the SOS (Fig. 20.9). The increasing voltage across Crev executes the magnetic reversal of the switch MS". After the operation of this switch, the reverse current / " , which is several times greater than / ^ , is passed into the opening switch, and the energy from Qev is switched into the inductance of the reverse triggering circuit (the inductance of the winding of the saturated switch MS" or an additional inductance). As the current is interrupted by the opening switch, energy is transferred to the load in a nanosecond pulse.


367

load

Figure 20.8, Circuit matching the MC and the SOS

f—. ^sos

u

Figure 20.9. Waveforms of the currents and voltages in the MC-to-SOS matching circuit

The above circuit concept was verified by developing and testing a series of setups with an all-solid-state switching system. Rukin et al (1995) describe a desktop small-sized generator intended for investigations of streamer coronas in air. The generator operates at an output voltage of 200 kV, a current of 1 kA, a pulse duration of 40-50 ns, and a pulse repetition rate of 30-50 Hz in continuous operation. In the mode of bursts of duration 1 min, the pulse repetition rate is 300 Hz. The housing dimensions are 650 x 600 x 320 mm and the generator mass is -80 kg. The Sibir system (Fig. 20.10) was developed (Kotov et al, 1995) to elucidate the possibility of creating generators capable of producing megavolt voltages with an average power of several tens of kilowatts. Its output parameters are as follows: pulsed voltage 1 MV, current 8 kA, pulse duration 60-100 ns, and pulse repetition rate 150 Hz. The input power is 10^ kW, the power delivered to the opening switch is 75 kW, and the design

Chapter 20

368

value of the output power is ---SO kW. The generator consists of three units: a thyristor charging device (TCD), an intermediate magnetic compressor (IMC), and a high-vohage unit (HVU) placed in a tank with transformer oil. The dimensions of the high-voltage unit are 3.7x1.4x1.2 m and its mass is about 7 t. IMC

air

air

xcD C,

MSi

-11 +

PT,

%.

oil

HVU SOS

C3 -^load

-rY-r^_^ MS"

^WW

f

SOS

Figure 20.10. Circuit diagram of the Sibir generator

One of the main inferences from the results of experiments on the Sibir system was that the SOS effect in the phase of current interruption is characterized by automatic uniform distribution of voltage over seriescoimected diodes (structures). This enables one to create megavolt opening switches by merely connecting in series a number of diodes without use of external voltage dividers. Based on SOS diodes, a series of small-sized generators repetitively operating on the nanosecond scale have been developed which are intended for experimentation in various fields of electrophysics. At the same time, these systems are used for testing SOS diodes, allowing one to obtain data on the characteristics and reliability of these devices under various operating conditions. The circuits of these generators embody the above principle according to which the energy necessary for the production of a pulse is initially stored in a TCD and then is compressed in time with the help of an MC. An opening switch based on SOS diodes executes the function of a final power amplifier, producing a nanosecond pulse at the output of the generator. Structurally, the generator elements inside the housing are separated into two main parts. In


369

the air part, the low-voltage elements of the TCD, the primary energy store, and the monitoring, alarm, diagnostics, and control circuits are placed. The high-voltage elements of the magnetic compressor and the SOS diodes are located in a tank with transformer oil, which is also disposed inside the housing. The front panel of the housing has a cut for a bushing insulator through which high voltage is led out. The TCD is cooled either with fans or with running water. The MC elements and the SOS diodes give up their heat to oil. To remove heat from the tank, running water is used. The absence of gas-discharge switches in these generators lifts the essential limitation on the pulse repetition rate. In continuous operation, the pulse repetition rate is limited by the heat loads on the elements of the generator, first of all, on the magnetic switch cores. When the generator operates in the burst mode, it is limited by the repetitive operation capabilities of the TCD, i.e., by the recovery time of the thyristors and by the charging time of the primary energy store. The burst mode, in which the generator operates during a time from some tens of seconds to about several minutes with the pulse repetition rate and output power being several times greater than their rated values, is important both for some technological applications and for the improvement and modeling of new technologies under laboratory conditions. Therefore, in developing these generators, in order that their repetitive operation capabilities be realized more completely, the TCD was designed proceeding from the requirement of the least time of energy storage, and the choice of the generator elements was based, among other things, on the results of the calculation of their adiabatic heating in the burst mode. These generators, when operated in the mode of a burst of duration from 30 to 60 s, allow a 5~10-fold increase in pulse repetition rate and output power against their rated values. Two megavolt SOS generators of the S-5N series have been developed and built at lEP (Mesyats et al, 2000). The generator circuit (Fig. 20.11) includes an input thyristor charging device and a preliminary energy compression stage, which are located in the air part of the housing. The elements of the high-voltage pulse former are placed in a tank filled with transformer oil. After preliminary compression, the energy is transferred through the pulse transformer PT2 into the intermediate energy store C3, which is charged to 134 kV within 18 |is. After inversion of the voltage across the bottom capacitor, the voltage at point 3 increases to 250 kV within 3 |Lis. As the core of the switch MS"^ is saturated, energy is transferred to the triggering capacitor C4 through the transformer PT3. As this takes place, the semiconductor opening switch, SOS, is pumped by the forward current and the capacitor is charged to 400 kV within about 0.5 )j,s. The saturation of the core of the switch of the transformer PT3 initiates the process of reverse triggering of the opening switch during which energy is transferred from the

370

Chapter 20

triggering capacitor, as it discharges, to the intermediate inductive energy store Lr, The reverse triggering current, depending on the inductance of the store L~ increases to 3-6 kA within about 100 ns. As this occurs, the current is interrupted by the opening switch within about 10 ns and the inductive energy store is connected to the external load where an output pulse of amplitude up to 1 MV and duration about 50 ns is generated. Table 20.3 gives the parameters of the process of energy compression in the elements of the generator. Table 20.3. Point number

Voltage

Time

1

llkV

130^8

2

134 kV

18^18

3

252 kV

3 jLis

4

405 kV

0.47 las

5

0.5-1 MV*

40-60 ns*

* depending on the load parameters.

load

Figure 20.11. Circuit diagram of the S-5N generator

•

..r-S.m.na^

^'"''^^ ; „.,.+,.,...,. -•-VH-^-M..

: 1.1 MV •

\b)

Figure 20.12. Waveforms of the reverse current (a) and voltage (b) of the semiconductor opening switch of the S-5N generator (time base scale: 20 ns/div)


371

Figure 20.12 presents the pulse waveforms that demonstrate the capabilities of the semiconductor opening switch. The peak reverse current through the opening switch was obtained in the mode with the store L' shortcircuited. The current amplitude prior to interruption was 7 kA and the interruption time was 8 ns. The peak voltage across the opening switch, obtained for Z" = 6 |iH and external load resistance i?ioad = 11 kQ was 1.1 MV with the pulse FWHM equal to about 50 ns. The situation in this field drastically changed once the phenomenon of subnanosecond interruption of current in high-power SOS diodes had been detected (Lyubutin et ai, 1998). The experimental and theoretical investigations of this phenomenon have shown that a SOS diode, being in essence a plasma-filled diode, has the property, inherent in other plasma opening switches, that the current interruption characteristic improves as the dl/dt of the trigger current for the opening switch is increased. As the triggering time was decreased from 300-600 ns to 35-50 ns for the forward current and from 80-100 ns to 10-15 ns for the reverse current, the current interruption time decreased from 5-10 ns to 500-700 ps.

REFERENCES Baksht, R. B. and Mesyats, G. A., 1964, Ferrite-Containing Circuit for the Production of Nanosecond High-Voltage Pulses, Prib. Tekk Eksp. 3:108-110. Fish, G. and Avery, K., 1990, Magnetic Materials Group; Working Group Report. In Proc. of Int. Magnetic Pulse Compression Workshop, California, Vol. 2, pp. 158-170. Grekhov, I. V., Efimov, V. M., Kardo-Sysoev, A. F., and Korotkov, S. V., 1994, RF Patent No. 2 009 611. Gyorgy, E. M., 1957, Rotational Model of Flux Reversal in Square Loop Ferrites, J, Appl Phys.2%\\0\\A0\S. Il'in, O. G. and Shenderovich, A. M., 1965, Shortening of the Rise Time of High-Voltage Pulses with the Help of a Nonlinear Inductor, Prib. Tekk Eksp. 1:112-117. Kerns, O. A., 1950, U.S. Patent No. 1 035 843. Kotov, Yu. A., Mesyats, G. A., Rukin, S. N., Filatov, A. L., and Lyubutin, S. K., 1993, A Novel Nanosecond Semiconductor Opening Switch for Megavolt Repetitive Pulsed Power Technology: Experiment and Applications. In Proc. IXth IEEE Intern. Pulsed Power Conf., Albuquerque, NM, Vol. 1, pp. 134-139. Kotov, Yu. A., Mesyats, G. A., Rukin, S. N., Tel'nov, V. A., Slovikovsky, B. G., Timoshenkov, S. P., and Bushlyakov, A. I., 1995, Megavolt Nanosecond 50 kW Average Power All-Solid-State Driver for Commercial Applications. In Ibid., Vol. 2, pp. 1227-1230. Kunze, R. C, Mark, E., and Wilder, H., 1966, Ferrit Decoupled Crowbar Spark Gap. In Proc. IVth Symp. on Eng. Problems in Thermonuclear Research, Institut fiir Plasmaphysik, Miinchen. Landau, L. D. and Lifshits, E. M., 1959, Electrodynamics of Continuous Media (in Russian). Fizmatgiz, Moscow.

372

Chapter 20

Lyubutin, S. K., Mesyats, G. A., Rukin, S. N., and Slovikovsky, B. G., 1998, Subnanosecond Current Interruption in High-Power SOS Diodes, Dokl ANRAS. 360:477-479. Meerovich, L. A., Vagin, I. M., Zaitsev, E. F., and Kandykin, V. M., 1968, Magnetic Pulse Generators (in Russian). Sov. Radio, Moscow. Melville, W. S., 1951, The Use of Saturable Reactors as Discharge Devices for Pulse Generators, Proc. lEE. 98, No. 53. Meshkov, A. N., 1990, Nanosecond High-Power Pulse Magnetic Generators, Prib. Tekh. Eksp. 1:24-36. Meshkov, A. N., Shishko, V. I., and Eremin, S. N., 1984, Nanosecond High-Power Pulse Generator,/Z)/J. 2:103-105. Mesyats, G. A., 1960, Production of Short-Rise-Time High-Voltage Pulses. In High-Voltage Test Equipment and Measurements (in Russian, A. A. Vorob'ev, ed.), Gosenergoizdat, Moscow-Leningrad, pp. 379-393. Mesyats, G. A., 1965, Ferrite Choke for Short High-Power Videopulses, Zh. Tekh. Fiz. 35:1685-1689. Mesyats, G. A., 1974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A. and Baksht, R. B., 1965, Deformation of Strong Waves Passing through a Ferrite Irregularity in a Line, Zh Tekh. Fiz. 25:889-895. Mesyats, G. A., Ponomarev, A. V., Rukin, S. N., Slovikovsky, B. G., Timoshenkov, S. P., and Bushlyakov, A. I., 2000, 1 MV, 500 Hz All-Solid-State Nanosecond Driver for Streamer Corona Discharge Technologies. In Proc. Xlllth Intern. IEEE Conf. on High Power Particle Beams, Nagaona, Japan, pp. 192-195. Nasibov, A. S., Lomakin, V. P., and Bagramov, B. G., 1965, Generator of Short High-Voltage Pulses, Pr/Z>. Tekh. Eksp. 5:133-136. Neau, E. L., Woolston, T. L., and Penn, K. J., 1984, "Comet-II", A Two-Stage, Magnetically Switched Pulsed-Power Module. In Proc. XVIth Power Modulator Symposium, New York, pp. 292-294. Pavlov, V. I. and Sirota, N. N., 1964, Evolution of the Process of Pulsed Magnetic Reversal of a Ferrite with a Rectangular Hysteresis Loop, Fiz. Tverdogo Tela. 6:1267-1270. Rukin, S. N., 1997, Device for Magnetic Compression of Pulses (in Russian). RF Patent No. 2 089 042. Rukin, S. N., Lyubutin, S. K., Kostirev, V. V., and Telnov, V. A., 1995, Repetitive 200 kV Nanosecond All-Solid-State Pulser with a SOS. In Proc. Xth Intern. IEEE Pulsed Power Conf, Albuquerque, NM, Vol. 2, pp. 1211-1214. Steinbeip, E. and Vogler, G., 1968, Uber eine Abschatzung der minimalen Schaltzeit der Rechterckferrite, ^««. Phys. 20:370-385. Wilhelm, R. and Zwicker, H., 1965, Uber eine einfache KurzschluP - Funkenstrecke fiir stopstromanordnungen, Z. fur angew. Physik. 19:428-431.

Chapter 21 LONG LINES WITH NONLINEAR PARAMETERS

1.

INTRODUCTION

In studying electromagnetic waves propagating in lines, the telegraph equations are known to be used. These equations are derived by simplifying Maxwell's equations. In the general form, they are linear with respect to the physical quantities involved, namely, the fields, the inductions, and the conduction current, and the space in which the wave propagates is of no concern. When seeking solutions to Maxwell's equations, it is necessary to define concretely the properties of this space. From the variety of the space properties, its geometry and the relation of the inductions and conduction current to the fields, which characterizes the medium occupying the space, are usually specified. If the space is boundless, the source generating the wave is pinpointed. In a limited space not containing wave sources, the type of "incident" waves that arrive from the outside at the space boundary and the properties of the neighboring space are specified. In both cases, it is necessary to know the medium state and the fields in the medium prior to the action of the wave. It is well known that a medium occupying a space can be characterized by permeability and conductivity. These parameters are factors of proportionality in the linear equations relating the inductions and the conduction current to the fields. The coupling equations can be written in functional form for the case of not too quickly varying fields. If the fields are rapidly varying, the conduction current and the inductions vary with some delay. This delay can be characterized by the time interval during which the medium comes to equilibrium after a stepwise change of the fields.

374

Chapter 21

Propagation of waves was usually considered in media whose parameters could be considered constants. As a result, a theory of electromagnetism was created which is based on linear equations. Obviously, if any of the above quantities is a function of the strength of even one field of the wave, the system of Maxwell's equations becomes nonlinear. Many interesting phenomena can be considered only within the framework of the theory based on the nonlinear equations. Electromagnetic shock waves are among these phenomena. Interest in these electrodynamic phenomena aroused in connection with the wide use of ferrites and ferroelectrics. The relation between inductions and fields in these media is nonlinear even if the fields vary only slightly. In some cases, the conduction current varies nonlinearly with electric field. These circumstances called for more general assumptions concerning the medium in which an electromagnetic wave propagates, such as the dependence of the permeability and conductivity of the medium on the fields of the wave. The profile of an electromagnetic wave propagating in a transmission line filled with a nonlinear medium has discontinuities, testifying that there occur electromagnetic shock waves (Kataev, 1963) similar to gas-dynamical and hydrodynamic shock waves. Mathematically, this implies that even if the solutions of Maxwell's equations for a nonlinear medium are smooth functions in some range of independent variables, they cannot be extended without breaks to other ranges where the equations remain regular. Obviously, for these conditions, the wave superposition principle will not work. These two circimistances make an analysis in nonlinear electrodynamics specific and difficult. Kataev (1963) considered a plane electromagnetic wave propagating in a medium with nonlinear permeability and permittivity. He obtained solitary waves and proved theoretically and experimentally the existence of electromagnetic shock waves (ESW's) in lines containing ferrites and ferroelectrics. In the experimental study, the problem was to find a more perfect, technically acceptable means for the production of large dlldt and short current pulses. The very first tests demonstrated that electromagnetic shock waves are promising for meeting this goal: leading edges of duration 10"^ s and shorter were obtained at pulsed currents of some tens and hundreds of amperes. The physics of this technical innovation (Kataev, 1958) that involved a number of new electrodynamic effects was of considerable interest. Gaponov and Freidman (1959) established the relation between the jumps of fields and inductions at a discontinuity or the boundary conditions at a discontinuity. Subsequently, solitary and electromagnetic shock waves in some particular types of transmission lines were investigated by Greenberg and Treve (1960).

LONG LINES WITH NONLINEAR PARAMETERS

375

Two mechanisms of the occurrence of shock waves can be distinguished. The first one is based on the drag of the wave vertex caused by the fact that its velocity is greater than the base velocity, resulting from the nonlinear permeability or permittivity of the medium or from the nonlinear running parameters L and C of the line. The second mechanism is associated with the dissipation of the wave front energy due to the energy losses by the magnetic viscosity or nonlinear conductivity of the medium.

2.

FORMATION OF ELECTROMAGNETIC SHOCK WAVES DUE TO INDUCTION DRAG

We first consider the formation of an ESW at a rather low rate of variation of the field. For an unbounded nonlinear nonconducting medium, the propagation of plane homogeneous linearly polarized electromagnetic waves, E = Ex(z,t), H = Hy(z,t), is described by Maxwell's equations which, in this case, are reduced to two first-order partial differential equations (Gaponov and Freidman, 1959): dH _ dz

1 SD c dt

dE _ 1 dB dz ' c dt'

D = eE,

B = B{H),

(21.1)

Here, we take the case of a space filled with ferrite where the relation between the D and E vectors of the electric field is assumed linear, while the relation between the B and H vectors of the magnetic field is considered nonlinear. For rather slow, quasistatic processes, the induction B at any point of space is uniquely determined by the field H at this point at the same point in time. For a bounded space, such as a transmission line of small cross section, the equations can be written as two first-order equations (telegraph equations) (Gaponov and Freidman, 1959, 1960): dz

dt

dz

dt

^

^

Here, V(z, t) is the voltage between the wires of a two-wire line in the cross section z; /(z, t) is the current in one of the wires in the same cross section; Q is the charge per unit length of the line, and O is the magnetic flux per unit length of the line. For rather slow processes, the flux O is considered only a function of current:

376

Chapter 21 0 = 0(7).

(21.3)

The charge Q is linearly related to the voltage: e = CF.

(21.4)

Here, C is the capacitance per unit length of the line. Equations (21.2) are applicable to nonuniform and artificial lines if the quantities involved are replaced by their average values on condition that the time and space scales of /(z, t) and F(z, t) are much greater than the respective scales of an individual unit of the line. The nonlinear equations (21.2)-(21.4) have not been solved for the general case. However, their particular solutions are known for the case of so-called solitary waves where one of the sought-for quantities is a onevalued function of another. Assuming that V = V(I), we find

-î,/¥

^^^^dl.

(21.5)

Then Eqs. (21.2) have solutions that can be written as (Morugin and Glebovich, 1964): z = ±1. Gaponov, A. V. and Freidman, G. I., 1959, On the Electromagnetic Shock Waves in Ferrites, Zh. Eksp. Teor. Fiz. 36:957. Gaponov, A. V. and Freidman, G. I., 1960, On the Theory of Electromagnetic Shock Waves in Nonlinear Media, Izv. Vyssh. Uchebn. Zaved, Radiofiz. 3:79. Greenberg, O. W. and Treve, Y. M., 1960, Shock Wave and Solitary Wave Structure in a Plasma, Phys. Fluids. 3:769-785. Kataev, I. G., 1958, USSR Inventor's Certificate No. 118 859. Kataev, I. G., 1963, Electromagnetic Shock Waves (in Russian). Sov. Radio, Moscow.

388

Chapter 21

Kataev, I. G., Meshkov, A. N., and Rozhkov, P. I., 1968, On the Transmission of Pulses through a Channel Containing a Line with Ferrite, /zv. Vyssh. Uchebn. laved., Radioelektronika. 11:5 70-577. Meshkov, A. N., 1965, Nanosecond High-Voltage Pulse Generator, Prib. Tekh. Eksp. 5:136-139. Meshkov, A. N., 1990, Magnetic Generators of Nanosecond High-Power Pulses, Ibid. 1:24-36. Mesyats, G. A., 1974, Generation of Nanosecond High-Power Pulses (in Russian). Sov. Radio, Moscow. Morugin, L. A. and Glebovich, G. V., 1964, Nanosecond Pulse Power Technology (in Russian). Sov. Radio, Moscow. Ostrovsky, L. A., 1963, Generation and Development of Electromagnetic Shock Waves in Transmission Lines with Nonsaturated Ferrite, Zh. Tekh. Fiz. 33:1080.

PART 8. ELECTRON DIODES AND ELECTRON-DIODE-BASED ACCELERATORS

Chapter 22 LARGE-CROSS-SECTION ELECTRON BEAMS

1.

INTRODUCTION

In this chapter, we consider the production of large-cross-section beams (LCSB's) by means of diodes with explosive electron emission (EEE). The random character of the occurrence of primary ectons at the cathode eventually results in a nonuniform electron beam. As a strong enough electric field is applied to a diode, primary ectons can appear within several nanoseconds due to the enhancement of the electric field at cathode microprotrusions, resulting in their explosion by the field emission current. It could be expected that for this time the expanding cathode plasmas of primary ectons will merge to form a uniform plasma surface, and this could provide the formation of a rather uniform electron beam. However, experiments show that the occurrence of an electron beam as a result of EEE abruptly reduces the electric field strength around the zone where EEE has arisen. This is due to the screening action of the space charge of electron microbeams originating from the ecton zone. Therefore, new ectons do not appear near the primary ecton zone, the covering of the cathode surface with plasma is complicated (emission centers are located far apart), and the problem of the production of a uniform beam demands special research. However, the "screening" effect is moderated to some extent by the socalled "pickup" effect. In this case, the plasma of primary ectons interacts with the cathode and initiates new ectons. It has also appeared that the beams fi-om closely located individual cathode flares (CF's) interact with one another, making the electron beam more irregular at the anode (the "stroke" effect).

392

Chapter 22

Let us consider the large-scale structure of electron beams in high-current diodes designed for the production of LCSB's. We shall mean by the diodes such devices in which the electrode separation is much less than the geometric dimensions of the electrodes (cathode and anode). Besides, we shall investigate the properties of diodes of this type, paying special attention to the cathode phenomena. A considerable body of the data presented in this chapter, including those on the above effects, was obtained in the main by the team headed by Mesyats at IHCE (Belomytsev et al, 1980; Koval et al, 1983; Mesyats, 1998; Bazhenov etal, 1970; Belomytsev et al, 1976; Bugaev et al., 1973a; Belomytsev et al., 1987). Recall that the phenomenon of explosive emission of electrons was considered in detail in Chapter 3.

2.

THE CATHODES OF LCSB DIODES

2.1

Multipoint cathodes

For the production of a great number of ectons per unit area, cathodes are used on which numerous points are specially made. Sometimes, a metal or other type conductor is used on the surface of which many ecton zones can naturally be formed at a high electric field. To obtain a uniform electron beam, it is important that the cathode surface be covered with plasma as uniformly as possible. If we assume that new ectons arise at a distance from each other not smaller than the radius of screening, rscr, the minimum time it takes for covering the cathode with plasma will be of the order / « ^scr/^c ? where Vc is the expansion velocity of the cathode plasma. Obviously, the longer the pulse duration, the more uniform is the coating of the cathode with plasma and, hence, the more uniform will be the electron beam. The second important parameter responsible for the production of a uniform beam is the rise rate of the electric field in the diode, dE/dt. The higher dE/dt, the larger the number of ectons that appear within the pulse rise time and the more uniform the electron beam produced (Hinshelwood, 1984). For multipoint cathodes, the basic challenge is to provide their stable operation and long lifetimes. These both characteristics depend on cathode material, emitter geometry, current carried by each emitter, applied voltage, and cathode-anode separation. A usual reason for failures of such cathodes is that the emitters are blunted because of material removal. When choosing the geometry of emitters, it is necessary to take into account two requirements. The first requirement is that the electric field strength must be such that the time delay to the explosion of points would be much less than the pulse rise time. The second one is reduced to providing a necessary lifetime of the cathode. These requirements are conflicting since an increase

LARGE-CROSS'SECTION ELECTRON BEAMS

393

in electric field is achieved by reducing the emitter radius, and the smaller the radius, the greater the mass of the material removed. Obviously, for the creation of reliable long-living explosive-emission cathodes, emitters with an invariable cross section (foils and wires) are most promising. Foil emitters are most popular (Proskurovsky and Yankelevich, 1983; Belkin and Aleksandrovich, 1972), and, when used in the nanosecond range of pulse durations, they show lifetimes of the order of 10^ shots. However, emitters of this type have a number of disadvantages. One of them is that the number and positions of ectons on the working edge of a foil cannot be controlled, and this results in a considerable nonuniformity of the electron beam (Bradley et al, 1972). Meanwhile, the localization of the current in a limited number of ecton zones shortens the delay time to the electrical breakdown of the acceleration gap. To clear up this trouble, attempts are made to use very thin (7-20 |Lim) metal foils for increasing the electric field at the cathode. However, for large-area cathodes operating on the microsecond scale of pulse durations, the appearance of leading ectons is detrimental to the formation of a beam. Moreover, cathodes made of thin metal foils are mechanically unstable. A given and controllable number of ecton zones on a large-area cathode can be created by using cylindrical emitters made of thin wires. A considerable advantage of this type of cathode is that there is a possibility to maintain uniform current extraction from all emitters by connecting a ballast resistor in the circuit of each of them (Link and Olander, 1969). The use of cylindrical emitters fabricated of thin wires makes it possible to create simple in design and convenient to service long-living explosive-emission cathodes of large area. Since the breakdown electric field, the erosion characteristics of the cathode, and the parameters of newly arising microprotrusions are determined by the emitter material, it is necessary to use materials preferable fi-om the viewpoint of creation of long-living cathodes. To reveal such materials, Proskurovsky and Yankelevich (1983) tested emitters made of various materials and having identical geometric parameters under the same conditions. The results obtained for cylindrical cathodes are presented in Fig. 22.1. It can be seen that copper emitters show the greatest resistance to erosion. Special attention should be given to graphite cathodes. The most uniform beams are obtained in tests with plane graphite cathodes. This is due to the fact that graphite shows short delay times to the explosion of microprotrusions, t^, at rather low macroscopic electric fields at the surface and small values of the critical current (Mesyats, 1998). In has been shown (Koval et al, 1983) that carbon-graphite materials have the best properties, and the lower the material density, the shorter the time t^ and the more

Chapter 22

394

uniform the electron beam (Fig. 22.2). For example, in the electron guns of the Aurora excimer laser (LANL) (Rosocha and Riepe, 1987), a graphite fabric of felt or velour type served as cathode material. This material is used because low voltages are necessary for microexplosions to occur at a cathode. This allows one to have uniform plasma as early as within the pulse rise time. The graphite fibers constituting the carbon-graphite fabric are about 20 |Lim in diameter. On the side surface, the fabric has knots about 1 |im in size. These fibers and knots promote explosive emission at low voltages (Erickson and Mace, 1983). Widely spread are multipoint cathodes made from a copper foil by the method of cold punching (Bugaev et al., 1984). 2/^

1.6

X

r—1

e

^/^\

5 0.8

1

2

4 6 A^-IO^ [pulse]

1

10

Figure 22.L Height decrement of a cylindrical emitter, A//, as a function of the number of current pulses passed through the gap, A^: 7 - W, 2 - Au, i - Ag, and ^ - Cu

2.2

4.0 5.6 £:iO-5 [V/cm]

7.2

Figure 22.2. Breakdown delay time ^^ as a function of macroscopic electric field E: 1 fme-grained graphite of density 2.2 g/cm^; 2 and 3 - carbon graphite of density 0.8 and 0.2 g/cm3, respectively

Liquid-metal cathodes

For a solid cathode, the emission centers are natural microirregularities or specially produced microprotrusions. In the presence of a liquid phase, the latter can be formed as a result of the disturbance of the surface of the liquid metal in a strong electric field (Frenkel, 1935). As shown for a liquid cathode, the vacuum breakdown is preceded by the occurrence of hydrodynamic capillary waves. The suppression of these waves increases the electric strength of the vacuum gap. The use of a liquid metal for the production of stable explosive emission is proposed by Bartashyus et al (1971). It is obvious that if EEE at the initial stage of a vacuum breakdown is determined by the explosion of microprotrusions, its stability should substantially depend on the conditions


395

of self-recovery of microprotrusions from breakdown to breakdown. It seems that for liquid metals the cathode operation should be much more stable because microirregularities are formed under invariable initial and boundary conditions. In addition, the formation of microirregularities on a liquid surface can be controlled by some artificial way. In particular, such they can be created by exciting the surface with a piezocrystal. If a liquid metal is placed over a vibrating piezoquartz or barium titanate plate, standing waves are generated on the liquid surface, which can serve as ordered and controllable microirregularities. For a square plate with a square side a, the relation between the number of vibrations n and their frequency fn is expressed by the formula (Pigulevsky, 1958)

where h is the height of the standing wave, p is the density of the plate material, and a is the Poisson coefficient. The corresponding relation for a round piezocrystal of radius r has the form A

=

«

p

i

.

(22.2)

In the experiment described by Bartashyus et al (1971), the frequency of the exciting vibrations ranged from 2 to 12 MHz. Thus, according to formulas (22.1) and (22.2), the density of the irregularities produced varied with frequency from 190 to 6-10^ cm"^. The calculated dimensions of microprotrusions (radii of curvature of their tips) ranged, respectively, from 37.2 to 1.34 |am. The height of a microprotrusion depended on the power supplied from a generator and could reach 10 |Lim. As the exciting vibration amplitude was increased, the breakdown voltage decreased. As this took place, the spread in breakdown voltages decreased as well. Simultaneously, a substantial increase in EEE stability was observed. Without excitation of the surface, the spread in values of the electron current made up 10-15%; when artificial excitation with the help of piezoquartz was used, the electron current was stable within 5%. It is of importance that with artificial excitation of the cathode surface the transferred electron charge increased. This can be explained by the development of an active surface and the increase in the number of simultaneously exploding emission centers. The electron current was 2-10^ A and the voltage was 300 kV. The electron component was separated from the plasma with a thin foil transparent to the electrons accelerated by the anode

396

Chapter 22

voltage. A new type of liquid-metal cathodes capable of operating at high repetition rates is described by Baskin et al (1994). A detailed study of the EEE process at the surface of a cathode of this type has been carried out by Batrakov (2002).

3.

METAL-DIELECTRIC CATHODES

3.1

Explosive electron emission from a triple junction

Attempts to produce uniform LCSB's due to more uniform covering of the cathode surface with plasma resulted in the creation of metal-dielectric cathodes (MDC's). With this type of cathode, EEE can be excited much easier and, as the velocity of motion of a plasma over the surface of a dielectric can be made higher than the velocity of expansion of a CF in vacuum, the covering of the cathode surface with plasma will occur more rapidly. Besides, metal-dielectric cathodes are easier to be made controllable, thus giving them new useful properties (Bugaev et al, 1973b; Mesyats, 1974). The operation of a metal-dielectric cathode is based on the excitation of EEE at a metal-dielectric-vacuum triple junction. We explain the mechanism of the operation of an MDC by the example of a metal needle leaning against the surface of a dielectric plate whose opposite side is metallized (Fig. 22.3) (Bugaev and Mesyats, 1971). In the sketch shown in Fig. 22,3, needle 7 is a cathode, plate 5 is an anode deposited on dielectric 2, and electrode ^ is a trigger electrode. Assume that the cathode 1 is grounded, and a pulsed voltage too low to initiate EEE from the cathode is applied to the anode 3. If now a pulsed voltage is applied to the electrode 4, a dielectric surface discharge in vacuum starts from the electrode 1, The current of this discharge will be closed on a microprotrusion of the cathode 1 leaning against the dielectric surface. This current just results in the explosion of the microprotrusion and in the occurrence of EEE from the metal emitter 1 toward the plane anode i. The current of the dielectric surface discharge is caused by an increase in the dynamic capacitance of the gap between the plasma moving over the dielectric surface and the metal layer deposited on the opposite side of the dielectric. This is a rather simple and efficient way of exciting EEE in a diode. Such a diode is a triggered device; that is, EEE is initiated only on application of a trigger pulse. This method is used with various types of cathode, for example, with one having imiformly distributed emission centers, which is made of a metal grid pulled over the surface of a dielectric ^Bugaev et al, 1973b). At the sites of contact of the grid with the dielectric, discharges

LARGE'CROSS-SECTION ELECTRON BEAMS

397

occur over the surface of the latter, resulting in the formation of EEE centers. For a higher efficiency of such a cathode, it is better to take a high-s dielectric. l\J

3

/,

^ ^ ^^m^ a^

8

1

64

^ 6

^

s/

"

-% 0

]

2 "•"-"•l^

0

1

1

2 Ko [kV]

1

3

4

Figure 22.3. Sketch of the initiation of an emission center: 1 - cathode, 2 - dielectric, 3 anode, 4 - trigger electrode, and the discharge current as a function of voltage for a BaTiOs plate of thickness 2 mm. Electrode 7 is a cathode with respect to electrode 4 (open circles); electrode 1 is an anode (solid circles)

The vacuum discharge over the surface of barium titanate (BaTiOs) with s = 1500 vâs studied by Bugaev and Mesyats (1971). A barium titanate disk 1 (Fig. 22.4) of thickness 2 mm was placed in a vacuum chamber. A silver layer 2 was burnt in one side of the disk, and a tungsten needle 3 was kept against another side. Electrons were extracted from the plasma by extractor 4. Between the electrodes 2 and 3, voltage pulses of amplitude 0.4-4 kV, rise time -1 ns, and fixed duration (2, 4, 8, 20, and 50 ns) were applied. The discharge current /d and the voltage across the dielectric V^ were recorded by a fast oscilloscope, and the luminosity of the discharge in the vicinity of the needle 3 was photographed by an electron-optical device equipped with a light amplifier. The discharge luminosity spectrum was recorded by a spectrograph with the recording chaimel containing a photomultiplier and a signal amplifier. A voltage of amplitude up to 30 kV, rise time 1 ns, and duration up to 500 ns was applied to the extractor 4. At a pulse duration of several nanoseconds, the discharge over the dielectric surface arises at a voltage exceeding some threshold value. As this takes place, the lines of neutral and singly ionized barium (Ba I and Ba II) are detected in the luminosity spectrum. As the voltage is further increased, the lines of Til, 0 1 , Oil, and tungsten (WI and WII) appear in the spectrum.

Chapter 22

398 To oscilloscope Rf -•—WW^

-TL o

ôscil

Figure 22.4. Schematic of an experiment on surface dielectric discharges: 1 - dielectric, 2 electrode, 3 - needle, 4 - extractor. Rf= 56 Q, RC^RQÎSQ

»

l l mml

#

I I—I I

2 ns

4 ns

8 ns

20 ns

(d)^f^ Figure 22.5. Discharge voltage (a) and current (b) waveforms; photographs of the discharge luminosity (c), and waveform of the emission current from the discharge plasma {d)

The discharge current is caused by the variation in the dynamic capacitance of the gap between the plasma moving with a velocity ^d over the dielectric, and the silver layer 2 (Fig. 22.5). For 8 » v^tp (6 being the dielectric thickness and tp the duration of the trigger voltage pulse of amplitude Fd), we have (Bugaev and Mesyats, 1971) v^ = AV^,

(22.3)

where ^ is a factor depending on the polarity of the needle relative to the electrode and on the dielectric type and thickness. For BaTiOa with 6 = 2 mm and the positive polarity of the needle, we have ^4 = 5-10^ cm/(s-V), while for the negative polarity A = 2-10^ cm/(s-V). The amplitude of the discharge current pulse is determined from the relation

h=4AeosVi

(22.4)

where 8o and 8 are, respectively, the dielectric constant of vacuum and the permeability of the dielectric. In Fig. 22.3, the dependence of /d on Vd is


399

shown for the positive and negative polarities of the point. In this experiment (Bugaev and Mesyats, 1971), BaTiOs of thickness 2 mm was used. A discharge current of several amperes can be obtained at a trigger voltage as low as 1-2 kV. This current is sufficient for a microprotrusion of radius --1 |Lim contacting to a dielectric to explode within ~10"^ s. Thus, this is a very efficient method of EEE excitation at the surface of a dielectric.

3.2

Metal-dielectric cathode designs

Mesyats and co-workers (Bugaev et ah, 1973b; Mesyats, 1974; Bugaev and Mesyats, 1971) designed a cathode on which emission centers were created in large numbers due to a discharge over the surface of a dielectric in vacuum and a discharge between a metal grid and the dielectric. Figure 22.6, a shows a grid located on a barium titanate dielectric substrate 7; the opposite side 2 of the substrate is metallized. We now consider an equivalent circuit of the electron source (Fig. 22.6, b). In this circuit, one can distinguish the capacitance of the dielectric surface elements relative to the bottom plate, Ci, and the capacitance of these elements relative to each other, C2, and relative to the grid, C3. Because of the high s of the dielectric, we have C2 and C3 jb changes to j^ = y'b ? where j^ and j \ are, respectively, the thermal

LARGE-CROSS-SECTION ELECTRON BEAMS

407

current density of plasma electrons at the emission boundary and the current density limited by the space charge of the electron beam. As the emission boundary goes over to saturation, the current rise rate at the initial stage of EEE drops. Since the emission boundary moves with a velocity lower than v and the internal layers of the plasma of secondary ectons, moving with a high velocity, can catch up with the boundary, the mechanism of the occurrence of plasma density fluctuations at the emission boundary is clear (Mesyats, 1998). If plasma blobs appear at the cathode surface, for instance, due to the formation of new ectons, the saturation condition is broken and the boundary speed up again as these blobs arrive at the emission boundary, and this will inevitably result in an increase in current (Burtsev et ai, 1978; Bazhenov and Chesnokov, 1976).

5.

DESIGNS OF LCSB ACCELERATORS

In the literature, a great number of accelerators designed for the production of large-cross-section beams are described. They vary in type of diode, power supply, application, current and voltage magnitude, etc. It is impossible to describe them within the framework of one section; therefore, we have to restrict ourselves by considering only some issues of principle. Examining the circuits of electron sources used in high-power gas lasers, one can distinguish two types of source: diode and triode. A diode source is most suitable if high current densities and low impedances are required. In this case, the energy source is a low-resistance pulse-forming line or a Marx generator. Application of a triode circuit is justified if the equivalent resistance of the diode is high enough (10^ Q) and the current density is low (about 10"^ A^cm^). The advantages of this circuit are the rather simple uniform ignition of the whole of the cathode surface and the possibility to control the impedance of the source. The disadvantages are the complexity of the synchronization circuits and the rather low electric strength of the acceleration gap. To moderate the role of the magnetic field of the electron beam, the concept of a segmented electron gun was proposed (Rosocha and Riepe, 1987). In such a gun, a large cathode is subdivided into several separate ones owing to which the self magnetic field decreases. Depending on the volume, a laser can be pumped on one, two, four, and six sides, as well as in a coaxial manner. The circuit of the diode of an accelerator intended for one-sided pumping of a pulsed CO2 laser with a pulse energy of up to 7.5 kJ is described by Koval'chuk et al (1976). The design of a laser system in which two EEE diodes are used is shown in Fig. 22.11. The beams are produced by a bilateral blade cathode fixed on an aluminum plate 25x200 cm in size.

408

Chapter 22

Tantalum strips of thickness 7.6 \xm are protruded for 2.7 cm above the surface of the cathode plate. The cathode is located in a rectangular vacuum chamber and suspended, with the help of the cathode holder, to a vacuum insulator. Electrons, through a window 35x200 cm in size, get in the laser cells where a volume discharge is initiated between the electrode and the protective grid of the window. A four-stage MG with an output voltage of 320 kV, a pulse rise time of 50 ns, and a capacitance of 1.25 |iF serves as a source of pulsed voltage. The voltage produced by the generator is supplied to the diode through a high-voltage cable.

Figure 22.11. Schematic diagram of a gas laser with a double-beam electron source: 1 vacuum insulator, 2 - cathode holder, 3 - foil emitter, 4 - extraction window, 5 - cell electrode, 6 - voltage lead-in, and 7 - laser cell

A description of a KrF laser pumped on four sides is given by Edwards etal, (1980). Pumping was performed by four accelerators, each having a two-cathode diode. Hence, it can be spoken in fact of an eight-sided pumping. The voltage across the diodes was produced by water lines charged from a 1-MV, 40-kJ MG. The diode voltage was 550 kV and the total energy of the electron beam produced by the four diodes was 28 kJ. A XeCl excimer laser having the shape of a cylinder of volume 600 1 was pumped on six sides from twelve accelerators arranged in two floors on each side (Mesyats et al, 1992) (Fig. 22.12). The accelerators were powered directly from Marx generators whose distinguishing feature was that they operated xmder conditions of vacuum insulation. Therefore, the laser had no

LARGE'CROSS'SECTION ELECTRON BEAMS

409

intermediate energy storage lines. The output voltage of the Marx generators was 600 kV, and the total electron current was 700 kA. This laser, because of the use of low-inductance vacuum MG's, was the most compact and reliable system at the time.

Figure 22.12. Sketch showing six-sided pumping of a laser: 7 - pulse generator, 2 - diodes of the electron accelerator, 3 - beam inlet window, and 4 - laser chamber pumped with electron beams

The six-sided and the eight-sided pumping are in fact close to that realized with a coaxial pumping system. In this case, intense and uniform pumping of gas lasers is achieved and the optical characteristics of the light beam are improved. A coaxial diode source was shown to be the best choice for excitation of excimer lasers (Eden and Epp, 1980). The source was a cylindrical coaxial diode with an electrode gap of 2.5 cm, powered from a low-inductance five-stage MG capable of producing 250-kV, 0.8 |LIS pulses. Used as cathodes were strips of titanium foil, coal fibers, or graphite felt fixed on the inner surface of an aluminum cylinder of length 55 cm and internal diameter 8.9 cm. The cathodes made of titanium foil of thickness 25 |im had were 6 mm high and 50 cm long. The anode shaped as a hollow cylinder of length 100 cm was welded from a titanium foil of thickness 25 |im. Coaxial diodes are efficient in pumping lasers that demand high beam current densities. Ramirez et al (1977) used for these purposes a diode with E = 1 MeV, / = 200 kA, y «130 - 260 A/cm2, and /p = 20 ns. Under these conditions, a coaxial diode has an advantage over a planar one: in strong electric fields necessary for the production of high currents, the beam is essentially nonuniform because of the discreteness of emission centers on the cathode surface; with radial injection, this nonuniformity is compensated.

410

Chapter 22

In creating diodes of high average power which would be capable of operating at pulse repetition rates of 50-100 Hz, the tasks to be solved are: to increase the lifetime of the cathode, to reduce the beam electron losses in the foil and support grid, and to provide operating vacuum conditions in the diode. Besides, it is necessary to have complete information on the characteristic time of deionization, i.e., on the recovery capabilities of the acceleration gap. Tests of blade cathodes made of tantalum foil of thickness 7.6 \xm (Loda and Meskan, 1977) have shown that a cathode of length 25 cm from which a current of 12 A with a duration of 10 |LIS was extracted at a voltage of 255 kV, was capable of operating with a frequency of up to 1000 Hz. The height of the blade decreased by 1 mm after application of 2-10^ pulses. To power repetitively pulsed diodes, high-voltage pulse generators with step-up transformers are often used. These devices, with the pulse-forming element connected in the primary circuit, have been developed for certain ranges of impedances, pulse durations, and output voltages, since they are used in radiolocation to modulate the pulses of high-power klystrons. A disadvantage of this type of circuit is the high leakage inductance of the high-voltage pulse transformer. An accelerator with a high-voltage pulse generator whose Tesla pulse transformer is combined with an intermediate energy store (coaxial pulse-forming line) connected to the secondary winding is described by Mesyats (1991a). At an accelerating voltage of 400 kV, a current of 8 kA, and a pulse duration of 25 ns, the average power of the beam is 5.5 kW. The pulse repetition rate is 100 Hz; the beam size at the exit is 10x100 cm.

REFERENCES Andrews, M., Bruza, J., Fleishman, H., and Rostoker, N., 1969, Effect of a Magnetic Guide Field on the Propagation of Intense Relativistic Electron Beams, Laboratory of Plasma Studies, Comell Univ., Ithaca, New York, p. 18. Bartashyus, Yu. I., Pranevichus, L. I., and Fursei, G. N., 1971, Study of the Explosive Electron Emission from a Liquid Gallium Cathode, Zh Tekh Fiz. 41:1943. Baskin, L. M., Batrakov, A. V., Popov, S. A., and Proskurovsky, D. I., 1994, Electrodynamic Phenomena on the Explosive-Emission Liquid Metal Cathode. In Proc. XVIISDEIV, Moscow, Russia, pp. 2-5. Batrakov, A. V., 2002, Plasma Properties of Arc Cathode Spot at Liquid-Metal Cathode. In Proc. XXISDEIV, Tours, France, pp. 123-130. Bazhenov, G. P. and Chesnokov, S. M., 1976, On the Maximum Current of Explosive Electron Emission,/zv. Vyssh. Uchebn. Zaved.^Fiz. 11:133-134. Bazhenov, G. P., Mesyats, G. A., and Chesnokov, S. M., 1975, On the Deceleration of the Emission Boundary of a Cathode Flare in a Diode Operating in the Mode of Explosive Electron Emission, Radiotekh Elektron. 20:2413-2415.

LARGE'CROSS'SECTION ELECTRON BEAMS

411

Bazhenov, G. P., Mesyats, G. A., and Proskurovsky, D. I., 1970, Investigation of the Structure of Electron Flows EmittedfromCathode Flares, /zv. Vyssh. Uchebn. Zaved, Fiz. 8:87-90. Belkin, N. V. and Aleksandrovich, E. G., 1972, A Two-Electrode Tube for the Production of Nanosecond X-Ray Flashes, Prib. Tekh. Eksp. 2:196-197. Belomytsev, S. Ya. and Mesyats, G. A., 1987, Structure of Electron Beams in High-Current Diodes, Radiotekh. Elektron. 32:1569-1583. Belomytsev, S. Ya., Il'in, V. P., Litvinov, E. A., and Mesyats, G. A., 1976, On the "Stroke" Effect in Explosive Electron Emission. In Development and Use of Intense Electron Beam Sources (in Russian, G. A. Mesyats ed.), Nauka, Novosibirsk, pp. 93-95. Belomytsev, S. Ya., Korovin, S. D., and Mesyats, G. A., 1980, The Screening Effect in HighCurrent Diodes, Pw'wflf Z/z. Tekh Fiz. 6:1089-1092. Bradley, L. P., Parker, R. K., and Martin, T. H., 1972, Characteristics of Relativistic Field Emission High Current Diodes. InProc. VISDEIV, Poznan, Poland, pp. 159-164. Bugaev, S. P. and Mesyats, G. A., 1971, Electron Emissionfromthe Plasma of an Incomplete Discharge over a Dielectric in Vacuum, Dokl. ANSSSR. 196:324-326. Bugaev, S. P., Kassirov, G. S., Koval'chuk, B. M., and Mesyats, G. A., 1973a, Production of Intense Microsecond Relativistic Electron Beams, Pis'ma Zh. Eksper. Teor. Fiz. 18:82-85. Bugaev, S. P., Koval'chuk, B. M., and Mesyats, G. A., 1973b, Pulsed Plasma Source of Charged Particles, USSR Inventor's Certificate No. 248 091. Bugaev, S. P., Kreindel, Yu. E., and Schanin, P. M., 1984, Large-Cross-Section Electron Beams (in Russian). Energoatomizdat, Moscow. Burtsev, V. A., Vasilievsky, M. A., and Gusev, O. A., 1978, Investigations of a Diode with an Explosive-Emission Cathode at Long Pulse Durations, Zh. Tekh. Fiz. 48:1494-1503. Eden, J. G. and Epp, D., 1980, Compact Coaxial Diode Electron Beam System: Carbon Cathodes and Anode Fabrication Techniques, Rev. Sci. Instrum. 51 (6):781-785. Edwards, C. B., O'Neill, F., and Shaw, M. J., 1980, 60-ns e-Beam Excitation of Rare-Gas Halide Lasers, Appl. Phys. Lett. 36:617-620. Erickson, G. F. and Mace, P. N., 1983, Use of Carbon Felt as a Cold Cathode for a Pulsed Line X-Ray Source Operated at High Repetition Rates, Rev. Sci. Instrum. 54:586. Frenkel, J., 1935, On Tonks's Theory of Liquid Surface Rupture by a Uniform Electric Field, Phys. Zw. Sowjet, 8:675-679. Garber, R. I., Granova, Zh. I., Mansurov, N. A., and Mikhailovsky, I. M., 1969, A FieldEmission High-Current Pulse Cathode, Prib. Tekh. Eksp. 1:196-198. Gundel, H., 1992, Electron Emission by Nanosecond Switching in PLZT, Integrated Ferroelectr. 2:202. Hinshelwood, D. D., 1984, Explosive Emission Cathode Plasmas in Intense Relativistic Electron Beam Diodes. Massachusetts Institute of Technology. Kotov, Yu. A., Litvinov, E. A., Sokovnin, S. Yu., Balezin, M. E., and Khrustov, V. R., 2000, Metal-Dielectric Cathodes for Electron Accelerators, Dokl. RAS. 370:332-335. Koval, B. A., Mesyats, G. A., Ozur, G. E., Proskurovsky, D. I., and Yankelevich E. B., 1983, Explosive-Emission Nanosecond Low-Energy Electron Sources for Surface Material Treatment. In Pulsed High-Current Electron Beams in Technology (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 26-39. Koval'chuk, B. M., Lavrinovitch, V. A., Manylov, V. I., Mesyats, G. A., and Rybalov, A. M., 1976, Pulsed Electron Accelerator for Excitation of Gas in Large Volumes, Prib. Tekh. Exper. 6:125-127. Levine, L. S. and Vitkovitsky, I. M., 1971, Pulsed Power Technology for Controlled Thermonuclear Fusion, IEEE Trans. Nucl. Sci. 18 (Pt 2): 105-112. Link, W. T. and Olander, W. C, 1969, U.S. Patent No. 3 484 643.

412

Chapter 22

Loda, G. K. and Meskan, D. A., 1977, Repetitively Pulsed Electron Beam Generator. In Proc. II Intern. Topical Conf. on High Power Electron and Ion Beam Research and Technology, Cornell, NY, Vol. 1, pp. 252-273. Loda, G. K., 1977, Recent advances in cold cathode technology as applied to high power lasers. Ibid, Vol. 2, pp. 897-890. Mesyats, G. A., 1971, The Role of Fast Processes in Vacuum Breakdown. In Proc. XICPIG, Oxford, England (Pt II), pp. 333-363. Mesyats, G. A., 1974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio: Moscow. Mesyats, G. A., 1991a, High-Power Particle Beams for Gas Lasers. In Pulse Power for Lasers III: Proc. SPIE, SPIE Press, Los Angeles, Vol. 1411, pp. 2-14. Mesyats, G. A., 1991b, Vacuum Discharge Effects in the Diodes of High-Current Electron Accelerators, IEEE Trans. Plasma Sci. 19:683-689. Mesyats, G. A., 1998, Explosive Electron Emission. URO-Press, Ekaterinburg. Mesyats, G. A. and Proskurovsky, D. I., 1971, Explosive Electron Emission from Metal Joints, Pis'ma Zh. Eksp. Teor. Fiz. 13:7-10. Mesyats, G. A., Bychkov, Yu. I., and Koval'chuk, B. M., 1992, High-Power XeCl Excimer Lasers. In Intense Laser Beams: Proc. SPIE, SPIE Press, Los Angeles, Vol. 1628, pp. 70-80. Miller, R. B., 1998, Mechanism of Explosive Electron Emission for Dielectric Fiber (Velvet) Cathodes, J. Appl. Phys. 84:739. Parker, R. K., Anderson, R. E., and Duncan, C. V., 1974, Plastmainduced Field Emission and the Characteristics of High Current Relativistic Electron Flow, J. Appl. Phys. 45:2463-2478. Pigulevsky, E. D., 1958, The Structure of the Piezoradiation Field in an Ultrasonic Microscope,/zv. LeningradElectrotechnical Inst. 34:213. Proskurovsky, D. I. and Yankelevich, E. B., 1983, A Large-Area Explosive-Emission Cathode. In High-Current Pulsed Electron Beams in Technology (in Russian, G. A. Mesyats, ed.), Nauka, Novosibirsk, pp. 21-26. Ramirez, J. J, and Cook, D. L., 1980, A Study of Low Current Density Microsecond Electron Beam Diodes, J. Appl Phys. 51:4602-4611. Ramirez, J., Prestwich, K., Clark, R., et aL, 1977, E-Beam for Laser Excitation. In Proc. II Intern. Topical Conf. on High Power Electron and Ion Beam Research and Technology, Cornell, NY, Vol. 2, pp. 891-902. Rosocha, L. A. and Riepe, K. B., 1987, Electron-Beam Sources for Pumping Large Aperture KrF Lasers, Fusion Technol. 11:577-611. Rukhadze, A. A., Bogdankevich, L. S., Rosinsky, S. E., and Rukhlin, V. G., 1980, Physics of High-Current Relativistic Electron Beams (in Russian). Atomizdat, Moscow. Schachter, L., Ivers, J. D., Nation, J. A., and Kerslick, G. S., 1993, Analysis of a Diode with a Ferroelectric Cathode, J. Appl. Phys. 73 (12):8097-8110. Smith, I., Champney, P., Hatch, L., Nielsen, K., and Shope, S., 1971, High Current Pulsed Electron Beam Generator, IEEE Trans. Nucl. Sci. 18:491-493. Voropaev, S. G., Knyazev, B. A., Koidan, V. S., Konyukhov, V. V., Lebedev, S. V., Mekler, K. L, Nikolaev, V. S., Smimov, A. V., Chikunov, V. V., and Scheglov, M. A., 1987, Production of a Microsecond High-Power REB of High Current Density, Pis 'ma Zh. Tekh. Fiz. 13:431-435.

Chapter 23 ANNULAR ELECTRON BEAMS

1.

PRINCIPLE OF OPERATION OF DIODES

A problem with EEE electron sources is to decelerate the expanding cathode plasma. Investigations in this field have gone in two basic ways. The first way (discussed in the previous chapter) involves application of an electric field, while the second one is based on the use of a magnetic field. In the first case, it is necessary to make the plasma corresponding to the mode of saturated electron emission, i.e., to reduce its density. With this purpose, the current through the ecton zone is reduced to have an average current density of 0.1-10 A/cm^. For the production of kiloampere currents in diodes of this type, large-cross-section electron beams are formed. A magnetic field applied transverse to the discharge gap, as shown in first experiments performed by Baksht and Mesyats (1970), also reduces the velocity of expansion of the cathode plasma. This allows one to eliminate or substantially reduce the current toward the anode, thus moderating the anode processes, and to do away with the anode foil - the weakest element in an explosive-emission diode. The first foilless coaxial diodes with magnetic insulation (magnetically insulated coaxial diodes, MICD's) based on EEE cathodes were proposed by Friedman and Ury (1970). Diodes of this type generate annular electron beams that are used for the production of microwave radiation. The operation of MICD's is described in detail in the monograph by Bugaev et al (1991). Relativistic microwave electronics became in fact the main consumer of the results of investigations of MICD's. We discuss this in detail in Chapter 27. Many design versions of magnetically insulated coaxial diodes are known. By the relative positioning of cathode and anode, MICD's can be

Chapter 23

414

subdivided into two types: normal and inverse (Fig. 23.1). In a normal MICD (Fig. 23.1, a, b\ the inner electrode is cathode, while in an inverse one (Fig. 23.1, y) it is anode. An annular electron beam is formed from the plasma generated at the cathode in the process of EEE and extracted from the diode into a vacuum drift tube along the lines of magnetic force. If a positive voltage pulse is applied to the inner electrode (see Fig. 23.1, b\ the diode becomes an inverse one. This type of diode is used to generate microwaves in inverted magnetrons (Close et ai, 1983) and to produce ion beams (Dreike et al, 1976; Luckhardt and Fleischmann, 1977; Bakshaev etal, 1979). From a diode of this type the electron beam is not extracted. Below we mean by MICD's normal diodes. (a)

12

3 4 5

(b)

12

3 4 5

(c)

1 2 3 4 5

Figure 23.1. MICD configurations: conical {a\ cylindrical {b\ planar (c), with a conical anode (d), with a multipoint cathode {e\ inverse-type ( / ) ; 1 - cathode, 2 - anode, 3 solenoid, 4 - drift tube, and 5 - magnetic lines

MICD's can also be classed by the configuration of lines of magnetic force. Diodes with a uniform (Fig. 23.1, c) and nonuniform (Fig. 23.1, a, d, e) magnetic field are distinguished. For MICD's of the first type, the induction of the magnetic field in the diode, B^, is equal to that in the region of beam transportation, BQ. The average radius of a thin-walled magnetized electron beam is approximately equal to the radius of the cathode (^b >rc). In a second-type MICD, the magnetic field at the cathode is lower than that in the drift tube. It increasesfi-omthe cathode in the direction normal to the lines of magnetic force. The degree of nonuniformity of the magnetic field is characterized by the bottleneck ratio (ratio of the magnetic field components parallel to the diode axis in the drift tube and at the cathode) k = BQ/B^ . The radius of a thin-walled annular beam for this type of diode with a magnetic field of uniform cross section, according to the law of conservation of magnetic flux, is given by

ANNULAR ELECTRON BEAMS

415 (23.1)

In inverse MICD's (see Fig. 23.1, /) both uniform and nonuniform magnetic fields are used. By the geometry of electrodes (Bugaev et al, 1991), conical (Fig. 23.1, a\ cylindrical (6), and planar diodes (c) are distinguished. In a conical diode, the beam radius and the electrode gap spacing can readily be controlled by moving the cathode along the axis. In a planar diode, it is possible to vary the transverse-to-longitudinal component ratio of the electric field at the cathode. However, in the region of the rectangular jump from the anode to the drift tube, the electric field is nonuniform, and this may result in an additional increase in transverse velocity of the beam electrons. The electric field can be made more uniform by using a conical anode (see Fig. 23.1, J). In MICD's, graphite and, more seldom, metal cathodes are used. Best investigated are plane (with a solid face surface) (see Fig. 23.1, b\ tubular (sometimes referred to as annular or edge) {b\ and multipoint cathodes (c). For electric field enhancement, the surface of a plane cathode facing the anode is made rough or, for a tubular cathode, the thickness of the wall is reduced. A disadvantage of a plane cathode is the emission current from the end face that occurs at a high electric field, which is parasitic in microwave devices. The use of multipoint cathodes is also limited by the EEE excited at the electrodes between which the points are located (see Fig. 23.1, e). Therefore, tubular cathodes are most widely used in relativistic microwave electronics. The induction of the magnetic field in an MICD is chosen so that, at a given voltage across the diode, the electrons emitted by the cathode do not cross the electrode gap of width t^ = |ra ~rc| (Fig. 23.1. b\ where r^ and r^ are the anode and the cathode radius, respectively. The magnetic field induction at which the electron current at the anode is cut off is referred to as critical, B^^. For relativistic electrons under the condition of conservation of the total magnetic flux in the electrode gap (Voronin and Lebedev, 1973; Lovelace and Ott, 1974), we have ll/2

ed,eff

2eV mc^ +

(23.2)

Here, d^f^ is the effective electrode gap spacing, which, in a planar diode, is equal to the cathode-anode separation. For a diode of cylindrical geometry (Lovelace and Ott, 1974), the effective gap spacing is given by Jefr=^(l-^/ra).

416

Chapter 23

For a cylindrical diode, the measured B^r (Bekefi et al, 1975; Orzechovski and Bekefi, 1976) coincides, within 5%, with that calculated by formula (23.2). However, both in normal diodes (Bekefi et aL, 1975; Gorev etai, 1985) and in inverse ones (Luckhardt and Fleischmann, 1977; Bakshaev et al, 1979), an unappreciable electron current across a magnetic field B>Bcr (less than 10% of the extracted electron beam current) was detected. The passage of this supercritical current in a diode, which is associated with diocotron instability of the electron layer around the cathode, correlates with the excitation of microwave oscillations of widely varying frequency (Bekefi et al, 1975; Orzechovski and Bekefi, 1976). For B>Bcr, the anode current may result in the formation of anode plasma, which is frequently undesirable. The conduction current flowing through the inner electrode (cathode) in a coaxial cylindrical diode with an external magnetic field B induces an azimuthal magnetic field BQ . In this case, the trajectories of electrons in the diode are determined by the combined influence of both magnetic fields (Voronin and Lebedev, 1973; Bekefi et al, 1975; Orzechovski and Bekefi, 1976). The insulation of an electrode gap created only by the field ê is termed magnetic self-insulation. It is widely used in high-current accelerators to transfer energy from energy stores to diodes through coaxial vacuum lines. The critical current at which the self-insulation mode is attained is given by 'cr'

7

eV

(23.3)

where Z^ is the wave resistance of the line and V is the voltage applied to the diode.

2.

DEVICE OF ELECTRON GUNS FOR MICD'S

The electron guns of MICD's intended for the production of high-current relativistic electron beams (REB's) have some design features. The main elements of such an electron gun (Fig. 23.2) are a vacuum insulator, a cathode-anode unit, and a magnetic system. The residual gas pressure in the acceleration tube is typically < 10"^ Pa. Vacuum insulators are made solid (Fig. 23.2, c) or section (Fig. 23.2, a, 6, d). Such an insulator is placed in a metal case {a, b) or serves as a case for the electron gun (c, d). The voltage is distributed over the insulator with the help of a capacitive, inductive, or resistive divider. If the first type of voltage division is used, the insulator sections - alternating dielectric and metal


417

rings - serve as capacitors. For inductive voltage division, a spiral is wound, with a certain pitch, on a solid insulator. For pulses of microsecond duration, resistive voltage dividers are used. For section insulators, these usually are chains of resistors fixed sequentially on grading metal rings. In solid insulators, resistive division of voltage can be realized with the help of a conducting liquid (electrolyte). In this case (Burtsev et al, 1979), the insulator (see Fig. 23.2, c) consists of two coaxial cylinders the space between which is filled with a solution of copper sulfate. The general requirement to voltage dividers is that the consumed current must be lower than the beam current. For a section insulator at a voltage pulse duration /p > 1 |Lis, the electric field strength averaged over the insulator length is chosen to lie within the limits 10-20 kV/cm (Martin and Clark, 1976). At nanosecond voltage pulse durations, it is several times greater, being typically < 80 kV/cm (Mesyats, 1974). {b)

(c)

1 2

^4

1 8

12

3

(d) ^ ^ 5 4 1 6

45

678

I

8

Figure 23.2. Schematic diagrams of the electron guns of MICD's: I - vacuum insulator, 2 cathode holder, 3 - reflector, 4 - anode, 5 - cathode, 6 - solenoid, 7 - magnetic lines, and 8 collector

Another challenge in providing efficient operation of electron guns is associated with the suppression of the backward current and the leakage from the cathode holder. These parasitic currents carry away part of energy and reduce the accelerator efficiency, which is determined as the ratio of the energy of the extracted electron beam to the energy of the high-voltage store. Besides, they influence the operation of the diode and the dielectric strength of the insulator. The backward current in an MICD is caused by the presence of an accelerating electric field component at the rear side of the cathode or cathode plasma. In first MICD's, the cathode was usually fixed on a holder of smaller diameter (see Fig. 23.1, a, b). At a high electric field, ectons arose at the rear side of the cathode, and the electron beam was accelerated along

418

Chapter 23

the lines of the falling magnetic field toward the vacuum insulator. In this electrode geometry, the backward current can exceed the current of the forward beam of electrons injected into the drift tube. As the electrons hit on the insulator, they initiate breakdown over its surface (Bugaev et al, 1991; Burtsev et al, 1979), while getting on the anode, they cause the formation of anode plasma and the breakdown of the diode. When the cathode and the cathode holder are of the same diameter, the backward current is formed at the rear side of the cathode plasma, which, at microsecond durations of the voltage pulse, expands for several centimeters transverse to a uniform magnetic field (see Fig. 23.1, c). In this case, the backward current is lower than the forward one and it increases as the cathode plasma expands. In a nonuniform magnetic field (see Fig. 23.1, J), this current arises simultaneously with the forward beam within the rise time of the voltage pulse upon excitation of EEE at the cathode edge. To suppress the backward current, it is necessary to realize conditions under which the lines of magnetic force that emerge at the surface of the anode unit and at the insulator do not cross the emitting surface of the cathode (Kovalev et al, 1977). With this purpose, a reflector of electrons of conical (Fig. 23.2. a\ plane {b) or spherical shape is generally placed between the cathode and the cathode holder. Thus the lines of magnetic force that, in view of the transverse expansion of the cathode plasma, correspond to the cathode radius should pass below the top of the cathode holder {a, b). Other methods of suppression of the backward current are based on a proper choice of the magnetic field configuration. Thus, the backward current in a uniform coaxial line, making 25-35% of the beam current, was eliminated by applying a magnetic field of bottleneck configuration behind the cathode (Bugaev et al, 1980). When the acceleration tube was immersed in a magnetic field (Fig. 23.2. c), the leakage current from the cathode holder (Burtsev et al., 1979) was also eliminated. In an electron gun (Voronin et al, 1981) where the solenoid was mounted inside the insulator {d), were practically no losses of the electron current. The efficiency of the accelerator with the conventional gun {b) at a voltage of 700 kV across the diode was 20%, while that of the accelerator with the gun shown in Fig. 23.2, d at the same voltage was 75-80%. These efficient electron guns are used only for the production of annular beams of small diameter. In the guns designed as one presented in Fig. 23.2, a, the cathode holder has a large area, especially in megavolt devices. This decreases the average electric field at which EEE arises and there is leakagefi*omthe cathode holder. Thus, in experiments carried out on the Gamma accelerator, the explosive emission delay time was 0.2-0.4 |is at JE' = 80-120 kV/cm and a few microseconds at E = 60 kV/cm (Bastrikov et al, 1988). The leakage currents were as large as 30-60 kA, and this substantially reduced the efficiency of the accelerator.


419

The advantage of the gun presented in Fig. 23.2, b is the small length of the cathode holder. For the reduction of the leakage current, an additional solenoid is used which is wound on the vacuum chamber.

3.

THE CATHODE PLASMA IN A MAGNETIC FIELD

As shown in Chapter 3, application of a magnetic field to an MICD does not change the time delay of EEE occurrence. However, this field strongly influences the process of plasma formation. Photographs of the plasma luminosity taken through the flange of the drift tube have shown that the number of EEE centers increases with magnetic field, improving the uniformity of the emission plasma layer. This also follows from the photograph of the plasma luminosity at the surface of a graphite cathode (Fig. 23.3). The processes of plasma generation were investigated in detail by Belomytsev et al (1980) and El'chaninov et al (1981). In an MICD, a voltage pulse of amplitude 200 kV and duration 5 ns was applied to a tubular graphite cathode whose wall thickness was 0.5 mm. The magnetic field in the diode was varied from zero to 10 kGs. The radius of the cathode flare (CF) was small (r = t^p = 0.1 mm). The principal screening effect was from the charge of the electron current. Investigations have shown that the number of emission centers increased in the main in the region of low magnetic fields, where TL » vt^ (rL being the Larmor radius of electrons). In this case, the linear density of flares over the perimeter can be approximated by the relation N oc 5", where a « 0.5, and the distance between two flares is -^45"^-^, where A - \ cm-kGs^^. In a rather strong magnetic field, where ''L'^ ^P5 the increase in number of ectons was slower.

Figure 23.3. Photographs illustrating the effect of the magnetic field on the density of cathode flares in a coaxial diode with a cylindrical cathode. B = 0 (a), 1 (b), 3 (c), and 10 kGs (d)

The formation of a plasma emission surface critically depends on the dynamics of formation of EEE centers, which was investigated for two

Chapter 23

420

essentially different experimental conditions (Mesyats and Proskurovsky, 1989). In one case, the electric field strength in the diode was insufficient for the excitation of explosive emission at the cathode and the primary ecton plasma was created by an igniting electrode powered from a special voltage source. In the other case, EEE was initiated by an external electric field. In the first experiment (Fig. 23.4, a), the cathode was a copper disk of diameter 12 mm and thickness 0.5 mm. The electrode separation was 5 mm. For studying the dynamics of formation of primary ectons, probes made of a thin copper wire were placed some distance fi-om the site of ignition. A rectangular voltage pulse of duration up to 1.3 |LIS and amplitude up to 30 kV was applied to the diode. Simultaneously, a pulse of duration 5 ns was applied to the igniting electrode, and thus the site of formation of a primary ecton was fixed. It was found that new ectons appeared practically only during the high-voltage stage of the vacuum discharge and were multiplied along the direction of the Ampere force. With the probes, the time delay t^ to the appearance of explosive emission fi-om a probe (Fig. 23.4, b) and the plasma potential at given points of the cathode were determined. The probe measurements and photographs of the plasma have shown that the velocity of motion of the boundary of formation of a primary ecton is (1-2)-10^ cm/s and does not depend on the magnetic field in the range 2-10 kGs.

4

6 8 jc [mm]

10

12

Figure 23.4. Sketch of a coaxial diode (a) and the time delay to the appearance of a signal from a probe placed at a distance x from the site of ignition (b)

The characteristics of the cathode plasma formed during EEE in a magnetic field were investigated by Mesyats and Proskurovsky (1989), Koshelev (1979), Gorbachev et al (1984), Stinnett et al (1982; 1984), and Baksht et al (1977). The ionic composition of the plasma was determined by its spectral luminescence in the region 200-700 nm. Both discharge-timeintegrated (Baksht et al, 1977) and time-resolved measurements were performed (Stinnett et al, 1982; 1984). The plasma density was measured with the help of laser interferometry (Baksht et al, 1911 \ Gorbachev et al, 1984), schlieren photography (Stinnett et al, 1982), and holography (Stinnett et al, 1984) and by the Stark breadth of the lines of hydrogen


421

(Bekefi et al, 1975; Baksht et al, 1977). The minimum plasma density evaluated by the above methods was 10^^-10^^ cm^; the spatial resolution was > 0.1 mm. The plasma temperature was estimated (Stinnett et al, 1982) by the relative intensity of the luminescence of spectral lines under the assumption of local thermodynamic equilibrium. The experiments were carried out with voltage pulses of nanosecond (< 100 ns) and microsecond (< 5 |is) duration and amplitude 0.2-2 MV. When comparing the results obtained under various experimental conditions, the linear current density I\= I/2nrc (current per unit length of the cathode perimeter) can be used as a parameter. Spectral investigations of the cathode plasma luminosity were carried out with graphite, aluminum, and copper cathodes (Baksht et al, 1973, 1977; Bugaev et al, 1981). The spectrograms obtained testified that the plasma contained species of the cathode material (All, AlII, AlIII, Cul, Cull), desorbed gas, and products of cracking of hydrocarbons (H, CI, CII, etc.), and the intensity of the luminescence of the last was much greater than that of the metal and was practically the same for all cathode materials (C, Al, Cu). Photometry in the axial direction showed a clear peak at the edge of the cathode. In the radial direction, the intensity of the lines of the metal (Cu I, Cu II) dropped in going deeper in the gap more abruptly than that of the lines of C2, Hp, and CII. The latter might be due to the different mechanisms of plasma expansion across and along the magnetic field. Investigations carried out by different researchers allow the following principal conclusions: the cathode plasma consists of the cathode material coming during EEE, the desorbed gas, and the products of cracking of the oil used for the production of vacuum in the diode; hydrogen can make an appreciable percentage of the plasma. For a wide range of experimental conditions {I\ = 0.1-10 kA/cm), the plasma density near the cathode is 10^^-10^^ cm"^ and quickly decreases in going deeper in the discharge gap. The plasma with a high density, n = 10^^-10^^ cm"^, which is necessary for self-maintenance of ectons, is localized near the cathode within 0.1 mm. The pressure of the magnetic field {B - 10"^ Gs) is considerably greater than the pressure of the cathode plasma (B^/Sn » nT) even at a distance of 0.1 mm from the cathode. After the occurrence of EEE, the cathode plasma appears in a magnetic field and starts moving both transverse to and along this field. It should be noted that the plasma processes were investigated in detail for a cylindrical MICD with a uniform magnetic field (Fig. 23.1, b). Therefore, it is convenient to consider the physical phenomena in an MICD of simple geometry as an example. To elucidate the role of the cathode plasma in the breakdown transverse to the magnetic field, the diode gap closure time /§ and the time delay to the

422

Chapter 23

appearance of cathode plasma were measured at different points in radius down to the anode with the help of the collector technique (Baksht et al, 1977). For tubular graphite and aluminum cathodes, the breakdown transverse to the magnetic field develops as the cathode plasma approaches the anode (Bugaev et al, 1981). The anode current before the closure of the diode gap was measured to be about 10% of the beam current. The time delay to the appearance of current toward the anode decreased with decreasing the electrode gap spacing d and for a current of 150 A and J = 0.65 cm it was ~ tJ2, Under these conditions, the velocity of the cathode plasma, v^^, averaged over the most part of the gap, and the rate of closure of the diode, dits, coincide to within the measurement error. Thus, the anode plasma, which can be formed if electrons reach the anode, has only a slight influence on the breakdown of the diode. Similar results were obtained for MICD's with plane graphite and copper cathodes (Baksht et al, 1977). Additional supporting evidence for the dominant role of the cathode plasma in the breakdown of a diode is experiments (Bugaev et ai, 1991) in which a change of the cathode geometry, with other things being equal, changed the value ofd/ts. Thus, for (i = 6 mm, F= 300 kV, and B>10 kGs, d/ts was 5-10^ cm/s for a plane cathode and < 2-10^ cm/s for a point cathode. For the latter type of cathode (d=3 mm, 5 = 1 2 kGs), d/ts, as follows from Table 23.1, varied with cathode material. Table 23.]. Material

Al

W

Mo

Cu

C

d/ts, 10^ cm/s

2.3

2.6

2.7

3.6

6.6

With the help of a drift tube, the dependences ts(Ib) and /s(^c) were investigated (Bugaev et al, 1983). The first one was obtained at a fixed voltage (F= 240 kV) and a fixed magnetic field {B = 24 kOs) for rc= 2.0 cm and d = 0.5 cm. The increase in beam current from 0.6 to 3.5 kA resulted in an insignificant (--15%) increase in diode closure time. Experimental check of the effect of re on 4 was carried out at a constant 5 = 24 kGs, J « 1 cm, and a linear beam current density I\J2Tirc « 0.09 kA/cm. As r^ was increased from 2 to 4.5 cm, the closure time increases from 1.4 to 1.8 |LIS. The dynamics of the cathode plasma motion transverse to the magnetic field in a cylindrical MICD depends on the cathode geometry and material, on the magnetic field, and on the plasma density and direction of its propagation (toward the anode or toward the axis of the diode) (Baksht et al, 1977). The plasma is essentially nonuniform: intense bursts are observed on the oscillograms of the collector current and PMT signal. Collector measurements for a graphite cathode have shown that the dynamics of the radial motion of the cathode plasma is different for


423

magnetic fields lower or greater of an optimum 5opt at which v^. averaged over the electrode gap is a minimum. For B < Bopu the radial velocity of the plasma, originally equal to 2-10^ cm/s, decreases and then increases a little. For B > Bopu it increases with distance from the cathode. In the case B « Bopu the plasma velocity in the gap is approximately constant. For metal cathodes (Al, Cu) and B > Bopu it increases with distance from the cathode. It seams that in this case, as well as for a graphite cathode at 5 > J?opt, the region where the plasma velocity decreases is closer to the cathode. It should be noted that at residual gas pressures over 0.1 Pa the velocity of propagation of the plasma front from cathode to anode does not depend on magnetic field (B = 6-27 kGs) and is invariable on a radius. The velocity of motion of the cathode plasma along the magnetic field, v\l, was measured with the help of a photoelectric technique (Bugaev et al, 1991), microwave interferometry (Nikonov et al, 1983), and capacitive voltage dividers (Bugaev et al, 1991). With an eight-millimeter-band microwave interferometer (Nikonov et al, 1983), it was possible to measure plasma densities « > 10^^ cm^ and thus follow the motion of low-density peripheral layers. Capacitive voltage dividers arranged along a drift tube are usually used to measure the potential difference between the electron beam and the drift tube, AFb, which is lower than the voltage applied to the diode. As the cathode plasma approaches a capacitive voltage divider, the amplitude of the signal of the divider increases to a value corresponding to the voltage across the diode. By the inflection in the oscillogram of the signal from the capacitive gage, the time is determined at which the plasma carrying the potential of the cathode approaches the gage. The velocity of propagation of the collector plasma along the magnetic field was also measured using a photoelectric technique (Bugaev et al, 1991) and microwave interferometry (Nikonov et al, 1983). Despite the rather small number of techniques used, the experimenters were managed to distinguish the contributions of the cathode and collector plasmas to the breakdown of a diode and to follow the expansion of the cathode plasma transverse to and along the magnetic field. The current pulse duration of the beam formed in an MICD can also be limited by the breakdown along the magnetic field. The mechanism of the vacuum breakdown of the cathode-collector gap and the motion of the cathode plasma along a uniform magnetic field were studied by Bugaev et al (1991) and Nikonov et al (1983). The longitudinal vacuum breakdown in diodes with tubular cathodes (C, Al) of external radius re = 3.0 cm {d = 2.6 cm) is best investigated. A voltage pulse of amplitude 200 kV and duration -3.5 \xs was applied to the diode: the beam current was about 1.5 kA. The distance was varied with the help of a movable collector. The magnetic field was varied in the limits 3-27 kGs; the residual gas pressure

Chapter 23

424

was 10"-^-10~^ Pa. To examine the propagation of the cathode plasma and the formation and expansion of the collector plasma use was made of a system of five capacitive voltage dividers, placed sequentially in the drift tube, and a photoelectric technique. With the help of these techniques, the time delay t^ to the occurrence of the cathode plasma at various distances from the cathode and the time of closure of the cathode-collector gap were measured. T

/

6 ^ -

ij

2X

^ y ^

-jj[-

1

10

1

1

20 30 z [cm]

1

40

Figure 23.5. Time delay to the appearance of the cathode plasma, /a, measured by a PMT (1-4) and capacitive voltage dividers (5), as a function of the distance from a graphite cathode and the time of closure along the magnetic field (6) as a function of the cathode-collector separation. B=\S kGs,p = 3-10-3 p^. ^ = ^QOFQ (7), 3Fo (2), 1.5Fo (3), andFQ (4)

All measurements were performed with graphite cathodes and a collector in a magnetic field of 18 kGs. From the results obtained (Fig. 23.5), it follows that the td values measured by two methods agree to each other and to the closure times for various cathode-collector separations [lc/t\i « (1-1.6)-10^ cm/s]. The increase in residual gas pressure from 10"^ to 10"^ Pa resulted in a 20-30% increase in t^ (4 = 20 cm), and /a increased as well. Measurements by the photoelectric technique have shown that the time delay to the occurrence of the cathode plasma at collectors made of graphite and stainless steel was equal, respectively, to 1.2 and 0.25 |as, and the velocity of its propagation along the magnetic field was about 5-10^ cm/s in both cases. The power density of the beam at a collector was -10 MW/cm^. The velocity of the collector plasma measured by a microwave interferometer under similar experimental conditions (Nikonov etaL, 1983) was (6-7)-10^ cm/s. At megavolt voltages across the diode and the beam power density at a collector equal to about 1 GW/cm^, the influence of the collector plasma on the breakdown along the magnetic field was found to be unappreciable (Bugaev et al, 1991). Thus, the breakdown of the cathodecollector gap in a uniform magnetic field is determined by the propagation of the plasma formed at the cathode during explosive electron emission.


425

1.00

0.75

0.50

Figure 23.6. Time delay to the appearance of the cathode plasma as a function of the distance from the cathode. 4 = 10 kA, F= 0.9 MB (7) and 20 kA, 1.3 MV (2)

The velocity of the cathode plasma front increases with current and reaches ?;|| «10^ cm/s for 4 ^ 1 0 kA. As the current is further increased, V\\ does not increase; however, the region of accelerated motion of the plasma near the cathode becomes smaller. The measurements of the time delay to the occurrence of the cathode plasma at various distances from the cathode for /b > 10 kA are given in Fig. 23.6. Thus, it is possible to distinguish two components in the motion of cathode plasma along a magnetic field: a hydrodynamic expansion with a constant velocity of (2-2.6)-10^ cm/s and an accelerated motion.

4.

FORMATION OF ELECTRON BEAMS

Let us consider the principal characteristics (current, potential, and structure) of annular electron beams formed in cylindrical (ra = R) MICD's (see Fig. 23.1, b) with a uniform magnetic field. Investigations have shown (Gleizer et al, 1975; Voronin et al, 1978) that the beam current depends on magnetic field. As the magnetic field is increased, the current increases for B < 5cr, reaches a maximum at 5 « B^x, decreases for B > 5cr, and becomes practically independent of magnetic field for B > (2-3)5cr. For B < B^r, the beam current is lower than the maximum current because of the arrival of electrons at the anode. At 5 « B^^, the thickness of an annular beam is a maximum and its external radius is close to the radius of the drift tube. The basic contribution to the beam current is made by the electrons emitted from the cylindrical surface of the plasma cathode transverse to the magnetic field. For B » B^v, the external radius of the beam is equal to the external radius of the cathode plasma and the main contribution to the beam current is made by the electrons emitted from the face surface of the plasma along the magnetic field.

426

Chapter 23

In solving the problem on the formation of an REB in an MICD, two models were used that supposed that the beam current is determined, respectively, by the throughput of the drift tube (Voronin and Lebedev, 1973; Nechaev and Fuks, 1977) and by the region of formation of the beam, i.e., by the diode (Fedosov et al, 1977; Fedosov, 1982). We now consider the second model since it better agrees with experiment. The problem was solved for a cylindrical MICD with a tubular cathode of wall thickness he and an infinitely strong guide magnetic field. The approximation of an infinitely strong magnetic field obviously holds if (Fedosov e/a/., 1977) (23.4)

where T = eERImc^ ^\; p = vjc {VQ being the velocity of electrons in the drift channel), and R = ra. The electron flow in a diode under these conditions is described by the Poisson equation A , = ^ ^ ,

, =U ^ ,

(23.5)

where j is the beam current density depending only on radius and v|/ is the potential. The boundary conditions are: y = F = 1 + eVImc^ at the anode and Y = 1 at the cathode. Besides, the emissivity of the cathode is assumed infinite. Multiplying (23.4) by dyldz, integrating over the internal space of the diode (except the volume occupied by the cathode), and using Eq. (23.5) for the drift space and the boundary conditions, we obtain

,,(,,.,)-2r = -.n|J^0j(..A].,..

(23.6)

Here, y^ = 1 + e\\fb/mc^ is the relativistic factor at the external boundary of the electron beam in the drift space, and the integration on the right side is carried out over the beam thickness at z = +oo. It should be noted that (23.6) is a consequence of the laws of conservation for the energy and the z-component of a pulse in the system. For a rather thin-walled beam we have rhc/\^rcln(rjrc)'\\\xs in MICD's of this type. Here, the increase in beam energy is due to the increase in dimensions of the region of REB formation. An increase in pulse duration ^p is achieved by using a nonuniform magnetic field increasing from cathode to anode (Dolgachev and Zakatov, 1983). Accelerators based on MICD's are described in Chapter 28 where we discuss the operation of high-power microwave generators.


431

REFERENCES Bakshaev, Yu. L., Blinov, P. I., Golgachev, G. P., and Skoryupin, V. A., 1979, Acceleration of Ions in a Magnetically Insulated Diode, Fiz. Plazmy. 5:129-131. Baksht, R. B., and Mesyats, G. A., 1970, Effect of a Transverse Magnetic Field on the Electron Beam Current at the Initial Stage of a Vacuum Discharge, /zv. Vyssh. Uchebn. Zaved, Fiz. 7:144-146, Baksht, R. B., Bugaev, S. P., Koshelev, V. I., and Mesyats, G. A., 1977, On the Properties of the Cathode Plasma in a Magnetically Insulated Diode, Pis 'ma Zh. Tekh. Fiz. 3:593-597. Baksht, R. B., Kudinov, A. P., and Litvinov, E. A., 1973, Investigation of Some Characteristics of the Cathode Flare Plasma, Zh. Tekh Fiz. 43:146-151. Bastrikov, A. N., Bugaev, S. P., Kiselev, I. N., Koshelev, V. I., and Sukhushin, K. N., 1988, Formation of Annular Microsecond Electron Beams at Megavolt Voltages across the Diode, Ibid. 58:483-488. Bekefi, G., Orzechovski, T. J., and Bergeron, K. D., 1975, Electron and Plasma Flow in a Relativistic Diode Subjected to a Crossed Magnetic Field. In Electron Research and Technology: Proc. Intern. Top. Electron Conf. Beam Res. Technol., Albuquerque, NM, Vol. 1, pp. 303-345. Belomytsev, S. Ya., Korovin, S. D., and Mesyats, G. A., 1980, The Screening Effect in HighCurrent Diodes, Pw'/wai Z/;. Tekh. Fiz. 6:1089-1092. Bolotov, V. E., Zaitsev, N. I., Korablev, G. S., Nechaev, V. E., Sominsky, G. G., and Tsybin, O. Yu., 1980, Examination of the Possibility of Diagnosing High-Current Relativistic Beams by the Ion Current Method, Ibid. 6:1013-1016. Bugaev, S. P., Kanavets, V. I., Koshelev, V. I., and Cherepenin, V. A., 1991, Relativistic Multiwave Microwave Oscillators (in Russian). Nauka, Novosibirsk. Bugaev, S. P., Kim, A. A., Klimov, A. I., and Koshelev, V. I., 1980, On the Mechanism of the Vacuum Breakdown and Cathode Plasma Expansion Along the Magnetic Field in Foilless Diodes, Zh. Tekh. Fiz. 5:2463-2465. Bugaev, S. P., Kim, A. A., Klimov, A. I., and Koshelev, V. I., 1981, On the Mechanism of the Propagation of the Cathode Plasma Transverse to the Magnetic Field in Foilless Diodes, Fiz. Plazmy. 7:529-539. Bugaev, S. P., Kim, A. A., Koshelev, V. I., and Khryapov, P. A., 1983, Experimental Investigation of the Motion of the Cathode Plasma Transverse to the Magnetic Field in Magnetically Insulated Diodes, Ibid. 9:1287-1291. Burtsev, V. A., Vasilevsky, M. A., Gusev, O. A., Roife, I. M., Seredenko, E. V., and Engelko, V. I., 1979, A Microsecond High-Current Electron Beam Accelerator, Prib. Tekh. Eksp. 5:32-35. Close, R., Palevsky, A., and Bekefi, G., 1983, Radiation Measurement from an Inverted Relativistic Magnetron, J. Appl. Phys. 54:4147-4151. Dolgachev, G. I. and Zakatov, L. P., 1983, On the Possibility of Increasing the Lifetime of a Magnetic Insulation, Pis 'ma Zh. Tekh. Fiz. 9:964-967. Dreike, P., Eichenberger, C , Humphries, S., and Sudan, R., 1976, Production of Intense Proton Fluxes in a Magnetically Insulated Diode, J. Appl. Phys. 48:85-87. El'chaninov, A. S., Zagulov, F. Ya., Korovin, S. D., and Mesyats, G. A., 1981, On the Stability of Operation of the Vacuum Diodes of High-Current Relativistic Electron Beam Accelerators, Zh. Tekh. Fiz. 51:1005-1007. Fedosov, A. I., 1982, Candidate's Degree Thesis Electron Flows in Magnetically Insulated Foilless Diodes and Lines (in Russian). Inst, of High Current Electronics, Tomsk. Fedosov, A. I., Litvinov, E. A., Belomytsev, S. Ya., and Bugaev, S. P., 1977, On the Calculation of the Characteristics of the Electron Beam Formed in a Magnetically Insulated Diode,/zv. Vyssh. Uchebn. Zaved, Fiz. 10:134-135.

432

Chapter 23

Friedman, M. and Ury, M., 1970, Production and Focusing of High Power Relativistic Annular Electron Beam, Rev. Sci. Instrum. 41:1334-1335. Fuks, M. I., 1982, Formation of a High-Current Relativistic Electron Beam in a Magnetically Insulated Coaxial Diode, Zh. Tekh. Fiz. 52:675-679. Gleizer, I. Z., Didenko, A. N., Zherlitsyn, A. G., Krasik, Ya. E., Usov, V. P., and Tsvetkov, V. I., 1975, Production of an Annular Relativistic Electron Beam in a Magnetically Insulated Coaxial Gun, Pis'ma Zh Tekh. Fiz. 1:463-468. Gorbachev, S. I., Zakharov, S. M., Pikuz, S. A., and Romanova, V. M., 1984, C02-Laser Interferometry of the Explosive-Emission Plasma in a Microsecond High-Current Diode, Zh. Tekh. Fiz. 54:399-401. Gorev, V. V., Dolgachev, G. I., Zakatov, L. P., Oreshko, A. G., and Skoiyupin, V. A., 1985, Dynamics of the Magnetic Insulation Breakage in an Electron Diode, Fiz. Plazmy. 11:782-786. Gorshkova, M. A., Il'in, V. P., Nechaev, V. E., Sveshnikov, V. M., and Fuks, M. I., 1980, The Structure of the High-Current Relativistic Electron Beam Formed by a Magnetically Insulated Coaxial Gun, Zh. Tekh. Fiz. 50:109-114. Jones, M. E. and Thode, L. E., 1980, Intense Annular Relativistic Electron Beam Generation in Foilless Diodes, J. Appl. Phys. 50:5212-5214. Koshelev,V. I., 1979, On the Expansion of the Cathode Plasma in a Transverse Magnetic Field, Fiz. Plazmy. 5:698-701. Kovalev, N. F., Nechaev, V. E., Petelin, M. I., and Fuks, M. I., 1977, On the Stray Currents in Magnetically Insulated High-Current Diodes, Pis'ma Zh. Tekh. Fiz. 3:413-416. Lovelace, R. N. and Ott, E., 1974, Theory of Magnetic Insulation, Phys. Fluids. 17:1263-1268. Luckhardt, S. C. and Fleischmann, H. H., 1977, Microsecond-Pulse Insulation and Intense Ion Beam Generation in a Magnetically Insulated Vacuum Diode, Appl. Phys. Lett. 30:182-185. Martin, T. H. and Clark, R. S., 1976, Pulsed Microsecond High-Energy Electron Beam Accelerator, Rev. Sci. Instrum. 47:46-463. Mesyats, G. A., 1974, Generation of High-Power Nanosecond Pulses (in Russian). Sov. Radio, Moscow. Mesyats, G. A. and Proskurovsky, D. I., 1989, Pulsed Electrical Discharge in Vacuum. Springer-Verlag, Berlin-Heidelberg. Nechaev, V. E. and Fuks, M. I., 1977, Formation of Annular Relativistic Electron Beams in Magnetically Insulated Systems (Approximate Calculations), Zh. Tekh. Fiz. 47:2347-2353. Nikonov, A. G., Roife, I. M., Saveliev, Yu. M., and Engelko, V. I., 1983, On the Operation of a Magnetically Insulated Diode with a Long Pulse Duration, Ibid. 7:683-690. Orzechovski, T. J. and Bekefi, G., 1976, Current Flow in a High-Voltage Diode Subjected to a Crossed Magnetic Field, Phys. Fluids. 19:43-51. Stinnett, R. W., Allen, G. R, Davis, H. P., Hussey, T. W., Lockwood, G. J., Palmer, M. A., Ruggles, L. E., Widman, A., and Woodall, H. N., 1984, Cathode Plasma Formation in Magnetically Insulated Transmission Lines. In Proc. XIISDEIV, Berlin, Vol. 2, pp. 397-400. Stinnett, R. W., Palmer, M., Spielman, R., and Bengtson, R., 1982, Small Gap Magnetic Experiments in Magnetically Insulated Transmission Lines. In Proc. XISDEIV, Columbia, SC, pp. 281-285. Straw, D. C. and Clark, M. C, 1979, Electron Beams Generated in Foilless Diodes, IEEE Trans. Plasma Sci. 26:4202-4204. Voronin, V. S. and Lebedev, A. N., 1973, Theory of Magnetically Insulated High-Voltage Coaxial Diodes, Zh. Tekh. Fiz. 43:2591-2598. Voronin, V. S., Krastelev, E. G., Lebedev, A. N., and Yablokov, B. N., 1978, On the Limiting Current of a Relativistic Electron Beam in Vacuum, Fiz. Plazmy. 4:604-610. Voronin, V. S., Zakharov, S. M., Kazansky, L. N., and Pikuz, S. A., 1981, A Microsecond Monoenergetic High-Current Electron Beam with a Stabilized Current, Pis 'ma Zh. Tekh. Fiz. 7:1224-1227.

Chapter 24 DENSE ELECTRON BEAMS AND THEIR FOCUSING

1.

THE DIODE OPERATION

In this chapter, we consider the diodes intended for the production and focusing of dense high-current relativistic electron beams (REB's) with a pulse duration tp < 10"^ s. Reviews of the studies in this field are given by Tarumov (1990), Gordeev (1990), and Mesyats (1994). By dense highcurrent REB's we imply such beams whose current is limited by the self magnetic field. This field can be used to focus the beam. The operation of this type of diode is strongly influenced by the cathode and anode plasma layers, and, unlike in the diodes described in the previous chapter, the anode plasma is present practically continuously due to the intense energy flux onto the anode. A feature of these devices is a strong electric field between the electrodes. This results in favorable conditions for a great number of emission centers and ectons occurring on the cathode resulting in the formation of uniform cathode plasma. To produce rectangular pulses, it is necessary to have a pulse rise time t^ /cr), but also the energy input to the anode material should surpass some critical level (300-450 J/g for copper and brass and 450-650 J/g for graphite). Comparing the current-voltage characteristics of the diodes of the Camel and OWL II accelerators, these authors suggested that the longest time of existence of the mode of focusing is achieved by the earliest and simultaneous fulfillment of these two conditions. In conclusion, we mention the sharp focusing of a high-current REB in the diode of the PROTO I accelerator (3 MV, 800 kA, 24 ns) attained as a result of careful optimization of the shape and dimensions of the cathode having a conical end (Jonas, 1978). The conclusion of this work is that to produce high current densities (>10 MA/cm^) and attain highly efficient focusing, it is necessary to use the least allowable cathode diameter and cathode-anode gap spacing by lowering the prepulse voltage. In this experiment, the average power density of the electron beam in the focal spot reached 10^3 W/cml

DENSE ELECTRON BEAMS AND THEIR FOCUSING

453

REFERENCES Arzhannikov, A. V. and Koidan, V. S., 1980, The Microstructure of an Electron Beam and the Current-Voltage Characteristic of a Relativistic Diode in a Strong Magnetic Field (in Russian). Preprint No. 80-73, Inst, of Nuclear Physics, Siberian Division, USSR AS, Novosibirsk. Babykin, V. M., Rudakov, L. I., Skoryupin, V. A., Smimov, V. P., Tarumov, E. Z., and Fanchenko, S. D., 1982, Inertially Confined Fusion Based on High-Current REB Generators, Fiz. Plazmy. 8:901-914. Barker, R. J., Goldstein, S. A., and Lee, R. E., 1980, Computer Simulation of Intense Electron Beam Generation in a Hollow Cathode Diode. NRL' Memorandum Rept. 4279. Sept. 5. Blaugrung, A. E., Cooperstein, G., and Goldstein, S. A., 1975, Processes Governing Pinch Formation in Diodes. In Proc, I Intern. Topical Conf. Power Electron and Ion Beam Research and Technology, Albuquerque, NM, Vol. 1, pp. 233-246. Bradley, L. P. and Kuswa, G. W., 1972, Neutron Production and Collective Ion Acceleration in a High-Current Diode, Phys Rev. Lett. 29:1441-1445. Breizman, B. R. and Ryutov, D. D., 1975, On the Theory of Focusing of Relativistic Electron Beams in Diodes, Dokl. ANSSSR. 225:1308-1311. Cooperstein, G., Goldstein, S. A., Mosher, D., et al., 1979, Generation and Focusing of Intense Light Ion Beams from Pinched-Electron Beam Diodes. In Proc. Ill Intern. Topical Conf High Power Electron and Ion Beam Research and Technology, Novosibirsk, Vol. 2, pp. 567-575. Davidson, R. C, 1974, Theory of Nonneutral Plasmas. Benjamin, London. Di Capua, M., Creedon, J., and Huff, R., 1976, Experimental Investigation of High-Current Relativistic Electron Flow in Diodes, J. Appl. Phys. 47:1887-1896. Goldstein, S. A., Davidson, R. C, Lee, R., Siambis, J. G., 1975, Theory of Electron and Ion Flow in Relativistic Diodes. In Proc. I Intern. Topical Conf. Power Electron and Ion Beam Research and Technology, Albuquerque, NM, Vol. 1, pp. 218-232. Goldstein, S. A., Davidson, R. C, Siambis, J. G., and Roswell, Lee, 1974, Focused-Flow Model of Relativistic Diodes, Phys. Rev. Lett. 33:1471-1474. Gordeev, A. V., 1987, On the Current of a Relativistic Blade Diode in a Strong Longitudinal Magnetic Field, Pis'ma Zh. Tekh. Fiz. 13: 410-417. Gordeev, A. V., 1990, Theory of High-Current Diodes. In Generation and Focusing of HighCurrent Relativistic Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 182-192. Gordeev, A. V., Zazhivikhin, V. V., Korolev, V. D., et al., 1982, Magnetic Self-Insulation of Vacuum Lines. In Problems of Physics and Technology of Nanosecond Discharges. Nanosecond Generators and Breakdown in Distributed Systems, Moscow, pp. 91-111. Goldstein, S. A., Swain, D. W., Hadley, G. R., and Mix, L. P., 1975, Anode Plasma and Focusing in REB Diodes. In Proc. I Int. Topical Conf. High Power Electron Beam Research and Technology, Albuquerque, NM, Vol. 1, pp. 262-283. Ignatenko, V. P., 1962, Ion Neutralization of the Space Charge of Relativistic Electron Flows, Zh. Tekh. Fiz. 32:1428-1432. Jonas, G., 1974, Electron Beam Induced Pellet Fusion: Sandia Rept. SAND-74-5367. Present. IVNat. School Plasma Phys., Novosibirsk, USSR. Jonas, G., 1978, Developments in Sandia Laboratories Particle Beam Fusion Programme. In Plasma Phys. and Control. Nucl. Fusion Res. (Vienna, IAEA 1978). In Proc. VII Intern. Conf, Innsbruck, Austria, Vol. 3, pp. 125-133.

454

Chapter 24

Jonas, G., Poukey, J. W., Prestwich, K. R., Freeman, J. R., Toepfer, A. J., and Clauser, M. J., 1974, Electron Beam Focusing and Application to Pulsed Fusion, Nucl Fusion, 14:731-740. Jonas, G., Prestwich, K. R., Poukey, J. W., Freeman, J. R., 1973, Electron Beam Focusing Using Current-Carrying Plasmas in High vly Diodes, Phys. Rev. Lett. 30:164-167. McClenahan, C. R., Backstrom, R. C, Quintenz, J. P., et al., 1983, Efficient Low-Impedance High Power Electron Beam Diode. In Proc. V Intern. Topical Conf. High Power Electron and Ion Beam Research and Technology, San Francisco, CA, pp. 147-150. Mesyats, G. A., 1994, Ectons (in Russian). Nauka, Ekaterinburg, Vol. 3. Mix, L. P., Kelly, J. G., Kuswa, G. W., Swain, D. W., and Olsen, J. N., 1973, Holographic Measurements of the Plasmas in a High-Current Field Emission Diode, J. Vac. Sci. Technol. 10:951-953. Morrow, D. L., Phillips, J. D., Stringfield, R. M., Jr., Doggett, W. O., and Bennett, W. H., 1971, Concentration and Guidance of Intense Relativistic Electron Beams, Appl. Phys. Lett. 19:441-443. Poukey, J. W., 1975, Z < 1 Q Pinched Electron Diodes. In Proc. I Intern. Topical Conf. High Power Electron and Ion Beam Research and Technology, Albuquerque, NM, Vol. 1, pp. 47-254. Poukey, J. W. and Toepfer, A. J., 1974, Theory of Superpinched Relativistic Electron Beams, Phys. Fluids. 1\\S%2A59\. Poukey, J. W., Freeman, J. R., and Yonas, G., 1973, Simulation of Relativistic Electron Beam Diodes, J. Vac. Sci. Technol. 6:954-958. Rukhadze, A. A., Bogdankevich, L. S., Rosinsky, S. E., and Rukhlin, V. G., 1980, Physics of High-Current Relativistic Electron Beams (in Russian). Atomizdat, Moscow. Sanford, T. W. L., Lee, J. R., Halbleib, J. A., Quintenz, J. P., Coats, R. S., Stygar, W. A., Clark, R. E., Faucett, D. L., Webb, D., and Heath, C. E., 1986, Electron Flow and Impendance of an 18-Blade Frustum Diode, J. Appl. Phys. 59:3868-3880. Seamen, J. F., Van Devender, J. P., Johnson, D. L., et al., 1983, SPEED, a 2.5 TW, Low Impedance Pulsed Power Research Facility. In Proc. IV Pulsed Power Conf, Albuquerque, NM, pp. 68-70. Spense, P., Triebes, K., Genuario, R., and Pellinen, D., 1975, REB Focusing in High Aspect Ratio Diodes. In Proc. I Intern. Topical Conf. Power Electron and Ion Beam Research and Technology, Albuquerque, NM, Vol. 1, pp. 346-363. Tarumov, E. Z., 1990, Production and Focusing of High-Current Relativistic Electron Beams in Diodes. In Generation and Focusing of High-Current Relativistic Electron Beams (in Russian, L. I. Rudakov, ed.), Energoatomizdat, Moscow, pp. 122-181. Ware, K., Loter, N., Montgomery, M., et al., 1985, Bremsstrahlung Source Development on Black Jack 5'. In Proc. V IEEE Pulsed Power Conf, Arlington, VA, pp. 118-121.

PART 9. HIGH-POWER PULSE SOURCES OF ELECTROMAGNETIC RADIATION

Chapter 25 HIGH-POWER X-RAY PULSES

1.

HISTORICAL BACKGROUND

First experiments on the production and application of high-power x-ray pulses were performed early in the last century. In these experiments, lightning discharges received by an antenna in the form of a wire stretched over insulators were used to generate high-voltage pulses of 12-15 MV that were supplied to a vacuum discharge tube. In this way, high-power pulsed x-rays capable of penetrating a 20-cm thick lead plate were obtained. However, systematic studies aimed at developing high-power x-ray pulse devices were started between the late 1930s and the early 1940s by Steenbeck (1938) and by Kingdon and Tanis (1938). The latter authors used the spark of an auxiliary discharge between a mercury cathode and an ignitor electrode to obtain an electron source. X-ray tubes were filled with lowpressure mercury vapor. An important step in the development of pulsed x-ray technology was the creation of sealed-off and demountable high-vacuum tubes. First coldcathode vacuum tubes intended to generate pulsed x-rays were developed by Mtihlenpfordt (1939) and Slack and Ehrke (1941). The sealed-off threeelectrode tube described by Slack and Ehrke (1941) had a plane tungsten anode and a focusing cathode head with a slot in which the cold cathode was mounted. The edges of the slot acted as an ignitor electrode. The demountable two-electrode tube with a conical tip anode and a conical hollow cathode with sharp edges developed by Mtihlenpfordt (1939) operated under continuous evacuation. Its modified version contained an ignitor electrode. Subsequently, tubes of this type were improved (Tsukerman and Manakova, 1957; Ftinfer, 1953) in order to produce more

458

Chapter 25

stable intense x-ray pulses. In particular, a dielectric was introduced in the space between the ignitor electrode and the cathode to stabilize the excitation of an igniting spark and to increase the amount of the spark plasma. Much work was performed to study the effect of the shape of the anode and cathode on the parameters of x-ray pulses. The pulse duration of x-rays produced by such tubes was 1-10 |is. Subsequently, two-electrode vacuum x-ray tubes came into use in pulsed x-ray technology. Based on studies performed by Dyke and co-workers (Martin et al, 1960), sealed-off multipoint pulsed tubes with field emission (FE) were developed. In order to obtain microsecond x-ray pulses, Tsukerman and Manakova (1957) used two-electrode vacuum tubes and were the first to design x-ray apparatus with a voltage of up to 1.5 MV, which was record voltage at that time. They also believed that field emission occurs in tubes of this type. However, investigations that have been performed since that time suggest that, besides, another type of emission, called explosive electron emission (EEE) (Mesyats and Proskurovsky, 1971), takes place in this case (see Chapter 3). The evolution of concepts concerning this type of emission is associated with two closely related trends: the study of FE mechanisms for the limiting current density and the transition of FE to a vacuum arc, on the one hand, and the study of the development of a vacuum breakdown between macroscopic electrodes, on the other hand. After a thorough analysis of the EEE phenomenon, the dynamic current-voltage characteristics of x-ray tubes and the parameters of x-ray pulses could be calculated and the mechanisms of the material removal ft'om cathode and anode could be understood. This makes it possible to design tubes with a long service life, taking into account prescribed pulse parameters. An important stage in the development of pulsed x-ray technology was the creation of high-power generators of nanosecond x-ray pulses (Tsukerman et al, 1971; Martin, 1996). Such generators are based on twoelectrode explosive-emission tubes with a high-power nanosecond pulse generator as a power supply. Powering x-ray tubes with such pulses makes it possible to reduce considerably the overall dimensions of the devices due to a significant increase in the electric strength of their insulation. The advances in this field were also determined to a considerable extent by achievements in the generation of high-voltage nanosecond pulses (Vorob'ev and Mesyats, 1963). In modem x-ray devices, tubes with EEE are mainly used for the production of high-power pulses. During the first years following their creation, pulsed devices were widely used for studying fast processes, but at present, such devices are employed for flaw detection of weld joints in industrial metal structures under nonstationary conditions, in medical

HIGH'POWER X-RAY PULSES

459

diagnostics, in the x-ray diffraction analysis of substances, in location, and in other fields of science and technology. The components of industrial devices (high-pressure spark gaps, pulsed capacitors, and primary switches) are being improved continually. Investigations aimed at a considerable reduction of pulse duration and an increase in power of pulsed x rays are being continued. Laboratory prototypes of subnanosecond x-ray pulse generators have already been developed. An important event in pulsed x-ray technology was the creation of superpower nanosecond devices with an energy of accelerated electrons of 10^ -10^ eV and a current of up to 10^ A. A review of publications in this field is given by Mesyats et al (1983). A lot of the credit must go to Martin (1996) who pioneered the creation of superpower x-ray generators, which are used both for x-raying and for studying the effect of superpower radiation on various objects. This facilitated the development of high-current beam technology. However, his work remained unpublished for many years. In this chapter, we will consider only two types of high-power nanosecond x-ray pulse generator. The first type includes small-size systems with a pulse power of 10^-10^ W, voltage of 100-500 kV, and pulse duration of 10"^-10"^ s. The other type includes superpower x-ray devices with a pulse power of 10^^-10^^ W, voltage of up to 10^ V, and duration of 10"^-10"^ s. The former are used in research work, flaw detection, medicine, for sterilizing microorganisms, etc., while the latter are used in x-ray diffraction analysis of high-energy density explosive processes and for studying the effect of superpower radiation on various objects.

2.

ON THE PHYSICS OF X RAYS

X rays are electromagnetic oscillations in the wavelength range 10-10"^ nm. They are excited by bombardment of a solid target with a highenergy electron beam. In modem devices used for the production of highpower x-ray pulses, the maximum electron energy reaches 30 MeV. Electrons penetrating into the target are scattered, i.e., deflected from the initial direction of motion, and lose their energy. For an electron energy W W^r the radiation loss is dominant. The value of the critical energy W^r (in MeV) is determined by the following approximate relation: ^cr«1600m,c2/Z.

(25.5)

For example, W^v^ 11 MeV for tungsten (Z = 74), which is widely used as the target material for pulsed x-ray tubes. As the electron energy is increased, the ionization loss first decreases and then slowly increases. The minimum losses for tungsten and aluminum targets correspond XoW^X and 1.5 MeV, respectively. The radiation loss is practically independent of the electron energy in the energy range W < nieC^ and monotonicly increases with Win the range of high energies. Thus, a beam of accelerated electrons bombarding a target excites two types of X rays simultaneously, viz., bremsstrahlung with a continuous spectrum and characteristic radiation with a line spectrum. The origins of these rays are basically different: bremsstrahlung is emitted by the bombarding electrons themselves, while characteristic radiation is emitted by target atoms ionized in their inner shells as they revert to the normal state. For high electron energies, the bremsstrahlung power is considerably higher than the characteristic radiation power. Therefore, we can refer to a pulsed device as a powerful source of bremsstrahlung pulses. However, by an appropriate choice of experimental conditions (acceleration of electrons to comparatively low energies, use of low-Z targets, and filtration of radiation), it is possible to obtain characteristic radiation with a pulse power exceeding that of the accompanying bremsstrahlung. Pulsed characteristic radiation is used, for example, in x-ray diffraction analyses. In order to generate bremsstrahlung, bulk and thin targets are used. In a bulk target, the kinetic energy of electrons is absorbed completely or almost completely (in contrast to a thin target in which a passing electron loses an insignificant part of its energy; in thin targets, nonradiative bremsstrahlung and multiple scattering processes practically do not occur). Targets of commercial x-ray tubes (including pulsed tubes) can be classified as bulk targets. Figure 25.1 shows the wavelength dependence of the spectral intensity for a bulk target. As the accelerating voltage is increased, the spectral intensity of radiation at a given wavelength grows. Simultaneously, the spectral composition of the radiation changes: the spectrum shifts toward shorter wavelengths.

Chapter 25

462

0.02

0.04

0.06 X [nm]

Figure 25J. Wavelength dependence of spectral intensity on for different electronaccelerating voltages

The same spectral intensity curves converted to those in terms of energy are approximated quite correctly by the expression (Blokhin, 1957) /e = const (8n,ax~e),

(25.6)

which is valid for the entire spectrum except a narrow region adjoining its boundary 8max • This conclusion is in good agreement with the theory of continuous spectrum developed by ICramers (Blokhin, 1957). Using classical notions and the correspondence principle, we can calculate the energy distribution of the bremsstrahlung flux excited in a bulk target. The corresponding expression in a slightly modified form convenient for applications is Pe=ô/2:(Smax-e),

(25.7)

where P^ is the spectral density of the radiation flux, ko is the proportionality factor, / is the electron current onto the target, and Z is the atomic number of the target material. It can be seen from this expression that an increase in atomic number (as well as an increase in current), other conditions being the same, leads to a proportional increase in Pg, while the spectral composition of the radiation remains unchanged. Using relation (25.7), we can find the bremsstrahlung power: P=^ll''^P,de = bIZV\ where b = koe^ll.

(25.8)

HIGH-POWER X-RAY PULSES

463

The bremsstrahlung spectrum is described by formula (25.6) only for relatively low electron energies (approximately up to 100 keV), although this formula is often used for approximate calculations in the range of much higher energies. In pulsed x-ray apparatus, the tube current and voltage vary in time during a pulse; therefore, the spectral intensity of the radiation is also a ftmction of time. The formula 7e(0 = COnst[8n,ax(0 " s] / ( O

(25.9)

clearly shows that a change in voltage leads to a synchronous change in the energy range of the spectrum since its instantaneous boundary is displaced in accordance with the equality ^r.^{t)êV{t).

(25.10)

The spectral intensity averaged over the period of voltage variation,

/(s) = ^ J / s ( 0 ^ ^

(25.11)

can be determined if we know the fiinctions 8max (0 ^^^ ^(0 appearing in the expression for /e(0- Since these fimctions are different in form for different apparatus, we will consider qualitatively some general features of the pulsed radiation spectrum / ( s ) . For this purpose, we compare the composition of a radiation generated at a constant voltage V with that of a radiation generated at a periodic pulsed voltage of arbitrary waveform with amplitude V^ = F. In both cases, we initially assume that the currents are constant and equal in magnitude. Since V^ = V, the maximum photon energy 8max is the samc for pulsed and constant voltages. However, in effect, the radiation generated at a constant voltage corresponds to shorter wavelengths as compared to the radiation generated at a pulsed voltage. This difference is due to the fact that radiation in the latter case appears, during a larger or smaller time interval, at instantaneous values of the applied voltage smaller than its amplitude value. In reality, this difference in the spectral composition of radiation is very substantial. The matter is that the current passing through a pulsed tube is not constant. A high instantaneous current passes through the tube when the voltage, having reached its maximum, decreases. However, the current at the maximum voltage is relatively low. Thus, during a certain time interval, when the voltage is low and the current is high, the tube generates a high-intensity long-wave radiation. This explains the fact that under identical conditions, the bremsstrahlung in pulsed devices is depleted in short wavelengths as compared to the radiation generated by apparatus operating at a constant voltage.

464

Chapter 25

The efficiency of conversion of the power released by an electron beam at a target to the bremsstrahlung power is characterized by the radiant efficiency r| = boZWo. According to experimental data, we have bo equal to (0.8±0.2)-10-^ keV"^ for W < 200 keV. The linear dependence of r| on Wo breaks down at higher energies, and the efficiency increases at a lower rate. In the low-energy range, the radiation efficiency has very low values (from a fi-action of one percent to a few percent). In a bulk target, almost the entire kinetic energy of electrons converts, through some intermediate processes, to heat. With increasing Wo, thefi-actionof energy lost for radiation increases, and the efficiency becomes higher. For a very high energy, the efficiency reaches tens percent. For example, for a lead target the efficiency is 60% for Wo = 40 MeV and 75% for PFo = 100 MeV.

3.

CHARACTERISTICS OF X-RAY PULSES

In order to calculate the parameters of radiation pulses generated by an xray apparatus, we must know the current-voltage characteristic (CVC) of the pulsed tube. For tubes with explosive-emission cathodes, the cathode plasma affects the shape of the CVC. In our earlier publication (Litvinov and Mesyats, 1972), we proposed to calculate the CVC's of EEE x-ray tubes using the idea that the current in the system formed by the front of the moving cathode plasma and the anode is space-charge-limited (Flynn, 1956). It was assumed that the plasma conductivity is much higher than the conductivity of the tube. It is difficult to obtain an exact solution to the system of partial differential equations describing the passage of electrons in the regime of space-charge-limited current for an arbitrary geometry of electrodes and plasma blobs. For this reason, we will use approximate methods for the case of nonrelativistic electrons. In our earlier calculations (Litvinov and Mesyats, 1972), we employed a method where the electrostatic capacitance of a diode with an arbitrary system of electrodes is equated to the capacitance of a plane cylindrical or spherical capacitor, for which the form of the "3/2-power" law is known. The dimensions of an equivalent system of simple geometry are determined and used in subsequent calculations of the current. The basic assumption in this method is that the shape of equipotential surfaces is the same whether or not a space charge is present, and only the potentials of these surfaces are different. This method was widely used in calculations of the CVC's of electron tubes. With this method, it was found that for the case of a spherical plasma cathode formed by the explosion of the tip of a point on a plane surface, the current / can be determined from the formula


,J2^p^^.,

465

,25.12)

d--vt this formula is valid for vt

80 -

4

D ^ ^

40 0

2 1

1

1

1

1

1

2

3

4

5

0

(

d [MM] Figure 253. Dependence of x-ray pulse duration and radiation pulse energy W^ on gap spacing d

0.4

0.8 d-^'^ [mm-1/2]

1.2

Figure 25.4. Dependence of the peak electron current in an x-ray tube on d~^''^


469

As follows from relations (25.18), the current pulse amplitude in a diode into which a capacitor is discharged is /^ oc d~^''^. This was confirmed in an experiment (Mesyats, 1974) (Fig. 25.4) where a capacitor (C = 30 pF, VQ = 180 kV) was discharged into a diode with a point cathode and a plane anode. For superpower x-ray diodes with relativistic electron beams, the CVC's must be calculated based on the data given in Chapter 24 of this monograph.

4.

HIGH-POWER PULSED X-RAY GENERATORS

4.1

X-ray tubes

In modem pulsed x-ray apparatus, sealed-off two-electrode tubes with a cold cathode are used as a rule. The role of the target in pulsed diodes is played by the anode. X-ray tubes with an electron beam extracted to the atmosphere are also used. In this case, the target is located outside the tube. In domestic industrial pulsed x-ray apparatus, x-ray tubes with explosiveemission cathodes (EEC's) are used (Mesyats et al, 1983). Let us consider the design of such tubes in greater detail. Pulsed tubes have a coaxial or planar electrode system. Tubes of the coaxial type are manufactured with a conical anode made of tungsten in order to obtain intense bremsstrahlung. Usually, a tungsten rod of diameter 3-8 mm is used. The cone angle is 10°-30°, and the radius of curvature of the top is 0.5-1 mm. In tubes of planar configuration, transmission anodes having the shape of thin plates made of tungsten, tantalum, and other heavy metals are used. Commercial pulsed tubes with EEC are manufactured with tungsten or tantalum blade cathodes. Such cathodes have the shape of a disk or several disks, one or several coaxial tubes with sharp edges, a ribbon coiled into a spiral, etc. Electron emission is initiated as the blade edge explodes under the action of a high-density field emission current. The insulating part of the envelope of a pulsed tube is made of high-s glass or ceramics. In domestic standard tubes, the envelope is made of molybdenum glass. The residual gas pressure in sealed-off tubes is 10""^-10"^ Pa. One of the main parameters of x-ray tubes is the size of the radiation source (focal spot). The actual focal spot of a tube is the region on the surface of the anode (target) in which electrons are decelerated. The larger its area, the lesser the anode heating, all other factors being the same. The projection of the actual focal spot in the direction of the working radiation beam axis onto a plane normal to this axis is called the effective focal spot, or merely the focal spot. Its size determines the geometrical blurring of the boundaries of the shadowgraph formed in the radiation beam passed through

Chapter 25

470

the object under examination. In order to obtain a sharp contrast of the image, one must use a tube with a sharp (i.e., small-size) effective focal spot. A sharp focal spot can be provided in a rather simple way by using a conical anode in the tube (Tsukerman et al, 1971). Figure 25.5 shows a schematic diagram of the IMA5-320D pulsed x-ray tube with a coaxial EEC designed for a voltage of 320 kV and intended for x-raying of materials. The tube is used in MIRA-3D apparatus. Blade cathode 3 shaped as a disk is made of 20 |im-thick tungsten foil. The inner edge of the disk serves as the emitting surface of the cathode. Anode 2 is made of a tungsten rod of diameter 4 mm with one end sharpened to form a cone. The cone angle is 14°, and the tip radius is 0.6 mm. The cathode-anode separation is 2.7 mm. The anode is soldered to a steel rod lead 7 connected to a small flange P. A large flange 4 is electrically connected to the cathode. To this flange, a 0.2-mm thick Kovar extraction window 1 in the form of a hemispherical dome is soldered. Owing to such a shape of the window, the tube is suitable for panoramic x-raying of hollow objects. The steel screen 6 on which the cathode is fixed is rigidly connected with the large flange through ring 5. The main purpose of the screen is to prevent deposition of tungsten vapors formed during a discharge in the tube on glass insulator 8. The x-ray tube is evacuated through an exhaust tube 10 (thin-walled copper pipe). The working medium of the tube is transformer oil.

130 mm Figure 25.5. Schematic of the IMA5-32D pulsed x-ray tube: / - window; 2 - anode; 3 cathode. The remaining notation is given in the text

In the 100-kV IMA6-D tube (Belkin and Aleksandrovich, 1972) intended for directional x-raying of objects and having a similar design, a plane extraction window made of 1-mm thick beryllium sheet is used. Beryllium is characterized by a small attenuation coefficient for long-wave radiation; therefore, such a window filters the radiation emitted by the tube only


471

slightly. For example, the long-wave component of radiation with a photon energy W = 5 keV is attenuated approximately to half its initial intensity. A glass window of the same thickness almost completely absorbs radiation with W 3 keV. A tungsten wire of length 3.5 cm and diameter 10-50 |am was used in this experiment. A pulse of duration 60 ns and energy 20-30 J (e > 1 keV) was obtained on the SNOP high-current generator (500 kV, 2.3 Q, 80 ns) (Baksht et al., 1980). In this case, a copper wire of length 2-4 cm and diameter 20 |im was used. An increase in x-ray yield was attained due to a special spark gap that ruled out the passage of current through the conductor during the charging of the pulse-forming line (Baksht et al., 1980). In recent years, a number of new experiments have been performed with currents of up to lO'' A on the Proto, Angara, and GIT-12 machines. Longwave x-ray flashes with a pulse energy of up to lO^-lO'' J were obtained.

REFERENCES Abramyan, E. A., 1970, A Short High-Intensity Hard X-Ray Pulse Generator, Dot Akad. Nauk. 192:76-77. Baker, W. L., Clark, M. C, Degnan, J. H., Kiuttu, G. F., McClenahan, Ch. R., and Reinovsky, R. E., 1978, Electromagnetic-Implosion Generation of Pulsed High-Energy-Density Plasma, J. Appl Phys. 49:4694-4706.


489

Baksht, R. B., Datsko, I. M., Korostelev, A. F., Loskutov, V. V., Luchinsky, A. V., Mesyats, G. A., and Petin, V. K., 1980, Soft X-Rays in a Nanosecond Explosion of Thin Wires, Pis 'ma Zh Tekh Fiz. 6:1109-1112. Barinov, N. U., Belen'ky, G. S., Dolgachev, G. I., Zakatov, L. P., Nitishinsky, M. S., and Ushakov, A. G., 1997, Repetitive Plasma Opening Switches and Their Application in High-Power Accelerator Technology,/zv. Vyssh. Uchebn. Zaved,Fiz. 12:47-55. Belkin, N. V. and Aleksandrovich, G. V., 1972, A Two-Electrode Tube Generating Nanosecond Pulsed X Rays, Prib. Tekh. Eksp. 2:196-197. Bernstein, B. and Smith, I., 1973, "Aurora", an Electron Accelerator, IEEE Trans. Nucl. Sci. 20:294-300. Blokhin, M. A., 1957, Physics ofXRays (in Russian). Gostekhizdat, Moscow. Burkhalter, P., Davis, J., Rauch, J., Clark, W., Dahlbacka, G., and Schneider, R., 1979, X-Ray Line Spectra from Exploded-Wire Arrays, J. Appl Phys. 50:705-711. Denholm, A. S., 1965, High Voltage Technology, IEEE Trans. Nucl. Sci. 12:780-786. Diankov, V. S., Kovalev, V. P., Kormilitsyn, A. I., and Lavrentiev, B. P., 1995, High-Power Pulse Generators of Bremsstrahlung and Electron Beams based on Inductive Energy Storage,/zv. Vyssh. Uchebn. Zaved,Fiz. 12:84-92. Filatov, A. L., Korzhenevsky, S. R., Kotov, Yu. A., Mesyats, G. A., and Skotnikov, V. A., 1996, Compact Repetitive Generators for Medical X Ray Diagnostics. In Proc. XI Intern. Conf. on High Power Particle Beams. Prague, Czechia, pp. 909-912. Flynn, P. T. G., 1956, The Discharge Mechanism in the High-Vacuum Cold-Cathode Pulsed X-ray Tube, Proc. Phys. Soc. 69B:748-762. Funfer, E., 1953, Der Hochvakuumdurchschlag und seine Anwendung beim Rontgenblitzrohr, Zeit.f.angew. Physik. 5:426-440. Griem, H. P., 1964, Plasma Spectroscopy. McGraw Hill, New York. Heitler, W., 1954, The Quantum Theory of Radiation. Clarendon Press, Oxford. Jamet, F. and Thomer, G., 1976, Flash Radiography. Elsevier, Amsterdam. Kalitkin, N. N. and Kuz'mina, L. V., 1978, Tables of Thermodynamic Functions of Materials for High Energy Concentrations (in Russian). Preprint Inst. Appl. Math., USSR Acad. Sci., Moscow. Kingdon, K. H. and Tanis, H. E., Jr., 1938, Experiments with a Condenser Discharge X-Ray Tube, Phys. Rev. 53:128-134. Kotov, Yu. A., Rodionov, N. E., Sergienko, V. P., Sokovnin, S. Yu., and Filatov, A. N., 1986, A Vacuum Insulator with a Screened Dielectric Surface, Prib. Tekh. Eksp. 2:138-141. Litvinov, E. A. and Mesyats, G. A., 1972, On the CVCs of a Diode with a Pointed Cathode in the Explosive Electron Emission Regime,/zv. Vyssh. Uchebn. Zaved.,Fiz. 8:158-160. Martin, E. E., Trolan, J. K., and Dyke, W. P., 1960, Stable, High Density Field Emission Cold Cathode, J. Appl. Phys. 31:782-789. Martin, T. H., Guenther, A. H., and Kristiansen, M., eds., 1996, J. C. Martin on Pulsed Power. Plenum Press, New York. Martin, T. H., 1969, Design and Performance of the Sandia Laboratories "Hermes-II" Flash X-Ray Generator, IEEE Trans. Nucl. Sci. 16 (Pt 1): 59-63. Mesyats, G. A., 1974, Nanosecond X-Ray Pulses, Zh. Tekh. Fiz. 44:1221-1227. Mesyats, G. A. and Proskurovsky, D. I., 1971, Explosive Electron Emission, Pis'ma Zh. Eksp. Teor. Fiz. 13:7-10. Mesyats, G. A., Ivanov, S. A., Komyak, N. I., and Peliks, E. A., 1983, High-Power Nanosecond X-ray Pulses (in Russian). Energoatomizdat, Moscow. Mosher, D., 1974, Coronal Equilibrium of High-Atomic-Number Plasmas, Phys. Rev. 10A:2330-2335.

490

Chapter 25

Mosher, D., Stephanakis, S. J., Vitkovitsky, I. M., Dozier, S. M., Levine, L.S., and Nagel, D. J., 1973, X Radiation from High-Energy-Density Exploded-Wire Discharges, Appl Phys. Lett. 23: 429-430. Muhlenpfordt, J., 1939, Verfahren zur Erzeugung kurzzeitiger Rontgenblitze. DR Patent No. 748 185. Pavlovsky, A. I., Gerasimov, A. I., Zenkov, D. I., Bosamykin, V. S., Klementiev, A. P., and Tananakin, V. A., 1970, Air-Core Inductive Linear Accelerator, At.Eenerg. 28:432-434. Ramirez, J. J., Prestwich, K. R., Burgess, E. L., et al., 1987, The Hermes III Program. In Proc. VI IEEE Pulse Power Conf, Arlington, VA, pp. 294-299. Slack, C. M. and Ehrke, L. F., 1941, Field Emission X-Ray Tube, J. Appl Phys. 12:165-168. Stallings, C, Nielsen, K., and Schneider, R., 1976, Multiple-Wire Array Load for High-Power Pulsed Generators, Appl. Phys. Lett 29:404-406. Steenbeck, M., 1938, Uber ein Verfahren zur Erzeugung intensiver Rontgenlichtblitze, Wissenschaftliche Verroffentlichungen aus den Siemens-Werken. XVII:363-380. Tsukerman, V. A., and Manakova, M. A., 1957, Short X-Ray Flash Sources for Investigating Fast Processes, Zh. Tekh. Fiz. 27:391-403. Tsukerman, V. A., Tarasova, L. V., and Lobov, S. I., 1971, New X-Ray Sources, Usp. Fiz. Nauk. 103:319-337. Turchi, P. J. and Baker, W. L., 1973, Generation of High-Energy Plasmas by Electromagnetic Implosion, J. Appl. Phys. 44:4936. Vorob'ev, G. A. and Mesyats, G. A., 1963, High-Voltage Nanosecond Pulse Formation Techniques (in Russian). Gosatomizdat, Moscow.

Chapter 26 HIGH-POWER PULSED GAS LASERS

1.

Principles of operation

1.1

General information

The application of the methods of nanosecond pulsed power technology and electronics has led to a revolutionary breakthrough in gas laser engineering. As a matter of fact, the use of high-power nanosecond electric energy pulses and high-power systems producing initiating electrons (ultraviolet radiation, x rays, electron beams, etc.) makes it possible to create low-temperature plasmas in large volumes (1-10"* liters) of various gases by discharges operating under high pressures (of the order of several atmospheres and higher). The population inversion in gas atoms or molecules in such plasma is developed as a result of various physical processes, the discharge being of the volume and not constricted type. High gas pressures and large volumes make it possible to attain high energies and powers in laser pulses. In order to simplify notation, we will refer to all highpower pulsed gas lasers as HPPG lasers. Before HPPG lasers were created, glow discharges were used in gas lasers. Since the gas pressure in a glow discharge is some fractions of or a few mmHg, unwieldy laser devices were required to attain high powers. The prevailing opinion in the literature on gas lasers was that the development of HPPG lasers was a consequence of evolution of laser systems proper. Considerable advances in the gas-discharge physics were disregarded to a certain extent. The author of this monograph firmly believes that the development of HPPG lasers is a direct consequence of advances in the gasdischarge physics. Among these advances, the discovery of multielectron

492

Chapter 26

initiation in nanosecond discharges and a discharge with direct injection of electrons into the gas, which have led to high-pressure volume discharges, should be mentioned in the first place. These problems were considered in detail in Chapter 6. The principle of operation of a laser is based on the concept of stimulated emission of radiation, which was formulated by Einstein in describing statistical properties of blackbody radiation under thermal equilibrium conditions. By way of a simple example, we consider a two-level atom. Let |l) and 12) be the nondegenerate ground state and an excited state of our hypothetical atom. We shall consider three processes, viz., absorption, spontaneous emission, and stimulated emission, involving both above states and photons with energy hv equal to the energy gap As between these two states. These three processes are presented in Fig. 26.1, a and are described, respectively, by the following equations: |l) + /iv ~> |2),

(26.1)

12) -^ Il) + Av,

(26.2)

\2) + hv ^

(26.3)

|l) + 2/2V.

In a sample containing particles in both states, any of the above processes (absorption, spontaneous emission, and stimulated emission) may take place. In the most general case, the populations of the ground and excited states are in thermal equilibrium, which can be described by the Boltzmann relation:

iV2=Mexp[^-0J,

(26.4)

where N\ and N2 are the population densities of the ground and the excited state, respectively, k is Boltzmann's constant, and 7 is the temperature. Since the absorption cross section is equal to the cross section for stimulated emission, the ratio of the probability of light amplification to the probability of light absorption is determined by the relative population densities of the excited and ground states. This is used to calculate the light amplification (or absorption) factor a (per unit length) by the formula a = ast(A^2-Aî),

(26.5)

where Gst is the cross section for the stimulated transition (or resonance absorption). Thus, in order to attain light amplification (a > 0), we must find

HIGH-POWER PULSED GAS LASERS

493

a method for carrying the majority of atoms to the excited state (A/2 > M). If we confine our analysis to positive temperatures, such a situation leads to violation of the requirements of statistical mechanics defined by relation (26.4). This violation can be eliminated if we recall that relation (26.4) presumes the existence of thermal equilibrium in the sample, which is not always the case in actual practice. Consequently, methods must be found by which population inversion can be realized. 12) Pumping

hv-r Spontaneous Stimulated emission emission

Pumping

Absorption

ID Figure 26.1. Simplified diagram of laser levels for a two-level (a) and three-level atom (b)

In the case of two-level systems, population inversion is most commonly developed if the laser medium originally contains no particles that could participate in lasing. Particles in an excited state are selectively produced, for example, by an electrical discharge. If the lower level |l) caimot be emptied rapidly and selectively, the resulting inverse population exists only for a limited time. In the typical case, we obtain a "self-contained" laser in which the inverse population and the gain decrease because of stimulated emission of radiation. In most lasers, particles involved in lasing have three or more energy levels. Such a situation is depicted in Fig. 26.1, b. In this case, an inverse population can be obtained in a much easier way. For this purpose, we must only find collisions processes in which the cross section for the excitation l0)-^|2) is larger than the cross section for the |0)->|l) process. Furthermore, the creation of an inverse population could be facilitated if the rates of radiative and collision-induced transitionsfi-omlevel |l) to level |0) would be much higher than the rates of the transitions fi'om level 12) to level |0). In the latter case, radiative and collision-induced processes do not limit the lasing time, and we can have a continuous laser. Thermodynamically, the laser excitation mechanism can be treated as energy transfer between two systems with different temperatures: laser particles initially have a low temperature, while the temperature of pumping particles is high. Obviously, we are not interested in equilibrium properties of the systems, but we must have information on the rates of excitation, emission, and relaxation processes.

494

Chapter 26

For an HPPG laser, a bulk plasma must be created which would contain as many as possible atoms and molecules providing for population inversion. Such a plasma is referred to as an active medium. This medium will emit laser radiation if it is in the so-called open resonator proposed by Prokhorov (1958). In this case, the radiation passes many times through the same plasma and leads to the emission of stimulated radiation, which is enhanced due to multiple reflections from the resonator mirrors. In its simplest form, an open resonator consists of two parallel mirrors separated by a distance /, which is much longer than the radiation wavelength X, i.e., l» X. The diameter of the mirrors is also much larger than the radiation wavelength. One mirror, which is partially reflecting, serves to extract the laser beam.

1.2

Types of gas lasers

The first gas (helium-neon) laser was proposed by Javan (1959) on the basis of detailed analysis of possible mechanisms of activation and deactivation that could lead to population inversion in gas mixtures excited by an electrical discharge. This laser belongs to the class of lasers with direct energy transfer. The basic principle of production of inversion is the excitation of helium atoms upon their collisions with electrons of a gas discharge. This process transfers a small portion of helium atoms from the ground state to the 2^S and 2^5 metastable states. Helium atoms in these excited states can collide with neon atoms, transferring the stored energy to the latter; as a result, two manifolds of energy levels of excited neon are populated selectively: 2p^5s in the vicinity of 20.6 eV and 2p^4s near 19.8 eV. Since the energy exchange reactions do not lead to population of the lower levels of neon, the local inverse population required for lasing is produced between the 2p^5s and 2p^4p levels (in the range 20.2-20.4 eV), between the 2p^5s and 2p^3p levels (18.5-19 eV), and also between the 2p^4s and 2p^3p levels. The CO2 laser is a typical representative of another type of lasers that harness the energy transfer process. There are three types of normal vibrations inherent in a CO2 molecule: symmetric valence vibrations Vi, deformation vibrations V2, and asymmetric valence vibrations V3. The deformation vibrations are degenerate. Accordingly, the filling of the vibrational levels of a CO2 molecule (including not only those with normal frequencies Vi, V2, V3, but also their overtones and compound vibrations) determines the set of vibrational quantum numbers, Vu V2, and F3, that describes the vibrational state of the molecule. Energy levels are denoted by a combination of the quantum numbers Vu V^, and F3. The superscript / has been introduced to reflect the degeneracy of the deformation vibrations of frequency V2. We are interested in the lower vibrational levels of the electron


495

ground state, which are depicted in Fig. 26.2 together with a sketch of the types of vibrations of the CO2 molecule. The coincidence of the vibrational frequencies Vi and 2v2 due to the Fermi resonance mixes these levels, and they often appear in kinetic processes as a single state. Consequently, we can expect that the energy transfer upon collisions of N2 (v = 1) and CO2 molecules will produce an inverse population between the selectively populated level 00^1 and the lower-lying unpopulated levels. ^ V i ^

V2

0-0-0

fc^^

0-0-0

F=l S 2 o CO

F=0 Figure 26.2. Diagram of the lower vibrational levels of CO2 and N2 molecules in the ground electronic state

Patel (1964) was the first to demonstrate lasing based on this principle. In a glow discharge with a reduced electric field Elp of 5 V/(cm-Torr) in the discharge plasma, from 40% to 80% of nitrogen molecules are excited for an electron energy of 2-3 eV (resonant excitation of vibrations of the N2 molecule in the range of F = 1-8) and for an electron density of (0.5-5)-lO^^cm"^. The excitation cross-section for nitrogen equals 3-10"^^ cm^. The rate of coUisional excitation energy transfer from nitrogen to CO2 is (1-2)-10"^ s"^-Torr"^ The energy transfer is efficient between the Q(fn harmonics of CO2 and N2 molecules up to the F= 4-5 vibrations of the N2 molecule. Thus, the upper laser level is populated in a CO2 laser. As regards the depletion of the lower laser level, it was found that the first excited level 01^0 of the deformation mode V2 effectively relaxes upon collisions with He atoms. Helium depletes the 01*0 level of CO2 at a rate of 4-10^ s"*-Torr"^ In this case, the 00^1 level of the V3 mode is practically not affected by helium. Subsequently, a large number of alternative schemes were proposed for the excitation of CO2 molecules using a discharge initiated or controlled by an electron beam, x rays, ultraviolet radiation, etc. to pump the laser

496

Chapter 26

medium. Owing to the high efficiency (-10%) and the abiUty to operate in the pulsed mode as well as in the CW mode with a high average power (10^-10^ W), this laser has been studied meticulously. It is worth noting that a CO2 laser is a typical molecular laser since its active medium is formed by molecular gases. This laser generates infrared radiation with a wavelength of 10.6 |xm. Another class of molecular lasers includes those with direct excitation of the upper level by electron impact or by some other method. To realize this type of lasing, particle species and excitation processes are required in which the upper laser levels would be populated selectively. The excitation of electronic states of diatomic molecules by direct electron impact makes it possible to create gas lasers with a wide spectrum of lasing wavelengths. In the first laser of this type, developed by Mathias and Parker (1963), the working molecule is that of nitrogen. These researchers observed lasing by the BÎig -> A^Zl transition in the near infrared spectral region. The same year. Heard (1963) attained lasing by the CÎiu "^ ^^n^ ultraviolet transition. Subsequently, lasers generating radiation with wavelengths in the range 3-4 |im by the a^Yig -> a'^Y.^ and wÂ„ "â^Hg transitions were developed (McFarlane, 1965). Among lasers of this type, the N2 (C - B) laser is most popular. The upper laser level N2(C^nM) is occupied due to the excitation upon collisions of electrons with N2 molecules being in the J^^Sg ground state, the cross section of this process being larger than the excitation cross section for the vibrational states of the lower laser level of N2 (^ÎTg). Lasing occurs mainly by the 0 - 0 transition of the C- B system (second positive system) at a wavelength of 337.1 nm. This laser has also found wide application in laboratory experiments mainly for pumping high-power pulsed dye lasers. The N2 laser is characterized by a low pulse energy (a few millijoules for a pulse duration of a few nanoseconds) and a low efficiency (about 0.1%) due to accumulation of particles during lasing at the lower laser level, i.e., by a rapid decrease in inverse population (bottleneck effect). Directly pumped lasers of another type are those operating by various transitions of the CO molecule (Leonard, 1965). Infrared generation by the vibrational transitions of the CO ground state was observed for the first time by Patel and Kerl (1964). An infrared CO laser operating in the wavelength range 4.87-6.7 jim is one of the most efficient lasers; its efficiency is over 20%. The complex kinetics of this laser is determined by excitation by electrons from the upper vibrational levels, leading to lasing at a series of wavelengths through cascade transitions of molecules to the lower vibrational levels. For the production of high-power coherent radiation fluxes in the ultraviolet and visible regions, excimer lasers are of considerable interest.

HIGH'POWER PULSED GAS LASERS

497

The term "excimer" is an abbreviation of the phrase "excited dimer" and refers to a molecule that may exist only in an electron-excited state. This state is comparatively long living and serves as the upper laser level. In the ground state, an excimer molecule decays within a short time (10~^^-10~^^ s), testifying to the depletion of lower laser level and the occurrence of a population inversion. As this takes place, lasing occurs by the transitions between the excited bound states and the ground repulsive or weakly bound state of the molecule. In excimer lasers, excited diatomic combinations of two inert gases or of inert gas and halide or oxygen are used. For the well-known excimer laser system where lasing occurs by transitions of the KrF molecule at a wavelength of 248 nm, an efficiency of-^10% was attained. This system can be scaled to obtain a high output power. Other systems lasing at longer wavelengths in XeF (353 and 483 nm), XeCl (308 nm), HgCl (558 nm), and HgBr (502 nm) show lower efficiency. First reports on excimer rare-gas halide lasers appeared in 1975 (Mangano and Jacob, 1975; Searles and Hart, 1975; Brau and Ewing, 1975). Lasing in XeBr* (282 nm), XeCl* (308 nm), XeF* (-^350 nm), and KrF* (-248 nm) was attained using an electron beam, an electron-beam-controlled discharge, or a fast discharge for the excitation of the laser medium. Excimer lasers are now the most powerful sources of ultraviolet coherent radiation, covering the vuv through visible spectrum (Rhodes, 1979; McDaniel and Nighan, 1982; Mesyats et al, 1995). They have a very important advantage: these lasers efficiently operate with various methods of pumping, and the pumping systems are universal and can be applied to various working mixtures. The wide spectrum of laser wavelength and high output energies make excimer lasers widely usable in scientific research and technology. One more advantage of excimer lasers is their broad bandwidth allowing frequency tuning over rather wide limits. To attain lasing in excimer rare-gas halides, ternary mixtures consisting of a buffer gas (argon, neon, or helium), a working gas (xenon, krypton, or argon), and a halide carrier (HCl, CCI4, F2, NF3, HBr, etc.) are generally used. The properties of laser radiation are determined by the specifically arranged potential curves of excimer molecules, by the kinetic processes occurring in the plasma upon excitation of the working mixture, and by the light amplification and absorption at the laser wavelength. In addition to lasers with energy transfer, lasers with direct excitation, and excimer lasers, which we discussed above, other gas lasers also exist (such as photodissociation and chemical lasers). We will consider below only two types of gas lasers: CO2 lasers and excimer lasers.

498

Chapter 26

2.

METHODS OF PUMPING

2.1

General considerations

First high-power gas lasers were designed as long glass tubes with a longitudinal glow discharge and gas flow (Karlov, 1983). Longitudinal discharges are the simplest to realize. It is only necessary to connect a series resistor of rather large resistance in the discharge circuit to restrict the discharge current and to compensate the effect of the descending segment of the current-voltage characteristic of the discharge gap. Longitudinal gas flow is required to remove the products of dissociation of the gas mixture. In such systems, the working gas is cooled due to its diffusion to the gasdischarge tube walls cooled from outside. For the longitudinal configuration of the discharge and gas flow, the maximal power per unit length (50-100 W/m) is independent of the gasdischarge tube diameter. Indeed, when the self-excitation threshold of a laser is exceeded significantly, the radiated power is determined by the product of the pumping rate A and the effective volume V of the active medium: P = AYhv.

(26.6)

For a cylindrically configured laser, V = TCD^//4 , where / is the discharge length and D is the tube diameter. The pumping rate A = dN(00^1)/dt is determined by the product of the density of molecules in the ground state. No, the electron density Ne, the cross section for electron impact excitation, a, and the average velocity of electrons u: A = NoNeau,

(26.7)

However, the product NeCu has the meaning of discharge current density y; hence, A = Aô7- The product jid^lA gives the value of the total discharge current /, and thus we obtain PÎNolhv.

(26.8)

Since Aô is proportional to the total pressure/? of the gas mixture, we have PocIpL

(26.9)

The product of current and pressure is known to be an important characteristic of plasma processes in long tubes. In a stationary glowdischarge plasma, the conditions are determined by the product pD (Paschen's law). The constancy of pD ensures the constancy of plasma


499

conditions. If an optimum pressure is fixed for a certain diameter, the optimum is preserved as long as the value of the product pD remains unchanged. Hence, we have/? = const/D and, since / = jnD'^/4, Ip oz const'jD.

(26.10)

On the other hand, the thermal regime is very important for a CO2 laser. The amount of heat liberated per unit volume is proportional to the current density j . In a laser of cylindrical geometry, the heat removed from the central part of the discharge channel to its periphery is proportional to l/D. In order to maintain a certain optimum thermal regime, the constancy of the product yZ) is required. Consequently, the product Ip is a, constant, and we arrive at the conclusion that under optimum conditions, the output power of a CO2 laser with a longitudinal discharge and gas flow is proportional only to the laser length: PocL

(26.11)

The highest power attained in such a longitudinal configuration was 1 kW for a discharge tube of length 20 m (Karlov, 1983). Thus, lasers with longitudinal discharge were very big because of the low pressure (of a few Torr) and low electric field (not higher than 10 V/cm). This problem was partly solved by Leonard (1965) who used a transverse discharge instead of a longitudinal one. The operation of pulsed gas lasers was further perfected by passing to the nanosecond range of pulse durations. Shipman (1967) used a pulse of duration 4 ns for pumping an N2 laser with a discharge current of 500 kA and dl/dt ~ 10^"^ A/s provided by a low-resistance double strip line. The plasma density was 10^^ cm"^ at a gas pressure of 30 Torr. However, a major breakthrough in the development of HPPG lasers was the use of methods of pulsed power technology for pumping lasers. This made it possible to develop lasers with a high gas pressure (one atmosphere and higher). As a result, the laser pulse power and energy increased by many orders of magnitude. There exist three basic methods for pumping highpressure gas lasers. The first method involves the use of a multielectroninitiated avalanche volume discharge, which develops between the electrodes of a discharge chamber on application of voltage pulses of duration 10"^~10~^ s, providing a pulsed electric field E much higher than the dc breakdown electric field E^c We will use the term electric-discharge lasers for devices of this type. This pumping method was developed based on the results of studies of nanosecond discharges in gases (see Chapter 4). The second method is direct pumping of the working gas by a highpower pulsed electron beam. In this case, the electron beam is injected into

500

Chapter 26

the laser chamber, as a rule, transverse to the laser beam path, and ionizes the gas in the chamber, creating a plasma that serves as the active medium of the laser. It should be noted that no electric field is applied in this case to the electrodes in the chamber, and the entire energy required for plasma production comes from the electron beam. This method basically differs from the above method where electrons only initiate a discharge, while plasma is created due to ionization processes in the gas. Finally, the third method is based on the application of an electric field weaker than the dc breakdown field £dc, and electrons, ions, or x rays are injected into the chamber. In this case, the gas discharge is referred to as an electron-beam-controlled discharge. This is a non-self-sustained discharge (see Chapter 4). It is clear that with E > E^c this method is similar to the first method since the injected electrons play the role of discharge-initiating electrons.

2.2

Electric-discharge lasers

Pulsed CO2 lasers were the first atmospheric-pressure electric-discharge lasers (Laflame, 1970). The creation of these lasers marked an important stage in the evolution of quantum electronics. These systems are simple in structure, reliable in operation, and possess high energy parameters. At the early stage of the development of atmospheric-pressure CO2 lasers, the medium was excited most often in a transverse system of electrodes, between a solid anode and an array of needles. For a discharge of duration 1 |is, the current through the needles was limited by a 1-kfl resistor (Laflame, 1970). Despite the nonuniform excitation of the working medium and the low efficiency, this system, owing to its simplicity, was in wide use. However, the main attention of researchers was subsequently concentrated on lasers in which uniform excitation of the working medium was attained due to preliminary ionization of the working medium. These devices together with lasers of the above type constitute a new class of lasers, viz., electric-discharge or TEA lasers. To excite the working medium in electric-discharge lasers, various electrode systems are used (Fig. 26.3). In the configurations shown schematically in Fig. 26.3, b-e, the required initial electron density in the main gap is provided by ultraviolet illumination of the gap which ionizes uncontrollable and easily ionizable impurity particles and by ignition of an auxiliary discharge whose plasma supplies electrons to the gap. The latter process leads to a redistribution of the electric field strength in the gap, eliminating the need to use specially shaped electrodes. The electrodes of the main discharge are specially shaped for the cases where the initial electron density is created by preliminary ionization of the


501

working medium with the ultraviolet radiation of an auxiliary discharge ignited in the vicinity of the main gap (Fig. 26.3,/, g). The electrode shaping can be performed in compliance with recommendations of Rogowski, Bruce, Harrison, Felicci, or Chang (Mesyats et al, 1995). Owing to the their simple shape, Chang's electrodes are in most common use. The main goal of shaping is to obtain a uniform electric field in electrode systems of finite width. It should be noted, however, that the reduced input energy in a gap with a uniform decreasing field is nonuniform (increasing from the edge to the center). Therefore, simpler (e.g., semicylindrical) electrodes as well as electrodes with a plane central part and rounded edges are also used. The latter electrode configuration provides the most uniform energy distribution in the gap. («)

(c)

(b)

g^^fe^

^///}/////)

(/////////A C MG

MG

MG

TTT id)

ie)

00

r^^

,iUU,

(y////////^ MG

MG

MG

r//////////^

^//W//A E-beam particles

(0

Qi)

^//}//////> A MG I ryS<wyyyyyy>d

V///////////J ^ MG

MG

zr

'M

^

r

STHTTS e

Figure 26.4. Electron-beam-pumped lasers with transverse pumping (a) and with a coaxial laser chamber and a coaxial cathode (b)

The following two schemes of electron-beam pumping are widely used at present (Fig. 26.4). A high-voltage pulse is applied to a vacuum diode whose cathode operates in the explosive electron emission mode. The operation of diodes of this type was described above. The anode is piece of thin metal foil or Dacron film through which electrons are injected into the laser chamber. In cases where higher working pressures are required, the foil is placed on a support grid on the vacuum side. Figure 26.4, a shows a schematic diagram of transverse pimiping with the electron beam injected from one side of the laser chamber. Such laser chambers make it possible to work with pressures of hundreds of atmospheres and are easy to operate. The disadvantages of this pumping scheme are nonuniform excitation of the laser medium and large beam current losses (up to 50-70%) at the support grid. Uniform excitation can be attained in lasers with multisided pumping. In this case, an

504

Chapter 26

electron beam is injected into the laser cell from two or more sides. In the general form, this can be coaxial pumping (Fig. 26.4, b). At the initial stages of evolution of laser technology, longitudinal electron-beam pumping was used (Rhodes, 1979; Hoffman et al, 1976). To conveniently operate the resonator, the electron beam is turned by a magnetic field; to reduce the debunch and losses of electrons at the laser chamber walls, the electron beam is focused by a magnetic field. This pumping scheme is used for electron energies >1 MeV or for low working mixture pressures. The main drawback of the longitudinal pumping scheme is that the creation of a pulsed magnetic field requires large amounts of energy, which are usually greater than the energy expended for the production of the electron beam. Let us consider the qualitative pattern of the interaction of an electron beam with a high-density cold gas. For the sake of simplicity, we take the gas to be atomic and its pressure to be high enough to assume that the beam energy is transferred to the gas mainly through binary collisions of electrons with atoms. Under these conditions, high-energy electrons of the beam entering the gas experience multiple elastic collisions with atomic nuclei and relatively infrequent inelastic collisions with atomic electrons, resulting in excitation and ionization of gas atoms. Electrons resulting from ionizing collisions and having energies higher than the excitation energy for the lower electron level can also ionize and excite the gas. Therefore, a cascade of ionizing collisions develops in the course of beam injection, and the number of low-energy electrons, ions, and excited atoms increases as in an avalanche; i.e., plasma is formed. The electron beam plasma differs from the electrical discharge plasma in a number of specific properties. For example, the density of charged particles in the electron beam plasma is much higher than the equilibrium density determined by the Saha relation, and the electron temperature is lower than its equilibrium value. For this reason, such electron beam plasma is also referred to as supercooled plasma. The intense recombination processes occurring in such plasma render it a promising laser medium. The characteristics of an electron beam plasma can be determined in much the same way as the characteristics of a discharge plasma, i.e., by solving the kinetic equations for particle densities and radiation together with the Boltzmann equation for the plasma electron distribution function (Evdokimov, 1982). The physics of the interaction of an electron beam with a gas is described elsewhere (Evdokimov, 1982; Berger and Seltzer, 1964; Vorob'ev and Kononov, 1966). The electrons of a beam entering a gas lose their energy through collisions until their average kinetic energy becomes comparable to the gas temperature. Such thermalized electrons (TE's) play the main role in the


505

build-up of space charge in a gas gap exposed to an electron beam. The space charge of TE's may produce strong electric fields (Mesyats, 1975), the field strength being determined by the TE distribution over the gap width. Calculations show that the absorbed energy distribution (AED) in a gas chamber (and, hence, the rate of generation of active plasma particles, ^ , and the rate of thermalization of electrons, q, strongly depends on many parameters such as the electron energy spectrum of the accelerated beam, the material and thickness of the input foil, the material of the rear wall of the chamber (anode), the gas type and pressure, etc. The foil separating the vacuum diode of the accelerator from the gas chamber is an important structural element of devices intended for gas excitation and ionization by an electron beam. In actual devices, aluminum or titanium foils of thickness 20-50 |am are generally used. These foils are "thick" for electrons with energies of 100-300 keV, whose extrapolated range in aluminum is 70-400 [am, and their effect on the AED may be significant. The reflection of electrons from the anode also affects the absorbed energy distribution, and the larger the atomic number of the material, the greater the number of reflected electrons and their mean energy. Consequently, the AED near the anode in a gas gap can be changed by changing the anode material. It is found experimentally that the delivery of the electron beam energy to the working gas is much more efficient if the laser cell is immersed in a longitudinal (relative to the beam direction) magnetic field of strength / / = 1-4 kGs (Cartwright, 1989). Figure 26.5 shows AED's calculated by the Monte Carlo method taking into account the magnetic field (Evdokimov, 1982) for the output laser amplifier LAM of the Aurora system whose working volume is 100x100x200 cm (Cartwright, 1989). The Ar-Kr-Fs gas mixture was excited by two electron beams injected toward each other through the side walls of the chamber. It can be seen from the figure that the magnetic field increases the total energy stored in the gas cell and improves the uniformity of pumping in the chamber cross section. The rate of gas ionization by an electron beam with a current density j is determined by the absorbed energy distribution

vF(z) = / ^ 5 M . e

(26.12)

8/

Here, S/ is the energy going into the formation of an electron-ion pair. If an electron of energy To gives rise to an ionization cascade, which is completely absorbed in the gas after (on the average) Ni ionizing collisions, we have

506

Chapter 26 S/ =

(26.13)

Ni

i.e., 8/ is the energy lost in the generation of one electron by the ionization cascade in the gas. It should be borne in mind that some part of the cascade energy goes into the excitation of electronic and vibrational levels and is lost in elastic collisions; therefore, we have 8/ > / . Laser cell

Foil-

Foil

\D [keV/cm]

Anode

Anode

Figure 26.5. Absorbed energy distribution in the cross section of an amplifier. TQ = 675 keV; the thickness of titanium (7, 3-5) and Dacron (2) foils is 50 jim; argon pressure is 1200 mm Hg (7) and krypton pressure is 600 mm Hg (2-5)\ H=3 (1-31 1 W and 0 kGs (5)

The energies of formation of an electron-ion pair were measured experimentally. The results of these measurements for pure gases are as follows: Gas

He

Ne

Ar

Kr

Xe

H2

Air

N2

O2

CO2

8,-,eV

42.3

36.6

26.4

24.2

22

36.3

34

35

30.9

32.9

Experiments have shown that 8, is practically independent of the spectral composition of the electron beam, but strongly depends on the gas purity, which is associated with Penning ionization processes.


2.4

507

Electroionization lasers

These are high-power gas lasers pumped with an electrical discharge controlled or triggered by an electron beam. This type of discharge, which was run for the first time by Mesyats et al (1970), was described in Chapter 4. The first pulsed high-pressure laser in which this type of discharge was used was developed by Basov et al (1971). Later, this discharge was successfully applied to produce lasing in KrF (Mangano and Jacob, 1975). A typical scheme of a laser excited by an electron-beam-controlled discharge is shown in Fig. 26.6. An electron beam is injected into the discharge gap; a capacitive energy store connected to the anode of the laser chamber can be operated permanently or through a switch to ensure pulsed voltage supply. The electron beam ionizes the working mixture, producing a conducting medium in the entire volume of the gap; the energy store is discharged through the gap, delivering energy to the volume discharge, which is similar to a glow. Two typical laser pumping modes can be distinguished: pumping with a non-self-sustained discharge and pumping with a gas-amplified discharge.

Figure 26.6. Schematic of a laser with combined pumping: case (7), insulator (2), anode contact (5), anode {4\ mirrors (5), foil (6), and grid (7)

A non-self-sustained discharge in rare-gas-halide mixtures is stable in weak fields, but constricts as the field exceeds a certain limit. It should be noted that the constriction of a discharge in rare-gas-halide mixtures differs significantly fi"om that of a discharge in nitrogen in that the conductivity of the channels is not very high and these channels can coexist with the volume stage of the discharge for a long time. The energy supplied to the gas by a non-self-sustained discharge appears to be comparable, because of the electron attachment, to the energy input from an electron beam.

508

3.

Chapter 26

DESIGN AND OPERATION OF PULSED CO2 LASERS

High-power pulsed CO2 lasers are pumped, as a rule, by a self-sustained discharge or by an electron-beam-controlled discharge. Lets us consider lasers of the first type. A typical schematic diagram of such a laser is shown in Fig. 26.3. Like all HPPG lasers, this is a laser with transverse pumping. Figure 26.7 shows schematically the circuit and design of a repetitively pulsed CO2 laser. Experiments proved that such a laser can operate at a frequency of up to 20 kHz with an average power density of 34 W/cm^ (Brandenberg et al, 1972), generate radiation pulses with an energy of-20 J at a frequency of 100 Hz (Jones, 1978), and radiate reliably an average power of -10 kW and higher. A comprehensive analysis of the energy characteristics of lasers of this type was carried out by McDaniel and Nighan (1982), Smimov (1983), and Mesyats et al (1995). These lasers operate in the non-self-sustained discharge mode; that is, the voltage applied to the laser cell is lower than the Paschen (dc breakdown) voltage.

Figure 26.7. Schematic of the excitation circuit (a) and design of a repetitively pulsed CO2 laser (b): case (7), pulse generator (2), electrodes (i), preionization systems (4), fan (5), and heat exchanger (6)

The CO2 lasers excited by a self-sustained electrical discharge seem to hold much promise. Such systems appeared later, after the development of methods for initiating self-sustained discharges in large volumes. Let us consider the most interesting high-power pulsed lasers. A plasma-electrode CO2 laser (Pavlovsky et aL, 1976) was assembled according to the scheme shown in Fig. 26.3, h. The working volume of the laser was confined between 80-cm long plasma electrodes and measured


509

15x15 cm in cross section. The pulsed power supply was a six-stage Marx generator. The reduced energy input in this laser reached 200 J/(l-atm), and the reduced radiation energy was 30 J/(l-atm) with an efficiency of 15%. This device features the use of plasma electrodes formed by a discharge over the surface of a dielectric. A further increase in volume of the active medium was achieved due to its preionization by an auxiliary discharge operating directly in the working zone. The principal units of the device (Fig. 26.3, c) were a gas-discharge chamber and high-voltage power supplies for the main and auxiliary discharges. The trigger electrode, cathode (C), and anode (A) of the main discharge gap were mounted in the chamber (Apollonov et al, 1987). The anode was 2.3 m long with a total width of 65 cm; the electrodes separation was 35 cm. The electrode system was placed in a dielectric tube of diameter 1 m and length 3 m. The power supply for the auxiliary discharge was a 24-stage 1-MV, 300-J Marx generator with a capacitance of 0.59 nF. The main discharge was initiated with the help of two five-stage Marx generators capable of storing 40 kJ and generated a pulse of peak voltage up to 300 kV. A total output energy of 8.4 kJ could be extracted from the entire volume with an efficiency of 21%. CO2 lasers with initial electrons transported to the main discharge gap firom an auxiliary discharge seem to allow more room for increasing the active volume. Measurements performed for a laser of this type have shown that for J = 40 cm and an absorbed energy of 150 J/1, the reduced radiation energy was 18 J/1, which corresponds to an efficiency of 15%. This value matches the results obtained for c/ = 15 and 20 cm and an atmospheric-pressure mixture of C02:N2:He =1:1:8. As a rule, electric-discharge CO2 lasers operate at near-atmospheric pressure of the working gas mixture. However, in some cases, the pressure may be as high as 10 atm and even more. High-pressure electric-discharge lasers are of interest as systems generating short radiation pulses and allowing continuous tuning. The first publication in this field (Hidson et al, 1972) described a CO2 laser with a gap of 2.5 cm between a cathode consisting of 120 tungsten points and a solid brass anode. The working pressure ranged from 1 to 5 atm. Subsequently, for electric-discharge lasers with preionization of the working medium at the stage of discharge initiation, the working frequency range was considerably extended and continuous tuning was realized (Alcock et al, 1973; Bychkov et al, 1977; Karlov et al., 1987). A rather wide continuous tuning range (46 cm"^) was attained by Karlov et al (1987) for a radiation pulse energy of up to 70 mJ. For the C02:N2 =1:1 working gas mixture at 8-atm pressure, continuous tuning was attained for the P- and /?-branches of the 00^1-10^0 and 00^1-02^0 transitions in the frequency ranges 938-951, 970-980, 1041-1054, and 1073-1083 cm-^ respectively.

Chapter 26

510

Considerable advances in increasing the peak power of CO2 lasers were made when an electron-beam-controlled non-self-sustained discharge was used for their pumping and the possibility of volume current passage in gaseous media at a pressure of up to 15 atm was demonstrated (Mesyats et al, 1972). The results of further work on this line (Evdokimov, 1982; Mesyats, 1975; Mesyats et al, 1995) formed the basis for the creation of high-power gas lasers. Lasers with the working medium pumped by a non-self-sustained discharge controlled by radiation from an external ionizer are referred to as electron-beam-controlled lasers. Lasers of this type were first built at the Physics Institute of the USSR Academy of Sciences (Basov et al., 1971) and later at Los Alamos National Laboratory (Fenstemacher et al,, 1971). The development of these lasers was a breakthrough in quantum electronics. 3

2

4 6

5

7 8

9

Figure 26.8. Schematic of the design and power supply circuit of the electron-beamcontrolied pulsed CO2 laser

A schematic circuit for the initiation of an electron-beam-controlled nonself-sustained discharge is shown in Fig. 26.8. The working medium fills a gas cell 7 containing a grid cathode 5 and a specially shaped solid anode 5, which form the active zone 5-8 of the laser. The gas cell is adjacent to a vacuum diode 2 in which an electron beam is formed between a bowl-shaped cathode 10 and foil 6 (or a special extractor), which also plays the role of a transparent anode. The electrode gap 5-8 is in a constant electric field, which provides the most efficient energy transfer to the upper laser level. As the spark gap SG operates, the capacitor C\ discharges into the explosiveemission vacuum diode that generates a large-cross-section electron beam. The electron beam entering the cathode-anode gap through the thin metal foil 6 ionizes the working medium and produces plasma with a charge carrier density n. The plasma, which is in an electric field, carries a current of density


r r\

J = evn = ec

PJ

511 (26.14)

n.

which delivers to the gas the energy required for pumping w =i:v£*. (26.15) Here, tp is the pumping pulse duration, n is the electron concentration, c is a constant characterizing the gas, and E is the electric field strength. The designs of electron-beam-controlled CO2 lasers are described in numerous publications. Let us consider some design versions. Figure 26.9 shows schematically the main units of the LAD-2 CO2 laser with an active volume of 270 1 (30x30x300 cm), developed at IHCE (Bychkov et al, 1976). The gas was ionized by an accelerated electron beam. The gas cell 1 of volume 4500 1 was made of steel; its inner surface was lined with fiber glass 3 to suppress corona discharges. Anode 2 of the gas cell with a working area of 30x300 cm was made of duralumin and specially shaped to prevent coronas. The cell was filled with an atmospheric pressure C02:N2:He =1:1:3 gas mixture. 2620 mm

Figure 26.9. Schematic of the LAD-2 electroionization CO2 laser

An electron accelerator produced an electron beam of cross section 30x300 cm with a current density of 0.4 A/cm^ uniform to ±15%. The average electron energy in a pulse of duration 1-3 \is was 200 keV. In the vacuum diode 4, a multipoint cold cathode 5 operating in the explosive emission mode was used. The beam was extracted through a window

512

Chapter 26

covered with polymer film 7 of thickness 150 |xm resting on a metal grid 6. The discharge current in the laser cell closed on a steel grid 8 that protected the film from the thermal action of the discharge. The total transparency of the window and the grid for 200-keV electrons was no less than 50%. The energy needed to excite the active volume of the gas cell was stored in a capacitor bank of capacitance 15 |xF and voltage 200 kV. High-voltage pulses of amplitude up to 500 kV were fed to the vacuum diode from a Marx generator whose capacitance with the capacitors connected in series was 0.67 îF. In this laser, use was made of a resonator with an output mirror 9 of diameter 240 mm, which was made of a plane-parellel KRS-6 plate with a 17% reflectance of an individual face. The totally reflecting mirror was a gold-plated quartz substrate of diameter 300 mm and radius of curvature 12 m. The radiation energy extracted in a pulse of 1.5 jis FWHM was 5 kJ with an efficiency of 20%. The use of an unstable resonator and the extraction of radiation from the entire volume made it possible to obtain with this laser a radiation energy of 7500 J (Mesyats et al., 1995). This design is quite conventional for pulsed CO2 lasers with various volumes and pressures. Its interesting version is a double-beam and, hence, doublecell CO2 laser producing 2.5 kJ of output energy in a pulse (Eninger, 1976). Further advances in laser technology were made in connection with the development of large-scale oscillator-amplifier systems intended for studying the applicability of CO2 lasers to ICF research. Over a short period, the Helios and Antares systems (Perkins, 1980) were developed which are capable of radiating 1-40 kJ in a nanosecond pulse. These systems are based on devices similar in design to those described above. The reduction of the overall dimensions of electron-beam-controlled CO2 lasers is important in the context of the creation of compact highsensitivity gas analyzers, lidars, high-resolution spectrometers, and other instruments in which the properties of overlapped laser amplification spectrum are used. In MIG-4, a compact repetitively pulsed electron-beam-controlled CO2 laser (Mesyats et al, 1995) (Fig. 26.10), the volume discharge intended to pump the working gas medium was initiated between a solid brass anode and a grid cathode and occupied a volume of 3x3.5x72 cm. The energy needed to initiate the discharge was stored in a low-inductance capacitor bank 3 of capacitance 0.19 |iF, which was charged from a dc voltage source to 50 kV. A volume discharge was initiated in the working zone of the laser by an electron beam with the following parameters: peak current 7.2 kA, crosssectional area 72x3 cm, duration 4.2 ns, average electron energy 155 keV, and pulse repetition rate 1-50 Hz.


513

This laser generated 30-J radiation pulses at a repetition rate of up to 50 Hz with up to 25% efficiency. In a quasistable medium, the radiation power at 50 Hz was --1 kW at the early stage and 400-500 W at the quasistationary stage up to the rupture of the foil. The chemical composition of the laser active medium changed in the course of repetitive operation, resulting in a decrease in output energy. This is due to the fact that as the laser turns on, there occur decomposition of CO2 and accumulation of CO and electronegative molecules of O2, NO, NO2, and N2O, resulting in a decreased discharge duration due to enhanced electron attachment and, hence, in a lower output energy. 4T

Figure 26.10. Block diagram of the MIG-4 CO2 laser: distributed-constant energy storage line (7), vacuum diode (2), storage capacitors (3), heat exchanger (4, 5), working wheel of the crossflow fan (6), and internal guide (7)

In electroionization CO2 lasers with a high gas pressure (10 atm and higher), a continuous tuning is possible (Bagratashvili et al, 1971). When the working mixture in a CO2 laser is at a pressure of 10 atm, the vibrationalrotational lines in the gain spectrum overlap and continuous tuning can be realized with the help of a selective resonator. This effect is described in detail elsewhere (Mesyats et al, 1995).

514

4.

Chapter 26

DESIGN AND OPERATION OF HIGH-POWER EXCIMER LASERS

For electron-beam pumping of excimer lasers, electron accelerators are used which produce electron beams of energy 0.1-2 MeV, current density 10-10^ A/cm^, and duration from 2 |LIS to 5 ns. When combined pumping by an electron beam and an external electric field is used, the beam current density can be several times lower. Figure 26.11 shows schematically a laser in which an electron beam is used for two-sided pumping. For combined pumping, energy storage capacitors are charged by a dc or pulsed voltage.

Figure 26.11. Schematic of a laser pumped from two magnetically focused beam accelerators: Marx generators (7), water lines (2), vacuum diodes (5), laser chamber {4), foil (5), and magnets (6)

The principle of operation of such devices is as follows: A Marx generator used as a power supply charges coaxial lines with a vacuum diode as a load. The cathode is a needle or a graphite plate operating in the explosive electron emission mode or specially created plasma. The anode is made of thin metal foil or Dacron film through which electrons are injected into the laser chamber. Since the working pressure in rare-gas-halide lasers ranges between 1 and 5 atm, the foil is supported by a grid on the vacuum side. As mentioned in Section 2 of Chapter 26, in the case of two-sided pumping, the plasma density distribution in the laser cell is spatially nonuniform. To make the plasma more uniform, multisided pumping is used. For example, four electron beams produced by planar-diodes accelerators were simultaneously injected in the chamber of the laser described by Edwards et al (1983). With such a design, the total current injected into the laser chamber can be increased without disturbing uniform pumping. Excimer lasers with a radiation energy of 10^-10"^ J are described by Rosocha et al. (1986). Much attention is being given to the development of KrF lasers (X = 249 nm) as the most efficient type of excimer lasers. The maximum radiation energy (-10 kJ) in a pulse of duration -500 ns was attained at LANL on the Aurora system (Rosocha et al, 1986). With KrF molecules, reduced output energies of up to 40 J/1 can be achieved with an


515

efficiency of up to 12% (Rica et aL, 1980). In designing wide-aperture devices capable of radiating over 10 kJ of energy, the rated specific energy density is usually taken as -10 mJ/cm-^ for an efficiency of 10%; in this case, the active volume of the laser must be over 10^ 1. Owadano et al (1987) described the design of a high-power laser pumped by a pulsed electron beam of duration -100 ns which is used as the third amplification stage in a laser system. The electron beam is formed by eight cathodes to which voltage is applied fi-om four water strip lines charged fi-om a high-voltage generator. For an active volume of 66 1, radiation of energy ~1 and 0.6 kJ and pulse duration 100 and 10 ns, respectively, was generated. Earlier, a similar KrF laser system generated radiation of energy -200 J (Edwards et al, 1983). Systems of this type show a rather high total efficiency [-2% for the laser described by Sullivan (1987)], but they can form only single radiation pulses in view of the technical difficulties associated with renewal of the active medium. The laser whose design is shown in Fig. 26.11 can be equipped with a working gas renewal system. It should be noted that the highest radiation energies have been achieved with lasers of this type (Cartwright, 1989; Rosocha et al, 1986; Ueda and Takima, 1988). The laser shown in Fig. 26.11 differs from one described by Owadano et al (1987) in that the electron beam is injected into the laser chamber firom two sides, and uniform energy input is provided by applying a magnetic field directed in parallel with the electron beam. The total efficiency of this type of laser is rather low since the creation of a magnetic field is power consuming. The electron beam in these two laser systems was formed by the same scheme. The laser design shown in Fig. 26.11 has been accepted as a basis for the development of systems capable of radiating up to 100 kJ of energy (Sullivan, 1987). A XeCl excimer laser {X = 308 nm) with six-sided electron-beam pumping is described by Mesyats et al (1992). Twelve accelerators with Marx generators discharged into explosive-emission graphite-cathode diodes were used. Each accelerator generated an electron beam (1 ^s) of energy 600 keV, current 60 kA, and beam cross-section 25x100 cm. The accelerators were arranged on two levels and pumped a coaxial laser cell of volume 6001. The Marx generators and the diodes were mounted in a common vacuum chamber. This resulted in a compact laser operating without coaxial energy storage lines. The Marx generators operated with a small jitter (-10 ns). The total electron current was 700 kA. The radiation pulse energy was 2 kJ (Mesyats et al, 1995). A schematic diagram of this laser is given in Fig. 26.12. Electric-discharge excimer lasers are also being extensively developed. The systems initiating a volume discharge in lasers of this type are similar to those shown in Fig. 26.3. For pumping excimer lasers, transverse discharges

516

Chapter 26

exhibit the most promise. With transverse volume discharges, pumping powers of 1-10 MW/cm^ have been attained for working mixtures of R:R*:X = 1000:10:1 at a pressure of several atmospheres. When a storage capacitor is discharged into a gap filled with a rare-gashalide mixture, the voltage waveform, in the case of formation of a volume discharge, indicates three characteristic stages of the process: a) the prebreakdown stage whose duration usually ranges from 50 to 100 ns; the gap voltage increases and, immediately prior to breakdown, becomes several times greater than the dc breakdown voltage; a volume discharge starts developing due to preionization; b) the stage of rapid voltage drop that lasts -10 ns; the current through the gap increases by several orders of magnitude, while the voltage decreases to a value several times smaller than the dc breakdown voltage; the formation of the volume discharge is completed; c) the quasistationary stage whose duration depends on a large number of parameters and may be over 1 |is. (During discharges in rare gases, the voltage at the quasistationary stage is considerably lower than the dc breakdown voltage due to the effect of stepwise ionization, while this voltage in nitrogen is approximately equal to the dc breakdown voltage.) The pumping of the active medium occurs at the stage of rapid voltage drop and at the quasistationary stage.

Figure 26.12. Schematic of an excimer laser with a transverse discharge and working mixture renewal: storage capacitor (7), peaking capacitor (2), thyratron (5), nonlinear iron-coil choke (4\ screen (5), grid anode (6), cathode (7), fluoroplastic plate {8\ gas chamber case (9), turbofan (70), auxiliary electrodes (77), and blocking capacitor (72)

HIGH'POWER PULSED GAS LASERS

517

At elevated pressures, only a multielectron-initiated volume discharge is possible (Mesyats et al, 1995). The conditions for the formation of a homogeneous discharge under elevated pressures can be formulated as follows: First, it is necessary that the density of initial electrons produced by an external ionizer be over {r^r)'^ (where r^^ is the critical radius of the electron avalanche head), the electron density at which a streamer starts developing. Second, in view of the fact that the preionizer usually operates for a short time and the initial electrons leave a layer of width x adjoining the cathode due to drift, the condition x < r^^ must be satisfied. In this case, the streamer formation can be avoided due to insufficient overlap of avalanches in the electron-depleted layer near the cathode. Thus, preionization makes it possible to produce initial electrons in the bulk of the gas and/or at the cathode from which electron avalanches develop. Overlapping of individual avalanches (the rate of evolution of avalanches depends on the applied electric field) leads to the formation of an elevated-pressure homogeneous discharge. The duration of the volume stage of a discharge at an elevated pressure is determined by many factors (specific input energy, mixture composition and pressure, electrode shape, material, and surface condition, etc.); however, the most common reason for discharge constriction is cathode instability (Mesyats, 1975; Mesyats etal, 1995). To attain lasing in high-pressure rare-gas-halide pulsed lasers, an energy of -0.1 J/(cm^-atm) must be supplied to the active medium within a short time (usually < 0.1 |is), thus providing for the operation of a volume discharge. Therefore, high-pressure lasers must incorporate both a pumping generator and a preionization system. The choice of the circuit design is dictated by the requirements on the pumping pulse. For capacitive energy storage, use can be made of individual capacitors or distributed-constant lines (e.g., water-insulated lines). It is very important to match the pumping generator to the discharge gap. Here, matching implies not only that the wave impedance of the generator must be equal to that of the gap, but also that the inductance of the discharge gap leads must be as low as possible to minimize the losses in delivering energy from the generator to the load. Figure 26.12 shows schematically a compact excimer laser with a transverse discharge and working medium renewal with the use of a turbofan (Mesyats et al, 1995). The energy storage capacitor is charged from a pulse generator producing pulses of duration 10 |is and peak voltage controllable in the range 10-35 kV. After the operation of the switch, a peaking capacitor is charged. For the switching element, a thyratron is used. This pumping generator operates with a voltage of 25 kV at a pulse repetition rate of up to 500 Hz.

518

Chapter 26

The physical processes occurring in other types of excimer lasers and their designs are described elsewhere (Rhodes, 1979; McDaniel and Nighan, 1982; Mesyats et al, 1995; Mangano and Jacob, 1975; Searles and Hart, 1975; Brau and Ewing, 1975; Eletsky, 1978; Evdokimov, 1982; Rosocha etal, 1986; Rica et al, 1980; Owadano et al, 1987; Ueda and Takima, 1988; Sullivan, 1987; Mesyats et al, 1992; Baranov et al, 1988; Ischenko etal, 1976; Smimov, 1983).

REFERENCES Alcock, A. J., Leopold, K., and Richardson, M. C, 1973, Continuously Tunable HighPressure CO2 Laser with UV Photopreionization, Appl Phys. Lett. 23:562-564. Apollonov, V. v., Baitsur, G. G., Prokhorov, A. M., Semenov, S. K, and Firsov, K. N., 1987, Dynamic Profiling of the Electric Field during the Formation of a Self-Sustained Volume Discharge under Intense Ionization of the Electrode Regions, Kvant. Elektron.

U'.im-iiio. Bagratashvili, V. N., Knyazev, I. N., and Letokhov, V. S., 1971, On the Tunable Infrared Gas Lasers, Opt. Commun. 4:154-156. Baranov, V. Yu., Borisov, V. M., and Stepanov, Yu. Yu., 1988, Electric-Discharge RareGaS'Halide Excimer Lasers (in Russian). Energoatomizdat, Moscow. Basov, N. G., 1964, Opening Remarks: Fourth International Quantum Electronics Conference,/^^£ y. Quant. Electron. 2:354-357. Basov, N. G., Belenov, E. M., Danilychev, V. A., and Suchkov, A. F., 1971, A Pulsed CO2 Laser with a High-Pressure Gas Mixture, Kvant. Elektron. 3:121. Berger, M. Y. and Seltzer, S. M., 1964, Tables of Energy Losses and Ranges of Electrons and Positrons. NASA Spec. Publ. No. 3012. Brandenberg, W. M., Bailey, M. P., and Texeira, P. D., 1972, Supersonic Transverse Electrical Discharge Laser, IEEE J. Quant. Electron. 8:414-418. Brau, C. A. and Ewing, J. J., 1975, 354-nm Laser Action on XeF, Appl. Phys. Lett. 1975. 27:435-437. Bychkov, Yu. I., Karlova, E. K., Karlov, N. V., Koval'chuk, B. M., Kuz'min, G. P., Kurbatov, Yu. A., Manylov, V. I., Mesyats, G. A., Orlovsky, V. M., Prokhorov, A. M., and Rybalov, A. M., 1976, A 5-kJ Pulsed CO2 Laser, Pis'ma Zh. Tekh. Fiz. 2:212-216. Bychkov, Yu. I., Osipov, V. V., and Savin, V. V., 1977, Electric-Discharge CO2 Lasers. In Gas Lasers (in Russian, R. I. Soloukhin and V. P. Chebotaev, eds.). Nauka, Novosibirsk. Cartwright, D. C, 1989, Inertial Confinement Fusion at Los Alamos. Vol. 1-2. Progress on Inertial Confinement Fusion Since 1985. Los Alamos. Chang, N. C, and Tavis, M. T., 1974, Gain of High-Pressure CO2 Lasers, IEEE J. Quant. Electron. 10:372-375. Edwards, C. B., O'Neill, F., and Shaw, M. J., 1983, "SPRITE" - a High Power E-Beam Pumped Kr-F Laser. In Proc. Conf Excimer Lasers, American Inst. Phys., New York, pp. 59-65. Eletsky, A. V., 1978, Excimer Lasers, Usp. Fiz. Nauk 125:279-314. Eninger, J. E., 1976, Broad Area Beam Technology for Pulsed High Power Gas Lasers. In Proc. I IEEE Intern. Pulsed Power Conf, Lubbock, TX, pp. 499-503. Evdokimov, O. B., ed., 1982, Injection Gas Electronics (in Russian). Nauka, Novosibirsk.


519

Fenstemacher, C. A., Nutter, M. J., Rink, J. P., and Boyer, K., 1971, Electron Beam Initiation of Large Volume Electrical Discharges in CO2 Laser Media, Bull. Amer. Phys. Soc. (Ser. II.) 16:42. Heard, H. G., 1963, Ultra-Violet Gas Laser at Room Temperature, Nature. 200(4907):667. Hidson, D. J., Makios, V., and Morrison, R. W., 1972, Transverse CO2 Laser Action at Several Atmospheres, Phys. Rev. Lett. 40A:413-414. Hoffman, J. M., Hays, A. K., and Tisone, G. C, 1976, High-Power UV Noble-Gas-Halide Lasers, Appl. Phys. Lett. 28:538-539. Ischenko, V. N., Lisitsyn, V. N., and Razhev, A. M., 1976, High-Power Superluminosity of ArF, KrF, and XeF Excimers in Electrical Discharges, Pis'ma Zk Tekh. Fiz. 2:839-842. Javan, A., 1959, Possibility of Production of Negative Temperature in Gas Discharges, Phys. Rev. Lett. 3:87-89. Jones, C. R., 1978, Optically Pumped Mid IR Lasers, Laser Focus. 4:68-72. Karlov, N. V., 1983, Lectures on Quantum Electronics (in Russian). Nauka, Moscow. Karlov, N. V., Kisletsov, A. V., Kovalev, I. O., Kuz'min, G. P., Nesterenko, A. A., and Khokhlov, E. M., 1987, Continuously Tunable High-Pressure CO2 Laser with a Plasma CathodQ, Kvant.Eelektron. 14:216-218. Kast, S. J. and Cason, Ch., 1973, Performance Comparison of Pulsed Discharge and E-Beam Controlled CO2 Lasers, J. Appl. Phys. 44:1631-1637. Laflame, A. K., 1970, Double Discharge Excitation for Atmospheric Pressure CO2 Lasers, Rev. Sci. Instrum. 41:1578. Leonard, D. A., 1965, Saturation of the Molecular Nitrogen Second Positive Laser Transition, Appl. Phys. Lett. 7:4-6. Mangano, J. A. and Jacob, J. H., 1975, Electron-Beam-Controlled Discharge Pumping of the KrF Laser, Ibid. 27:495-498. Mathias, L. E. S. and Parker, J. T., 1963, Stimulated Emission in the Band Spectrum of Nitrogen, Ibid. 3:16. McDaniel, E. W. and Nighan, W. L., eds., 1982, Gas Lasers. Acad. Press, New York. McFarlane, R. A., 1965, Observation of a n~^S~ Transition in the N2 Molecule, Phys. Rev. 140 (4A): 1070-1071. Mesyats, G. A., 1975, Electric Field Instablilities in a Volume Gas Discharge, Pis'ma Zh. Tekh. Fiz. 1:660-663. Mesyats, G. A., Osipov, V. V., and Tarasenko, V. F., 1995, Pulsed Gas Lasers. SPIE Optical Engineering Press, Bellingham. Mesyats, G. A., Bychkov, Yu. I., and Koval'chuk, B. M., 1992, High-Power XeCl Excimer Lasers. In Proc. SPIE. Intense Laser Beams, SPIE Press, Los Angeles, Vol. 1628, pp. 70-80. Mesyats, G.A., Koval'chuk, B.M., and Potalitsyn, Yu.F., 1972, USSR Inventor's Certificate No. 356 824; 1970, Dokl. Akad Nauk. 191: 76-78. Owadano, Y., Okuda, I., Tanimoto, M., Matsumoto, Y., Kasai, T., and Yano, M., 1987, Development of a 1-kJ KrF Laser System for Laser Fusion Research, Fusion Technol. 11:486-491. Patel, C. K. N., 1964, Selective Excitation through Vibrational Energy Transfer and Optical Maser Action inNe-C02, Phys. Rev. Lett. 13:617-619. Patel, C. K. N. and Kerl, R. J., 1964, Laser Oscillation on XÊ"' Vibrational-Rotational Transitions of CO, Appl. Phys. Lett. 5:81-83. Pavlovsky, A. I., Bosamykin, V. S., and Karelin, V. I., 1976, Electric-Discharge Laser with Active Volume Initiation, Kvant. Elektron. 3:601-604.

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Perkins, R. B., 1980, Progress in Inertia! Research at Los Alamos Sci. Lab. In VIII Intern. Conf, on Plasma Phys. and Control Nucl Fusion Res., Brussels, IAEA-CN-38/B-2. Prokhorov, A. M., 1958, On a Molecular Amplifier and Submillimeter Wave Generator, Zh. Eksp. Teor Fiz. 34:1658-1659. Rhodes, Ch. K., ed., 1979, Excimer Lasers, Springer, Berlin. Rica, J. K., Tisone, G. C, and Patterson, E. L., 1980, Oscillator Performance and Energy Extraction from a KrF Laser Pumped by a High Intensity Relativistic Electron Beam, IEEE J. Quant. Electron. 16:1315-1325. Rosocha, L. A., Bowling, P. S., Burrows, M. D., Kang, M., Hanlon, J., McLeod, J., and York, G. W., Jr., 1986, An Overview of Aurora: a Multi-Kilojoule KrF Laser System for Inertial Confinement Fusion. In Laser and Particle Beams [Selected papers from CLEO'85 - 13* Int. Conf. on Quantum Electronics (Laser and Electro-Optics), May 1985], Baltimore, Vol. 4, P t l , pp. 55-70. Searles, S. K. and Hart, G. A., 1975, Stimulated Emission at 281.8 nm from XeBr, Appl. Phys. Lett. 27:243r247. Shipman, J. D., Jr., 1967, Traveling Wave Excitation of High Power Gas Lasers, Ibid. 10:3. Smimov, B. M., 1983, Excimer Molecules, Usp.Fiz. Nauk 139:53-81. Smimov, B. M., ed., 1983, Pulsed CO2 Lasers and Their Application in Isotope Separation (in Russian). Nauka, Moscow. Sullivan, J. A., 1987, Design of a 100-kJ KrF Power Amplifier Module, Fusion Technol. 11:684-704. Ueda, K. I. and Takima, H., 1988, Scaling of High Pump Rate 500-J KrF Laser. In Proc. Conf. Lasers and Electro-Optics, Annaheim, CA., Vol. 7, pp. 2-4. Vorob'ev, A. A. and Kononov, B. A., 1966, Passage of Electrons Through Matter (in Russian). Tomsk State University Publishers, Tomsk.

Chapter 27 GENERATION OF HIGH-POWER PULSED MICROWAVES

1.

GENERAL INFORMATION

The progress in many fields of science and technology is closely connected with advances in creating new pulsed oscillators capable of producing coherent electromagnetic radiation in various wavelength ranges. A great deal of effort was directed for mastering the microwave range, especially the range 10"^-1 m. Microwave devices must meet a large nimiber of requirements set by their specific application (efficiency, overall dimensions, bandwidth, coherence, pulse duration, etc.). In many fields of use, such as radio detection and ranging, plasma physics, and accelerator technology, the maximum output power level is of major importance. High radiation powers are usually generated within short times, i.e., in the pulsed mode. The use of high-power electron beams produced due to explosive electron emission has made it possible to increase the microwave power by many orders of magnitude and bring it to 10^^ W and higher in pulses of duration of the order of 10"^-10"^ s. This caused a revolution in the views of the potentialities of pulsed microwave electronics which became possible owing to comprehensive investigations of the interaction of highpower charged particle flows with electromagnetic waves. One line of investigation has been the study of stimulated emission of electron flows and its applications for the creation of high-power sources of coherent electromagnetic radiation in a wide range of wavelengths and pulse durations. In this respect, high-current pulsed electron accelerators considered in previous chapters possess unique potentialities. In electron accelerators intended for microwave electronics applications, magnetically

522

Chapter 27

insulated coaxial diodes (see Chapter 23) or, more seldom, e.g., in vircators, planar diodes without a magnetic field are used. The first attempt to generate high-power pulsed microwaves was made by Nation (1970). At that time, the systems for beam formation and electron energy extraction were far fi-om perfect. This was the reason for the low efficiency of the microwave oscillator (much lower than 1%). First important results were obtained researchers of the Institute of Applied Physics (Nizhni Novgorod) and Institute of General Physics (Moscow) (Kovalev et al, 1973). Microwave pulses of power 3-10^ W and duration 10"^ s with efficiency over 10% were generated at a wavelength of 3 cm. The next important step on this line was the creation of microwave oscillators operating at high pulse repetition rates at IHCE (El'chaninov et al, 1979). To induce oscillations, stimulated emission of various types of radiation (Cherenkov radiation, cyclotron radiation, transient radiation, etc.) is used. The most common microwave devices using high-current electron beams are the relativistic backward-wave oscillator (BWO or carcinotron) (Kovalev etal, 1973; Carmel et al, 1974; El'chaninov et ai, 1979; Levush et al, 1992; Moreland et al, 1994), multiwave Cherenkov oscillator (MWCO) (Bugaev et al, 1991), relativistic klystron (El'chaninov et al, 1982; Friedman et al, 1990), reltron (Miller et al, 1992), plasma-assisted Cherenkov oscillator (Kuzelev et al, 1982), plasma-assisted slow-wave oscillator (PASOTRON) (Goebel et al, 1998), relativistic gyrotron (Ginzburg et al, 1979), relativistic magnetron (Didenko and Yushkov, 1984), magnetically insulated line oscillator (MILO) (Clark et al, 1988), and virtual cathode oscillators (vircators) (Didenko and Yushkov, 1984; Jiang et al, 1999; Kitsanov et al, 2002). Mechanisms of the stimulated emission of radiation by high-current electron beams and the results of investigations of high-power microwave oscillators and accelerators used for their power supply are described in collection of papers (Gaponov-Grekhov, 1979-1992; Mesyats, 1983) and in monographs (Bugaev et al, 1991; Didenko and Yushkov, 1984; Benford and Swegle, 1992; Granatstein and Alexeff, 1987; Barker and Schamiloglu, 2001). Among the above microwave oscillators, carcinotron using Cherenkov radiation is most generally employed. For this reason, we will mainly consider in this chapter the microwave oscillators based on carcinotrons. From the viewpoint of the generation of coherent electromagnetic radiation, a free electron has the following obvious advantages over bound (in quantum-mechanical sense) particles (electrons and atoms): a) in going from one state of its continuous energy spectrum to another, a fi-ee electron emits a photon whose energy (frequency) can be varied over a wide range by properly choosing the static field and the slow-wave structure;

GENERATION OF HIGH-POWER PULSED MICROWA VES

523

b) it can give up a large number of identical (or almost identical) quanta to the radiation field. The first circumstance allows devices based on classical principles to cover continuously a wide frequency range, while the second one makes them capable to efficiently generate high-power radiation. The stimulated emission process in microwave devices includes an rf current appearing in the electron beam due to electron grouping induced by the rf field and the reverse action of this current on the radiation field. Steady progress in classical microwave electronics made it possible to predict that the performance of microwave devices could be essentially improved by using relativistic electron beams. However, it was obvious that the currents of electron beams produced by "ordinary" accelerators were too low for stimulated emission could be realized. Hopes for the production of electron beams in which relativistic energy of particles would be combined with a high density became reasonable only in the late 1950s owing to the progress in pulsed power technology. First high-current electron accelerators were developed in the 1960s.

2.

EFFECTS UNDERLYING RELATIVISTIC MICROWAVE ELECTRONICS

We start our analysisfi-omthe conditions that must be realized for at least one electron to emit photons. The main prerequisite to efficient emission is the so-called phase synchronism under which the velocity of a particle is close to the phase velocity of the wave. Therefore, a particle (or group of particles) "immersed" in the decelerating phase of the field may reside in this phase for a long time and give up a considerable portion of its energy to the wave. To realize the mode of synchronism, one of the methods illustrated in Fig. 27.1 can be used (Gaponov-Grekhov and Petelin, 1979). First, this may be slowing down a wave or its spatial harmonic. In the case of a homogeneous or spatially periodic medium (Fig. 27.1, a, b), Cherenkov radiation is generated, while in the case of an inhomogeneous medium (Fig. 27.1, c), this is transient radiation. Second, an electron can be set into motion with a varying transverse velocity (Fig. 27.1, d). From the viewpoint of rf electronics, of particular interest are the cases where an electron emits photons as an oscillator during its periodic motion in a static field such as a uniform magnetic field (cyclotron or magnetic bremsstrahlung. Fig. 27.1, e) or a spatially periodic field (undulator radiation. Fig. 27.1, g). A combination of the above methods can also be used. Such a combination leads to an essentially new effect, viz., anomalous Doppler

Chapter 27

524

effect, such that the oscillatory velocity of an electron increases during the emission of bremsstrahlung, and the oscillator energy and radiation energy are taken from the translational motion of the electron. In addition to single photon (in reference to one electron) emission processes, multiphoton (combination) scattering processes may also take place where a wave incident on a moving electron is re-emitted as another wave (Fig. 27.1, A). / / vy-77V

.US''

(d) Cherenkov and transient radiation

/

/ ^/'//Â (b)

G>

(c)

Q-

m m m m \A

m

id)

Bremsstrahlung

Wave scattering

(e)

^fU

(h)

Figure 27.1. Mechanisms of the emission of radiation by an electron

For the conditions of distributed interaction of an electromagnetic wave with an electron beam guide by a static (uniform or spatially periodic) magnetic field, the criterion for synchronism can be written as o) = A:||^ll+«Q (« = 0, ±1,...)

(27.1)

where co and k\\ are the wave frequency and constant of its propagation through the waveguide and Q and V\\ are the oscillation frequency and translational velocity of the electrons. In going from nonrelativistic to relativistic velocities, the emission of electrons changes qualitatively. Let us

GENERATION OF HIGH-POWER PULSED MICROWAVES

525

consider this phenomenon for Cherenkov radiation (see Fig. 27.1, c). In this case, n = 0 in formula (27.1). Radiation of this type is used, e.g., in a traveling-wave tube. Let an electromagnetic wave with constant amplitude and phase velocity interact with an electron flow, steady-state and monoenergetic at the entrance, on a bounded segment. If the wave and the flow are in strict synchronism, the integrated energy balance of their interaction is obviously equal to zero since electrons are displaced "symmetrically" toward the nodes of the varying field and therefore the energy absorbed by accelerated electrons and the energy radiated by decelerated electrons are mutually compensated. If the phase velocity of the wave is slightly higher than the initial velocity of the electrons, the latter are grouped in the acceleration phase of the ac field. Charged particle accelerators employed in nuclear physics operate in such a mode. If, on the contrary, the wave "lags behind" the electrons, the latter, in the course of grouping, are shifted into the deceleration phase and give up their energy to the wave; this is the mode of operation for generators of electromagnetic radiation. For a microwave oscillator to operate with high efficiency and high output power, the following four conditions must be satisfied (GaponovGrekhov and Petelin, 1979): 1. The electron beam must transfer a high power, i.e., the beam current and particle density must be high. 2. The beam electrons must be grouped to form compact clusters. To this end, their dynamic displacement relative to one another due to the action of the wave on a segment of length L must be of the order of the "retarded" wavelength Xr = ^P*. dvT-^K.

(27.2)

where 5v is the change in electron velocity under the action of the wave, T = L/vo, p = VQ/C, and X = 2TIC/W .

3. Each cluster must go to the middle of the deceleration phase of the wave. For this to occur, the kinematic displacement of electrons associated with an excess A-y = -ô - v^^ of their initial velocity -ô over the phase velocity i;ph of the wave should be comparable to the "retarded" wavelength: AvT-K,

(27.3)

4. Finally, the energy 58 -- eEL taken away by the electric field E of the wave from the electrons must be comparable to the initial energy of the electrons, s: 58^8, or, which is the same.

(27.4)

526

Chapter 27 EL-V,

(27.5)

where V is the accelerating voltage of the electron injector. The difference between the slightly relativistic (P

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