Quasi-Optical Control of Intense Microwave Transmission

Quasi-Optical Control of Intense Microwave Transmission NATO Science Series A Series presenting the results of scient...

Author: Jay L. Hirshfield | Michael I. Petelin

79 downloads 1038 Views 8MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Quasi-Optical Control of Intense Microwave Transmission

NATO Science Series A Series presenting the results of scientific meetings supported under the NATO Science Programme. The Series is published by IOS Press, Amsterdam, and Springer (formerly Kluwer Academic Publishers) in conjunction with the NATO Public Diplomacy Division.

Sub-Series I. II. III. IV.

Life and Behavioural Sciences Mathematics, Physics and Chemistry Computer and Systems Science Earth and Environmental Sciences

IOS Press Springer (formerly Kluwer Academic Publishers) IOS Press Springer (formerly Kluwer Academic Publishers)

The NATO Science Series continues the series of books published formerly as the NATO ASI Series.

The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally supported are “Advanced Study Institutes” and “Advanced Research Workshops”, and the NATO Science Series collects together the results of these meetings. The meetings are co-organized by scientists from , NATO countries and scientists from NATO s Partner countries – countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series was re-organized to the four sub-series noted above. Please consult the following web sites for information on previous volumes published in the Series. http://www.nato.int/science http://www.springeronline.com http://www.iospress.nl

Series II: Mathematics, Physics and Chemistry – Vol. 203

Quasi-Optical Control of Intense Microwave Transmission edited by

Jay L. Hirshfield Yale University, New Haven, CT, U.S.A. and

Michael I. Petelin Institute of Applied Physics, Nizhny Novgorod, Russia

Published in cooperation with NATO Public Diplomacy Division

Proceedings of the NATO Advanced Research Workshop on Quasi-Optical Control of Intense Microwave Transmission Nizhny Novgorod, Russia 17- 20 February 2004 A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN-10 ISBN-13 ISBN-10 ISBN-10 ISBN-13 ISBN-13

1-4020-3637-X (PB) 978-1-4020-3637-8 (PB) 1-4020-3636-1 (HB) 1-4020-3638-8 (e-book) 978-1-4020-3636-1 (HB) 978-1-4020-3638-5 (e-book)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

www.springeronline.com

Printed on acid-free paper

All Rights Reserved © 2005 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands.

CONTENTS

Preface ……………………………………………………………..……..…ix Acknowledgements …………………..………………...……………………xi

Chapter 1 Quasi-Optical Components – Theory and Experiments ……………………………………… 1 Measurement of Near-Megawatt Millimeter-Wave Beams ……...…..…. 3 V. I. Malygin, V. I. Belousov, A. V. Chirkov, G. G. Denisov, G. I. Kalynova, V. I. Ilin, L. G. Popov

Oversized Transmission Lines for Gyrotron-Based Technological Ovens and Plasma-Chemical Reactors …….…………….15 A. Bogdashov, G. Denisov, G. Kalynova

Development of Lumped and Distributed Models for Accurate Measurements of Q-Factors of Quasi-Optical Resonators ……………...25 B. Kapilevich

The Mode-Matching Technique and Fast Numerical Models of Arbitrary Coordinate Waveguide Objects ……………………...……. 41 A. A. Kirilenko, V. I. Tkachenko, L. A. Rud, D. Yu. Kulik

Electric Field Integral Equation Analysis and Advanced Optimization of Quasi-Optical Launchers used in High Power Gyrotrons …..……….55 J. Neilson

Comparison of Two Optimization Criteria for Quasi-Optical Power Transmission Lines ………..………...……………65 N. N. Voitovich, B. Z. Katsenelenbaum, O. V. Kusyi

A General Purpose Electromagnetic Code for Designing Microwave Components ...………………………….……...73 W. Bruns, H. Henke

v

vi

Contents

Chapter 2 Quasi-Optical Devices and Systems ………….....93 Amplification and Generation of High-Power Microwave by Relativistic Electron Beams in Sectioned Systems ……..…….………95 E. Abubakirov, N. Kovalev, V. Tulpakov

Microwave Devices with Helically Corrugated Waveguides …….…….105 V. L. Bratman, A.W. Cross, G. G. Denisov, A. D. R. Phelps, S.V. Samsonov

Quasi-Optical Transmission Lines at CIEMAT and at GPI …………..115 A. Fernández, K. Likin, G. Batanov, L. Kolik, A. Petrov, K. Sarksyan, N. Kharchev, W. Kasparek, R. Martín

Superradiance of Intense Electron Bunches ………….………………...131 N. Ginzburg, M. Yalandin, S. Korovin, V. Rostov, A. Phelps

Transmission Line Components for a Future Millimeter-Wave High-Gradient Linear Accelerator …………………..…...……………..147 J. L. Hirshfield, A. A. Bogdashov, A. V. Chirkov, G. G. Denisov, A. S. Fix, S. V. Kuzikov, M. A. LaPointe, A. G. Litvak, D. A. Lukovnikov, V. I. Malygin, O. A. Nezhevenko, M. I. Petelin,, Yu.V. Rodin, G.V. Serdobintsev, M.Y. Shmelyov, V.P. Yakovlev

Ferrite Phase Shifters for Ka Band Array Antennas ……...…………...165 Yu. B. Korchemkin, V. V. Denisenko, N. P. Milevsky, V. V. Fedorov

Propagation of Wave Trains of Finite Extent on Wide, Thin-Walled Electron Beams ….……………….………………………..177 E. Schamiloglu, N. Kovalev

Quasi-Optical Multiplexers for Space Communication and Radar with Synthesized Frequency Band ……...………...……………..185 M. Petelin, G. Caryotakis, Yu. Postoenko, G. Scheitrum, I. Turchin

Active Compression of Rf Pulses ……………………………….………..199 A. L. Vikharev, O. A. Ivanov, A. M. Gorbachev, S. V. Kuzikov, V. A. Isaev, V. A. Koldanov, M. A. Lobaev, J. L. Hirshfield, M. A. LaPointe, O. A. Nezhevenko, S. H. Gold, A. K. Kinkead

Control of Intense Millimeter Wave Propagation by Tailoring the Dispersive Properties of the Medium ……………………219 A. Yahalom, Y. Pinhasi

Contents

vii

High-Power Millimetre Wave Transmission Systems and Components for Electron Cyclotron Heating of Fusion Plasmas ………………….…241 W. Kasparek, G. Dammertz, V. Erckmann, G. Gantenbein, M. Grünert, E. Holzhauer, H. Kumric, H. P. Laqua, F. Leuterer, G. Michel, B. Plaum, K. Schwörer, D. Wagner, R. Wacker, M. Weissgerber

Space-Frequency Model of Ultra Wide-Band Interactions in Millimeter Wave Masers …………………………………..……….…253 Y. Pinhasi, Y. Lurie, A. Yahalom

Chapter 3 Applications of Quasi-Optical Systems ………….271 Bi-Static Forward-Scatter Radar with Space-Based Transmitte r .…... 273 A. B. Blyakhman

Analysis of Nanosecond Gigawatt Radar ………………………..……...283 A. Blyakhman, D. Clunie, G. Mesiats, R.W. Harris, M. Petelin, G. Postoenko, B Wardrop

High-Power Microwave Spectroscopy …...……………………...………297 G. Yu. Golubiatnikov

A Multipactor Threshold in Waveguides: Theory and Experiment …..305 J. Puech, L. Lapierre, J. Sombrin, V. Semenov, A. Sazontov, M. Buyanova, N. Vdovicheva, U. Jordan, R. Udiljak, D. Anderson, M. Lisak

Quasi-Optical Mode Converters in Advance High-Power Gyrotrons for Nuclear Fusion Plasma Heating ………..…325 M. Thumm, A. Arnold, O. Drumm, J. Jin, G. Michel, B. Piosczyk, T. Rzesnicki, D. Wagner, X. Yang

Radar and Communication Systems: Some Trends of Development …353 A. A. Tolkachev, E. N. Yegorov, A.V. Shishlov

On Antenna Systems for Space Applications ……………..…………….371 K. van’t Klooster

Intense Microwave Pulse Transmission through Electrically Controlled Ferrite Phase Shifters ……………..…………...393 N. Kolganov, N. Kovalov, V. Kashin, E. Danilov

Index of Authors ………...………………………………...………………399

PREFACE

Between February 17 and 20, 2004, approximately fifty scientists from ten countries came together at the Institute of Applied Physics (IAP), Nizhny Novgorod, Russia to participate in a NATO-sponsored Advanced Research Workshop whose appellation is reflected in the title of this volume, namely Quasi-Optical Control of Intense Microwave Transmission. The fashionable label “quasi-optical” has come into use in recent decades to denote structures whose characteristic dimensions exceed (sometimes by large factors) the free-space radiation wavelength. Such structures were and are developed to replace the traditional single-eigenmode ones in situations when high frequencies (short wavelengths) are combined with high powers, a combination that could otherwise lead to RF breakdown and high Ohmic wall heating rates. Treatments of guided wave propagation in oversized structures is aimed at preserving the propagating field coherence and thus to provide efficient transmission of RF power to remote destinations such as antennas, microwave ovens, plasma-chemical reactors, nuclear fusion machines, and the like. For the participants, this Workshop provided an unusual opportunity to meet and exchange ideas with, and learn from, colleagues from many countries working in a rather diverse agglomeration of fields. The attendees found themselves to be coupled in the common goals of characterizing, designing, and building quasi-optical structures for the control and transmission of intense microwave power flows. A number of junior research staff and students from IAP were also able to participate as informal onlookers, to witness first-hand the exciting give-and-take typical of an open international scientific forum. The 27 original formal presentations at the Workshop that are collected as individual sections in this volume represent contributions by 116 authors, some to more than one of the sections. Papers are grouped— somewhat arbitrarily—into three chapters: Quasi-Optical Components— Theory and Experiments, Quasi-Optical Devices and Systems, and Applications of Quasi-Optical Systems. Applications of quasi-optics extend to use of high-power microwaves (including millimeter-waves) for radar and communications (especially deep space millimeter wave systems, space debris detection radar, and radar for detection of small targets moving over heavy clutter); particle accelerators (especially for a future high-accelerationgradient electron-positron collider); plasma research (especially for controlled nuclear fusion and waste decontamination); and material processing (in particular, ceramic sintering with millimeter waves, and coating of metal surfaces with protective dielectric films.). ix

Preface

x

It is hoped that readers of this volume come to more deeply understand and appreciate the need and remarkable capability of quasi-optical structures, and their utility in this wide range of applications. J. L. Hirshfield and M. I. Petelin, Editors

ACKNOWLEDGMENTS

The Advanced Research Workshop on Quasi-Optical Control of Intense Microwave Transmissions was sponsored by the North Atlantic Treaty Organization (NATO) Public Diplomacy Division’s Collaborative Programmes Section on Physical and Engineering Science & Technology. NATO support provided for travel to Nizhny Novgorod for foreign and nonlocal Russian participants, and for costs incurred in organizing and sustaining the Workshop. Appreciation is extended by the Workshop co-chairmen to NATO for its selection of this Workshop as one of those deemed worthy of support during 2004, and for its far-sighted policy of supporting international conferences and workshops to foster close, productive collaborations between scientists in the former Soviet Union and those working in NATO-member and non-affiliated countries. Financial support for the Workshop was also contributed by Russian Academy of Sciences (RAS); Institute of Applied Physics (IAP), Nizhny Novgorod, Russia; and by the small research and development firm Omega-P, Inc., of New Haven, Connecticut, USA. Appreciation is extended for this support to Professor Gennady Mesyats, Vice-President of RAS; Professor Alexander Litvak, Director of IAP; and to Dr. George Trahan, Vice-President of Omega-P. Professor Litvak also deserves thanks for making available a new bright and attractive lecture hall within IAP where the sessions of the Workshop were held. Further individuals who were of inestimable help in dealing with the myriad logistical and organizational steps necessary to the success of such an endeavor include Mr. Vladislav Agaphonov, Deputy Director of IAP; Mr. Edward Abubakirov, Mr. Anatoly Turko, and Ms. Natalie Bondarenko, members of the Local Organizing Committee. Special thanks are due to Miss Enid Stanley of Omega-P, Inc., without whose persistent and indefatigable efforts neither the Workshop nor this volume could have come into being. Finally, appreciation is extended to the participants whose presence at the Workshop helped make it the success that it was; it is their contributions that this volume records. J. L. Hirshfield, and M. I. Petelin, Workshop Co-Chairmen

xi

CHAPTER 1

QUASI-OPTICAL COMPONENTS – THEORY AND EXPERIMENTS

MEASUREMENT OF NEAR-MEGAWATT MILLIMETER-WAVE BEAMS

V. I. Belousov1, V. I. Malygin 1, A.V. Chirkov1, G. G. Denisov1, G. I. Kalynova1, V.I. Ilin2, L. G. Popov3 1

Institute of Applied Physics of Russian Academy of Sciences; Institute of Nuclear Fusion RRC “Kurchatov Institute”; 3 Gycom Ltd. 2

Abstract:

To measure parameters of microwave beams produced by modern gyrotrons, a number of special devices have been developed: quasi-optical filters, bidirectional couplers, calorimetric loads, etc. The wave beam pattern is studied by measuring intensity distributions at several cross-sections, which is used to reconstruct the beam phase distribution and design proper matching mirrors.

Key words:

microwave beams; gyrotron; beam phase front; quasi-optical transmission line; matching quasi-optical filter; meter of transmitted and reflected power; calorimetric load.

1.

INTRODUCTION

Gyrotrons are the most advanced high-power sources of millimeter wavelength radiation. They have been used for many years in electroncyclotron-wave (ECW) systems of many existing fusion installations. For the next generation of fusion installations, such as ITER or W7-X, the ECW systems based on gyrotrons capable to produce 1 MW / CW radiation are considered. Modern megawatt power level CW gyrotrons imply the use of complicated internal quasi-optical converters. The required accuracy of manufacturing of these quasi-optical converters is comparable with the limiting accuracy of machine tools, and sometimes exceeds it. Also, manufacturing of a gyrotron as a whole is a very complicated process at which gyrotron is exposed to high temperatures. Hence, some distortions of the form of the quasi-optical converter inside gyrotron are possible and therefore, there is the necessity of measuring real gyrotron wave beam parameters. The problem of loss-minimization for the microwave energy, on 3 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 3–13. © 2005 Springer. Printed in the Netherlands.

4

V. I. Belousov, et. al.

the way from a gyrotron to a fusion installation, indicates the need for knowledge of real wave beam parameters. Thermovision measurements are used as the method of measurement of a power distribution of a gyrotron microwave radiation at megawatt power level1. Measurement of power of a gyrotron wave beam and absorption of its energy at a megawatt power level in a continuous wave regime, is a very serious problem during the tests of gyrotrons. It is possible to use quasi-optical bi-directional couplers for measurement of a power of a gyrotron wave beam, and a calorimetric load made of stainless steel, for absorbing of all energy of a gyrotron wave beam.

2.

MEASUREMENTS AMPLITUDE AND PHASE DISTRIBUTION OF A GYROTRON WAVE BEAM

Measuring the intensity distribution of a gyrotron beam occurs as follows. The beam in free space passes a thin flat dielectric plate inserted along its propagation path This plate has a low loss of microwave radiation and small coefficient of heat conductivity, thus the main power of the gyrotron wave beam goes into a load. The wave beam passing through a plate heats it and the distribution of temperature to its surface is registered by means of the infrared camera. As the plate has small a coefficient of heat conductivity, the distribution of temperature to its surface will correspond to distribution of power in a transmitted wave beam. The scheme of measurements of a gyrotron wave beam power distribution is presented in Figure 1.

Figure 1. The scheme of measurements of a power distribution of a gyrotron wave beam.

The measured distributions of amplitude of a field of a gyrotron wave beam "Vesuvius - 5" (170GHz / 1MW) at several distances from a gyrotron window are presented in Figure 2. Using an amplitude distribution of a field

Measurement of Wave Beams

5

in five sections, not including the distribution at the gyrotron flange, preliminary reconstruction is made of the phase front of a wave beam on the basis of a technique described by Chirkov 2.

Figure 2. Distribution of amplitude of a field of a gyrotron wave beam "Vesuvius - 5" at several distances from gyrotron window z (mm): 62, 312, 562, 812, 1062, 1412.

Because the gyrotron wave beam at the gyrotron flange also contains spurious radiation that sometimes reaches up to 15 %, this cross-section is excluded from procedure of reconstruction of a phase front of a wave beam. If the coupling coefficients in the procedure are rather high (K t 97%), then the infrared measurements of a wave beam are considered as suitable for further analysis, as shown in Figure 3.

Figure 3. Preliminary reconstruction of the phase front of a gyrotron wave beam at five sections (mm): 312, 562, 812, 1062, 1412. Coupling coefficients K(%): 97, 98, 98, 97, 97.

6


Where K

º ª i « ³ A( x, y , z k ) A ( x, y , z k )ds » ¼ ¬s 2

2

2

,

i ³ ( A( x, y, zk )) ds ³ ( A ( x, y, zk )) ds s

s

A(x,y,zk) is an amplitude distribution measured at the z = zk cross section, and Ai(x,y,zk) is an amplitude distribution during the i-th iteration. Furthermore, on the basis of these intensity measurements, the wave beam phase front is retrieved more precisely on three sections as seen in Figure 4, corresponding with the method 2 that defines parameters of the wave beam.

Figure 4. Reconstruction of the phase front of a real gyrotron wave beam on three sections: 312 mm, 562 mm ɢ 812 mm.

Using the phase received as a result of reconstruction and real amplitude of a wave beam in section z = 312 mm, is possible to calculate amplitude and a phase distributions of the wave beam on the gyrotron output flange, as shown in Figure 5. For testing continuous megawatt power level gyrotrons, there are the objective difficulties connected, first, with absorption of such power, and second, with its measurement and control over time. The gyrotron wave beam consists of paraxial beam and spurious radiation. The share of parasitic radiation reaches from 5 % up to 15 % of a full gyrotron microwave power.


7

Therefore, it is necessary to filter and absorb parasitic radiation and to transform the paraxial beam to an optimum wave beam for a transmission line. This function can be carried out a two-mirror quasi-optical filter.

Figure 5. The reconstructed amplitude and a phase of a wave beam on a gyrotron flange. Gaussian contents: Șa(Șa,ph) = 94,3% (93.4%), rx = 16.0 ɦɦ, ry = 15.5 ɦɦ.

3.

TWO-MIRROR QUASI-OPTICAL FILTER

In order to reduce losses in the transmission line it is necessary to use shaped mirrors 3, 4, 5 based upon knowing the distributions of amplitude and phase of the gyrotron beam (see Figure 5). Quasi-optical filter consists of a metal box (aluminum or stainless steel) with input and output apertures for a wave beam. The absorber of parasitic microwave radiation is located on the inner walls of the filter. It is possible to use water flowing inside Teflon tubes or ceramics cooled by water, as an absorber. The cooling water flows at about 2 liters per second. Mirrors have a water cooling system for operating in a continuous regime. Subsequently, it is necessary to absorb and measure full microwave gyrotron power at the output of a quasi-optical filter, but it is a very difficult problem to combine both functions into one device. It is much easier to solve this problem by dividing these functions into two devices. One device is to simply absorb the full gyrotron microwave power into a load. The second device is to measure and control in time transmitted and reflected gyrotron power at the load.

8

4.


BI-DIRECTIONAL COUPLER

Measurement of continuous microwave radiation at the megawatt power level is a very difficult problem. Therefore by means of a corrugated mirror, it is possible to derive a wave beam of low power, namely about 0.5 % that of the full wave beam6. If a sine corrugation on a mirror surface makes an angle of 45° to the incident plane of an initial wave beam, the coupled wave beam will be distributed in a plane perpendicular to the plane of the mirror in a direction at an angle of 45° to the incident plane of the initial wave beam (Figure 6). Transmitted and reflected coupling wave beams are distributed on the different sides corresponding to the incident plane of main wave beams and consequently, there is a good decoupling of the transmitted and reflected coupled channels. The period of sine wave corrugations of the mirror (d) in this case will be equal to a wavelength (O). y Pin

z

2l0

Pref

d

Pref −1 x

Figure 6. The corrugated coupling mirror.

The share of the coupled power (Pref-1) depends on depth of a corrugation (l0): Pref-1 a (k l0)2 Pin, where Pin – power in an initial wave beam. If an incident wave beam is large, then it is possible to corrugate only the central part of a mirror, and thus the depth of a corrugation has a Gaussian distribution (Figure 7). The shape of a corrugation of a mirror surface is described by the following formula: § § x2 y2 · · ¸ § ¨ ¨ ¸ ¹ ¨ 1 1 ·¸ x y §¨ 1 1 ·¸ ¸* ª1 cos§ 2ʌ x ·º Z(x,y) l 0* exp¨ © ¨ ¸» « ¨ ¸ ¨ ¸ 2 © d ¹¼ ¨¨ © a 2 b2 ¹ © b 2 a 2 ¹ ¸¸ ¬ © ¹


9

where l0 = 0.08 mm – amplitude of depth of a corrugation, a = 31.46 mm – semi axis an ellipse of a corrugation in a plane of a falling wave beam, and b = 47.16 mm – semi axis an ellipse of a corrugation in a perpendicular plane to a plane of incidence of the wave beam. X (mm) 0

10

20

30

40

50

Y

0.0

-0.4

X Z / lo

-0.8

-1.2

-1.6

-2.0

Figure 7. The coupling mirror with corrugation in the central part.

The schematic drawing of a measuring unit is represented in Figure 8. The coupled wave beam from the first corrugated mirror (Ʉcoup1 = 0.55 %) propagates to the second corrugated mirror and to a calorimeter. The calorimeter measures power in the coupled wave beam, and in view of a coupling coefficient (Ʉcoup1) full power in an incident wave beam. The coupled wave beam from the second corrugated mirror (Ʉcoup2 = 1.5 %) propagates to a taper with the detector on the end. The detector measures the power in an incident wave beam depending on time. In the reflected channel is established only the taper with the detector, as the reflected power should be about two orders of magnitude less than the transmitted power.

Figure 8. The meter of transmitted and reflected power: main channel and coupled wave beams.

10


Thus, the meter measures transmitted and reflected power of the wave beam and controls changing of this power in time.

5.

CW CALORIMETRIC LOAD FOR MEGAWATT POWER LEVELS

The basic problem of a load for continuous microwave radiation megawatt power level is the overheating of an absorber causing its breakdown and destruction. For resolution of this problem, it is necessary to reduce the density of power on absorbing parts of a load, and to more uniformly distribute this power on the absorbing surface. The design of a load in many respects depends on the material of the absorber. If the absorber absorbs at normal incidence about several percents from the incident power, (stainless steel, for example) then design of a load would require a wave beam to fall repeatedly on the absorber. Such a load-type is represented in Figure 9. In this load, the absorber consists of stainless steel tubes where cooling water is flowing. The wave beam, formed by two mirrors, and a quasi-optical filter inserted ahead of the load, enters into the load through a narrow aperture ( = 63.5 mm) and propagates to the defocusing mirror located at the bottom of the load. The scattered wave beam is distributed on stainless steel tubes, dissipates and partly absorbed in them. Repeated absorption of a wave beam in the load is thus reached. Power distribution at the wall of the load after the defocusing mirror is presented in Figure 9. The area of the absorbing surface of the load is much greater than the area of the entrance aperture of the load, therefore the share of the reflected power is small and reaches for the load that was tested not more than 5 %. Thickness of stainless steel tubes is about 1 mm. The flow of cooling water should be about 5 – 7 liters per second for absorption of 1 MW continuous microwave power. To obtain power distribution uniformity on the wall of the load in an azimuth plane, the linear polarization of a wave beam was converted to circular by help of a polarizer. The parabolic mirror installed before the load is very good for this purpose.


11

Figure 9. The load with a two-mirror quasi-optical filter and distribution of the power at the wall of the load after defocusing mirror.

6.

SET-UP FOR TESTING GYROTRONS OF MEGAWATT POWER LEVEL

The real scheme of a set-up for power measurement is diagrammed in Figure 10. This transmission line has shielding to contain stray microwave radiation. The diffraction losses in this transmission line are about 5%.

12


Figure 10. The scheme of a set-up for test of a gyrotron « Vesuvius -5 » 170 GHz / 1 MW / CW at INF RRC « Kurchatov institute ».

In experiments during the test of a gyrotron « Vesuvius - 5 » at a power level of about 900 kW, microwave radiation was obtained in pulses of 20 seconds; and at power levels of about 700 kW, in pulse durations of 40 seconds. The limitation of pulse duration is basically connected to breakdowns in the load. Apparently, the density of power on some parts of the load exceeded allowable values that resulted in overheating of the surface and as consequence, breakdowns. For absorbing 1 MW continuous microwave power, it is necessary to increase the area of an absorbing surface of the load.

7.

CONCLUSION

Methods of measurements of parameters of gyrotron wave beams, described in this article, allow one to carrying out tests of powerful continuous wave gyrotrons in real regimes. The Thermovision method of measurement of parameters of a real gyrotron wave beam allows production optimum mirrors of the quasi-optical filter to minimize losses of power in transport of the microwave energy of a gyrotron up to calorimetric load. A quasi-optical bi-directional coupler, used in a transmission line, allows measurement of the microwave radiation power during gyrotron operation, and a calorimetric load on the end of a transmission line allows absorbing all microwave energy of a gyrotron.


8.

13

REFERENCES 1.

2.

3. 4. 5.

6.

Kuznetsov S.O. and Malygin V.I., Determination of gyrotron wave beam parameters, International Journal of Infrared and Millimeter Waves, 12, (11), 1991, pp 1241-1252. Chirkov A.V., Denisov G.G., Aleksandrov N.L. 3D wave beam field reconstruction from intensity measurements in a few cross sections. Optics Communications. Vol. 115 (1995), pp. 449-452. L.B. Tartakovsky, V.K. Tikhonova. Synthesis of linear array with given amplitude distribution. Journal of radiotechnics & electronics, 12, pp. 2016-2019, 1959. B.Z. Katsenelenbaum, V.V. Semenov. Synthesis of the phase correctors forming a given field, Journal of radiotechnics & electronics, 2, pp. 244-252, 1967. Bogdashov A.A., Chirkov A.V., Denisov G.G., Vinogradov D.V., Kuftin A.N., Malygin V.I., Zapevalov V.E. Mirror synthesis for gyrotron quasi-optical mode converters. International Journal of Infrared and Millimeter Waves, Vol. 16, No. 4, 1995, pp. 735-744. Belousov V.I. at all. Coll. Pap. “Gyrotron”, Ed. Flyagin V.A., Inst. Appl. Phys., USSR, Gorky, 1989, 155 - 160.

OVERSIZED TRANSMISSION LINES FOR GYROTRON-BASED TECHNOLOGICAL OVENS AND PLASMA-CHEMICAL REACTORS

A. Bogdashov, G. Denisov, G. Kalynova Institute of Applied Physics (IAP RAS) 46, Ulyanov str., Nizhny Novgorod - 603950 ,Russia Abstract:

High-power millimeter-wave gyrotrons are used in a number of technologies: ceramics sintering and joining (including nanoceramics), functionally graded coatings, rapid annealing of semiconductors, microwave plasma assisted chemical vapor deposition, and multiply charged ion production are among the most advanced developments. The paper presents the status and examples of transmission line developments for such gyrotron-based systems.

Key words:

microwave transmission lines, gyrotron, mode converter, mode filter.

1.

INTRODUCTION

A growing demand of the nuclear fusion community in the millimeterwave power sources resulted in the development of gyrotrons capable of producing about 1 MW in practically continuous wave (CW) regime at frequencies of up to 170 GHz [1]. Electron cyclotron plasma heating is a unique area of gyrotron application to this date. However, it has become evident during the last decade that many microwave energy applications might greatly benefit from an increase in the frequency of radiation. High temperature processing of materials, e.g. advanced ceramic sintering, was one of the first fields where the advantages of the millimeter-wave (mmwave) heating as compared with conventionally-used power of 2.45 GHz have been demonstrated [2]. The capability of efficient volumetric heating of low-loss ceramic materials and rapid uniform sintering oflarge size specimens and batches of samples is of great importance for the successful development of processes of industrial interest. Very high uniformity of the mm-wave heating is of paramount importance for the annealing of silicon wafers of

15 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 15–23. © 2005 Springer. Printed in the Netherlands.

A. Bogdashov, G. Denisov, G. Kalynova

16

large diameter ( 300 mm), a necessary step in the manufacturing of ultra large integrated circuits [3]. Significant improvement of performance characteristics of the electron cyclotron resonance ion sources can be achieved with an increase in the frequency of the applied microwave power [4]. The microwave-assisted chemical vapor deposition of diamond films is another process which gains drastically in the rate of deposition if the plasma is sustained by the mm-wave power [5]. The application of the mm-wave beams for surface treatment of materials is a promising method which in many cases is competitive with the surface heating by other concentrated energy flows, such as laser, ion or electron beams, plasma flow [6]. Awareness of the potential of the mm-wave power use in technology initiated in the beginning of 1990’s, the development of the first gyrotronbased system purposely designed for research in material science [6]. Since then, several types of gyrotron systems of different power, operating at various frequencies, have been developed.

2.

EXPERIMENTAL FACILITIES

The general concept of the gyrotron system architecture remains invariable despite the differences in the technical specifications of the gyrotrons that are used and the nature of applications (Fig. 1). A gyrotron system is made up as a standard computer-controlled device to which the feedback loop is applied. The gyrotron systems do not differ from microwave sources of other frequencies in terms of control. However, the difference in the operating frequency results in a drastic dissimilarity of all major components. The gyrotron systems are designed as an integrated set of the following principal components: x a gyrotron, the source of the mm-wave power, x transmission line for transport of mm-wave power to an applicator, x an applicator, x diagnostic subsystem and PC controller for automatic/manual processing. The specific design of these components is flexible and depends on a particular application. The output power of gyrotrons can be smoothly regulated from about 5% to 100% of the full power by variation of the electron beam voltage. All CW gyrotrons can operate in pulse regime with the same or slightly higher output power Typical operating voltage of these gyrotrons is in the range of (15-30) kV, and the electron beam current is (1-2.5) A. An efficiency of the standard .

Oversized Transmission Line

17

gyrotrons operating in frequency range of (20-80) GHz is about 0.3–0.4, and about 0.60-0.65 in the gyrotrons with a depressed collector [7].

High Voltage Power Supply

Gyrotron

Transmission Line

Applicator

Solenoid Power Supply

Power Meter

Process Parameters

PC - based Control System T

3.

Figure 1. Block diagram of the gyrotron system. T

TRANSMISSION LINES

Microwaves leave a gyrotron via a waveguide, which is oversized as compared to the wavelength of radiation. Various transmission lines (TL) can be designed for the transport of microwaves from the gyrotron to an applicator. The design of these TL depends mostly on what one would like to have at the input of the applicator in terms of the electromagnetic field pattern and polarization. At frequencies above 20 GHz, a TL can be built either as an oversized waveguide, a set of quasioptical mirrors, or can be of a mixed type.

3.1

The 28 GHz 10 kW CW Transmission Line for Electron Cyclotron Resonance Ion Source

A schematic drawing of the waveguide TL of the 28 GHz gyrotron system designed for powering the electron cyclotron resonance ion source is shown in Fig.2. The structure of this TL is based on waveguide components. However, it should be realized that at a high frequency the TL is composed of multi-mode components. Therefore, the design and principle of operation of these components usually differ greatly from those used at lower frequencies. The transmission line includes the following components: x a bi-directional coupler,


18

x a 90° quasioptical mirror bend. This section can be also used for measuring the absolute value of microwave power produced by gyrotron. For this purpose, the bend is cooled with water and furnished with a set of temperature sensors, x a mode convertor, which transforms the operating mode of the gyrotron, TE 02 , into the TE 01 mode, x a mode filter, which serves to protect a gyrotron against the microwave power reflected back from the ion source. Operation of the filter is based on selective absorption of power of non-symmetrical modes, x a launcher, which produces the required electromagnetic field pattern at the input of the ion source, x additionally, the line is equipped with an arc detector, which serves to shut off the power if, by some reason, arcing occurs in the transmission line. An efficiency of the mm-wave power transport through the entire TL is over 97%. B

B

B

T

B

Figure 2. 28 GHz gyroton-based system for ion source. T


19

gyrotron, mode TE02

fiber to Arc-detector

attenuator

to amplifier diode

compensator

mode converter TE02 o TE01

water in out to meter of transmitted power

out

out

compensator

waveguide bend water in

mode filter

in vacuum proof window

Figure 3. 28 GHz 10kW transmission line for ECR ion source.

T

T

3.2 24 GHz, 3 kW Transmission Line for Ceramics Sintering One of the promising areas of mm-wave industrial applications is high temperature processing of materials, such as sintering and joining of advanced ceramics, annealing of semiconductors, etc. Most of the gyrotrons systems designed to this date are furnished with a microwave furnace, which comprises a large cavity resonator, that can be evaculated and backfilled to operate over a wide pressure range (10 -4 -2 bars). High uniformity of the microwave energy distribution in the furnace is an essential prerequisite for the processing of large size specimens and for reproducible heating of many specimens processed simultaneously in one batch. The approaches to attaining a distribution of high spatial uniformity are different for the multimode applicators fed with the mm-wave (L >> O) and microwave (L t P

P


20

O) radiation (where L is the size of applicator and O is the wavelength of radiation). The mm-wave radiation usually enters the furnace as a wave beam (see, for example, Fig. 3) or through an opening in the multimode waveguide. High uniformity of the microwave energy distribution in the furnace is achieved as the result of superposition of the electromagnetic fields of hundreds simultaneously exited modes.

3

4

5

2

6 1

T

Figure 4. 24 GHz 3 kW transmission line for ceramics sintering. T

The 24 GHz, 3 kW gyrotron system shown in Fig. 4 features an unparalleled capability of both volumetric heating of specimens by the mmwave energy uniformly distributed over the whole volume of the cavity, and local heating by a focused wave beam [10]. This is achieved by the use of two types of mirrors alternatively directing the wave beam entering the applicator to the stirrer or to a specimen. Transmission line consists of following components (referred to Fig.4): 1 – TE11 mode polarizer, 2 – waveguide bend (>99% TE11 mode efficiency), 3 – mode filter serves to protect a gyrotron against the microwave power reflected back from the sintering oven, 4 – mode converter creates Gaussian wave beam at the microwave oven (see Fig.5), 5 – barrier ceramic window, 6 – sintering oven. Measured power transmission coefficient is 97r1%.


T

21

a) b) Figure 5. Thermo-paper images of microwave intensity a)TE11 mode with vertical polarization, b)Gaussian wave beam. T

3.3 The 30 GHz, 15kW Transmission Line for CVD Diamond Growing Microwave system for CVD diamond growing is very attractive branch of material processing. Total time of polycrystalline diamond growing strongly depends on plasma density and radiation frequency. To investigate respective plasma-chemical reactions, gyrotron-based system was developed at Institute of Applied Physics [5]. Transmission line is shown in the Fig. 6. It includes following microwave components: 1,2 – beam forming quasi-optical mirrors, 3 – plane mirrors of power splitter, 4 – square corrugated waveguide for microwave power splitting, 5 – reaction position (discharge region), 6 – wavebeam waist in the discharge region, 7 – circular corrugated waveguides, 8 – low-loss HE11 mode miter bend, 9 – 30GHz / 15kW gyrotron, 10, 11 – TE02 – Gaussian wavebeam mode converter and focusing mirrors with special profiles,


22

T

Figure 6. 30GHz 15kW transmission line for CVD diamond reactor. T

Preliminary tests show a relatively low power transmission coefficient of 86%. Further development of the TL includes some additional improvements of microwave components: TE02 – Gaussian wave beam mode converter, HE11 miter bend and power splitting system. Nevertheless, the gyrotron system demonstrates stable operation in CW regime. It’s very useful for CVD reaction experiments.

4.

CONCLUSIONS

Wave transmission and control systems used in technological applications of gyrotrons are simple, reliable and have over 95% transmission efficiency.


23

5. REFERENCES 1. G.Denisov, Development of 1MW output power level gyrotrons for fusion systems, in Proc. 4 th Intern. Workshop "Strong microwaves in plasmas", Nizhny Novgorod, Russia, August 2000, pp. 967-986. 2. M. Janney and H. Kimrey, Diffusion-Controlled Processes in Microwave-Fired Oxide Ceramics, in Mat. Res. Soc. Symp. Proc., v. 189, Pittsburgh, PA, 1990, pp.215-227. 3. Yu. Bykov, A. Eremeev, V. Holoptsev, I. Plotnikov, and N. Zharova, Spike annealing of silicon wafer using millimeter-wave power, in Proc. 9 th Int. Conf. on Advanced Thermal Processing of Semiconductors - RTP 2001, Anchorage, Alaska, September 2001, pp.232239. 4. R. Geller, B. Jacquot, and P. Sortais, The upgrading of multiplied charge heavy-ion source MINIMAFIOS, Nucl. Instrum. Methods Phys. Rev A.. 243, 1986, p. 244-254. 5. A. Vikharev, A. Gorbachev, A. Litvak, Y. Bykov, G. Denisov, O. Ivanov, V. Koldanov, RU patent application, #2002125807 dated 30.09.2002. P

P

P

P

DEVELOPMENT OF LUMPED AND DISTRIBUTED MODELS FOR ACCURATE MEASUREMENTS OF Q-FACTORS OF QUASIOPTICAL RESONATORS B. Kapilevich Dept. of Electrical and Electronic Engineering, the College of Judea and Samaria, Ariel, Israel – 44837

1. INTRODUCTION Power mm-wave sources based on relativistic electron beams require high-Q resonators for a single-frequency and single-mode operation. Such a resonator can be formed on the basis of quasi-optical waveguides. A critical point in the practical study of these resonators is an accurate measurement of unloaded and loaded Q-factors. This is necessary for estimating the electron beam parameters required for reaching lasing threshold and mm-wave generation. The elements used for an excitation of quasi-optical resonators may cause additional diffraction losses. As a result, an amplitude response of a resonator is considerably deformed causing problems in accurate Q-factors measurements and preventing application of conventional measuring techniques. In this paper, several models of quasi-optical resonators excited by polarized grid couplers are developed for measurement of Q-factors using a scalar mm-wave HP-Network Analyser. Three models are considered below: 1. Lumped model: In this model, both a resonator and coupler are represented by its equivalent R-L-C parameters and a section of lossy line is introduced for simulating diffraction losses; 2. Mixed model: In this model, a resonator is represented by its equivalent short-circuited transmission line and coupling element which is replaced by an equivalent inductor loading this line; 3. Distributed model: In this model a distributed network circuit in terms of transmission matrix describes both resonator and coupler.


26

Kapilevich

By using the models suggested, the equation determining the condition of critical coupling of a resonator with feeding waveguide was derived. This was used to estimate the unloaded Q-factor of the quasi-optical resonator of the Israeli Free Electron Maser (FEM) that recently generated output power of approximately 1 KW at W-band. Examples of Q-factor measurements using the models considered are discussed.

2. CONFIGURATION OF EXPERIMENTAL SETUP Figure 1 demonstrates a configuration of a quasi-optical resonator used in millimeter-wave FEM of Tel Aviv University [1]. The resonator is composed of a parallel curved plate waveguide (PCPW) section [2] shorted at the end. The polarising grid coupler is illuminated by a free space Gaussian beam formed by means of mode exciter and mirror as described in [3]. HP-8757D Network Analyser, is employed for measurement of a reflection coefficient. However, critical problems in characterization of quasi-optical resonator is a good matching of coupler and mirror with guiding system. Bad matching may lead to considerable return loss causing problems in accurate Q-factors measurements and preventing application of conventional measuring techniques. To solve the problem, different calibration procedures have been suggested to take into consideration coupling losses [4-8]. However, they don’t take into account diffraction losses playing important an role in the characterization of quasi-optical resonators. Mirror Transmission line

Reflecting grids of a variable coupler

Mode exciter

Shorted-line resonator

To network analyzer

Electron beam

Figure 1. Experimental setup used in measurements of a quasi-optical resonator excited by mode exciter and focusing mirror.

Development of Models

27

3. LUMPED MODEL OF A QUASI-OPTICAL RESONATOR Following [6] we can introduce a virtual line whose characteristic impedance is known, but the propagation constant may be unknown. The latter is reconstructed further from measured values of return loss. The virtual line is loaded by equivalent resonator’s circuit consisting of lumped elements R0, L0, and C0 representing its interior parameters [9], Fig.2. Hence, the input resonator’s impedance can be written as: § 1 1 Z in Z ¨¨ jZC 0 jZL0 R0 ©

· ¸ ¸ ¹

1

(1)

Figure 2. Lumped Model of a Quasi-Optical Resonator.

The input impedance ZCSin(Z) of the coupling line loaded by a resonator is calculated as follows:

Z inCS (Z) Z virt (Z)

Z in (Z) jZvirt (Z) tan[(E jD )Leff ) Z virt (Z) jZin (Z) tan[(E jD )Leff )

(2)

where Zvirt(Z) is the impedance of virtual line, E - jD is the complex propagation constant, Leff is the effective length of virtual line, Z is angular frequency. A return loss (RL) measured by scalar the Network Analyser can be written now in the form:

RL(Z )

20 log S11

20 log

Z inCS (Z ) Z 0 Z inCS (Z ) Z 0

(3)

28

Kapilevich

where | S11| is a reflection coefficient, Z0 is a system impedance of the Network Analyser’s input waveguide. The expression (3) can be used for direct reconstruction of the interior parameters of a quasi-optical resonator from measured data employing curve fitting procedure [10]. The reference level of return loss RLref, in a vicinity of resonance frequency corresponding to a shorted regime of the virtual transmission line must be determined on the basis of real measurements. Figure 3 shows the results of measurements of equivalent FEM resonator parameters for the mode resonating at the frequency 99.999GHz in PCPW resonator of the length l=1.56m.

RL dB

Figure 3. Comparison modeling (solid line) and measured (dotted line) results. The dashed line corresponds to the reference level: R0 =19.5 Ohm, C0=1.0394E-9 F, L0 =2.4375E-15 H, Qload =12800.


29

4. MIXED MODEL OF A QUASI-OPTICAL RESONATOR A drawback of the technique based on lumped model is the difficulty in separating external coupling elements from internal resonating elements. In order to carry out such a separation, the model of a FEM resonator based on shorted-line representation is preferable. Such a model provides some advantages: x A possibility to simulate all longitudinal modes resonating within a specified frequency range; x Elements responsible for resonance or coupling effects can be easily separated; x A possibility to estimate frequency dispersion effects of the FEM resonator. The FEM resonator can be presented by the equivalent schematic shown in Fig.4, [11]. It consists of a shorted-line section of the length l corresponding to the physical length of the FEM resonator

Figure 4. The equivalent schematic of inductively coupled shorted-line resonator [11].

The equivalent inductor L corresponding to the polarizing grids coupler shunts its input. The model allows extracting Q factors in a relatively easy way. The formulation can be done using the inductively coupled shortedline resonator model [11]. As a result, the following expression can be derived for the magnitude of input reflection coefficient S11(Į,L,Ȧ)

Z jZL 1) 01 tanh[(D jE )l ] Z0 Z0 Z jZL ( 1) 01 tanh[(D jE )l ] Z0 Z0 (

S11 (D , L, Z )

jZL Z0 jZL Z0

(4)

30

Kapilevich

where: L is the inductance; Z0 and Z01 are the system impedance of both the network analyser waveguide and of the resonator waveguide mode, D is the attenuation constant. Figure 5 demonstrates behaviour of the magnitude of S11 in the space of {D,L}. This shows a presence of global minimum corresponding to a near critical coupling condition at the resonance frequency f = 99.99 GHz. The following parameters of the resonator were used in calculation l = 1.56 m, Z0 = 467 Ohms, Z01 = 377 Ohms.

Figure 5. Behavior of the magnitude of S11 in a space of {D,L} near resonance frequency f0 = 99.99 GHz.

To formulate the algorithm for reconstructing D and L, one must take two measurements of S11 magnitude: first, at the resonance frequency f0 and second, at the frequency near resonance, f1. Assuming that their magnitudes are A0 and A1, respectively, the system of two non linear equations can be written for D and L:

S11(D,L,Z0 ) = A0 S11(D,L,Z1 ) = A1

(5)

The system (5) can be solved numerically by iterations. When solving equations numerically, it is necessary to define values from which the solver


31

should start its search for a solution. The details of this process can be found in [12]. The unloaded Qun and external Qe factors are calculated using formulas (9.23) and (9.28) from [11]:

Qun = E /2D Qe = [BL +I(1+BL2)]Z0/2Z01

(6) (7)

where BL = Z01/2S f0 L, I = 2S f0 l/c The example below illustrates Q-factor measurements obtained for the resonator excited in under-coupled regime, Qe > Qu. Weak coupling of the resonator can be realized by setting small angles between the inner polarizing grid and the external ones (about 10 – 15 deg.). The measured magnitudes of S11 at the resonance frequency f0 and at the frequency near the resonance f1, are given in the Table 1. The solution of the system (5) is found using preliminary determined guess values of D and L. Based on values of D and L determined from solution of the system (5), we can reconstruct frequency dependencies of S11 for Q-factors given in Table 1 (see Fig. 6) Agreement between these data is observed in a vicinity of the resonance frequency. Table 1. Results of measurements and reconstructing Q-factors for under-coupled regime

f0 = 99.99 GHz S11 =0.9099 f1 = 99.985 GHz S11 =0.96039 Guess values D = 0.05(1/m), L = 0.1 (nH) Solutions of the system (2.4) D =0.0844(1/m),L = 0.053(nH) Q – factors Qun = 12393 Qe = 261883 Qload = 11833

32

Kapilevich

Fig.6 Reconstructed and measured behavior of S11 as a function of frequency.

5. DISTRIBUTED MODEL OF A QUASI-OPTICAL RESONATOR In order to arrive at the maximum power delivery-point of the maser, the quasi-CWFEMwaveguide resonator’s output coupler is an important element in its operation. The ability to adjust, in real time, its out-coupling coefficient, the ability to continuously adjust the resonant frequencies of the resonator in order to allow fine tuning (between longitudinal modes) of the FEM lasing


33

frequency, and take full advantage of the high coherence and wide range tuneability of this maser, are highly desirable. In order to predict basic characteristics of such a resonator, a distributed model of a quasi-optical resonator is preferable. The coupler (shown schematically in Fig. 7), consists of three polarizing wire grids illuminated by a free-space Gaussian beam propagating along the z-axis. The electrical lengths between grids are (I Sfd) are I1 and I2. The wires of the external grids are perpendicular to the incident electric field. The inner grid orientation angle T with respect to the external one can be varied so that the total system transmittance is adjustable from 0 to 1. When such a coupler is placed at the output of the quasi-optical resonator, an optimisation of the output coupling conditions can be obtained by rotating the inner grid within the range T = 0 to 900. In addition, the fine frequency tuning of the quasi-optical waveguide resonator can be obtained by judicious displacement of the entire grid assembly along the resonator axis relative to the resonator output plane. These two degrees of freedom have been realized using remotely controlled stepping motors to provide the rotary and linear motions [13].

θ

E

φ1

φ2

Figure7. Scheme of 3 grids tunable coupler.

Calculationof the 3 grid system parameters can be done using a transmittance matrix approach. According to [14], a system consisting of 3 grids can be

34

Kapilevich

fully characterized in terms of the electrical lengths I1, I2 and inner angleT. The total transmission matrix of the 3 grid system was determined and power transmission coefficient can be written as follows: 4z4 (8) T 2 2 2 2 y1(z x2 ) y2 (z x1 ) 2 x2(z2 x12) x1(z2 x22) 2 [2x1x2 ] [x1y2 x2 y1 ] y2 y1 y1 y2

where z = cosT , x1 = sin)1, x2 = sin)2, y1 = cos)1, y2 = cos)2 For example, Fig.8 illustrates the angular behavior of the power transmittance of a 3 grid system calculated from (8) for equidistant ()1 = )2 = 450) and non-equidistant ()1 = 450 and )2 = 830) grid’s spacing as a function ofT. In both cases, the change of power transmittance lies within the interval 0 < T < 1 however, the equidistant configuration displays symmetry relative to lines T = 0.5 and T = 450 and preferable in practice.

(a)

(b)

ș Figure 8. Calculated power transmission coefficient T for equidistant (a) and non-equidistant (b) grids.

Assuming I1 I2 = 450 the following expression for the magnitude of reflection coefficient S11 as function of T can be derived:

S11

(sin 2 T i cos 2T ) tanh Jl i sin 2 T (sin 2 T i cos 2T ) tanh Jl i sin 2 T

(9)


35

Figure 9 illustrates the input reflectance |S11| dB of the quasi-optical resonator calculated from (9) for unloaded Q = 2E/D = 10470, ) = 450 , l = 1.532m and different angles of the inner grid T varying within the range 30 – 55 degrees. It is clearly observed that a gradual transition from undercoupled (T < 450 ) toward critically coupled (T = 450 ) and then to overcoupled (T > 450 ) regimes of the resonator considered with increasing T .

6. THE ANGLE OF CRITICAL COUPLING According to (9) two basic factors determine reflectance of the resonator loaded by grid’s coupler as a function of frequency-angular position of inner grid T and unloaded Q = 2E /D of quasi-optical resonator itself for a fixed resonator length. The exact value of the angle corresponding to zero reflectance, S11 = 0 (critical coupling of the resonator with a guide), can be determined from (9) as a solution of the following equation:

(sin 2 T i cos 2T ) tanh Jl i sin 2 T

0

(10)

Figure 9. Input reflectance of the FEM resonator with 3 equidistant grids coupler for angles of the inner grid: ƑƑƑ T = 600, + + + T = 550, o o o T = 500, T = 450, ¸ ¸ ¸ T = 350different.

36

Kapilevich

Equation (10) is equivalent to a nonlinear system of two equations for two unknown parameters T and f: sinh 2Dl sin 2 T sin 2 El cos 2T 2(sinh 2 Dl cos 2 El ) sin 2 T 0 ® 2 2 2 ¯ sin T sin 2 El cos 2T sinh 2Dl 2(sinh Dl cos El ) 0

(11)

There are infinite numbers of roots satisfying system (11). Table 2 presents some of them calculated in the vicinity of resonance frequency near 100GHz for the same resonator’s dimensions as used in Fig.9 Table 2. The values of critical angle coupling Tc calculated from (11) for different Q

Qun-factor Grid’s angle, Resonance frequency f [GHz] Tc [grad] 5000 28.350 100.021 10470 38.760 100.025 21000 46.20 100.029 42000 52.260 100.032 To avoid wrong roots that can appear in a process of numerical solution of (11), a validation of data shown in Table 2 must be carried out. True critical coupling must reveal a zero reflectance at resonance frequencies for critical angle and to increase reflectance with any changing inner grid's angle. To validate the theoretical data the experiments have been done with the tunable 3-grid coupler to provide both angular adjusting of the inner grid and longitudinal shift of coupler itself [13]. The HP-8757D network analyzer was used to measure reflectance (transmittance) of the 3-grid coupler and the quasi-optical resonator. Figure 10 shows measured power transmittance of the 3-grid coupler in a free space. The spacing between grids is Ȝ/8 = 0.375mm (Ȝ = 3mm). The measurements were done at frequencies 95, 100 and 105 GHz. The curve corresponding to 105 GHz demonstrates almost symmetrical behavior respectively axis Tpower = 0.5 and ș = 45 deg that is closed to the theoretical prediction. The measured reflectivity of the FEM's resonator with 3 grid coupler is depicted in Fig.11. The curves are similar to the theoretical ones depicted in Fig.9 demonstrating under-coupled, critical and over-coupled conditions. Critical coupling corresponds to T near 45o (marked by circles). According to the Table 2 and the Q-factor corresponding with this angle, it is about 20000. This is in a good agreement with independent measurements using other techniques.


37

1

Tpower 0.8

T_95

0.6

T_100 T_105

0.4

0.2

0

0

20

40

60

80

100

θ Angle of inner grid, degrees

Figure. 10 The angular behavior of a power transmittance of the 3 grids coupler at frequencies 95, 100 and 105 GHz.

Frequency, GHz Figure 11. Measuredreflectivity of the of quasi-optical resonator with3 grids tunable couplerin a single mode operation for different T. The critical angle is Tc= 45o and marked by circles.

38

Kapilevich

7. CONCLUSION Both lumped and distributed models have demonstrated reliable results, and can be used for measurements and characterization of quasi-optical resonators. However, the distributed model is preferable since it provides direct links between angular-longitudinal coupler configurations and the resonator's properties.

8. ACKNOWLEDGEMENTS Author would like to thank: Prof. A.Gover, Prof. Y.Pinhasi and Dr. A.Yaholom for useful discussions concerning both models considered and measurements, Dr. A.Abramovich for development of LabView interfaces, MS students A.Faingersh and A.Eliran for assistance in arrangement of experimental setups. This work was done in the Israeli FEL Knowledge Center with partial support of the Israeli Ministry of Science.

9. REFERENCES 1.

I.Yakover, Y.Pinhasi, and A.Gover, Resonator Design and Characterization for the Israeli Electrostatic FEL Project, Nuclear Instr.& Methods in Physics Research, Section A.358, 1995, pp.323-326. 2. Nakahara and N. Kurauchi, Guided Beam Waves Between Parallel Concave Reflectors, 1967 Trans. MTT, vol.15, no.2, pp.66-71, 1967. 3. M.A.Shapiro and S.N.Vlasov, Study of a Combined Millimeter-Wave Resonator, IEEE Trans. MTT, nol.45, no.6, pp.1000-1002. 4. E-Y. Sun and S.-H.Chao, Unloaded Q Measurement the Critical-Points Methods. IEEE Trans. MTT, vol. 41, no.8, 1995, pp.1983-1986. 5. R.S.Kwok and J-F.Liang, Characteristics of High-Q Resonators for Microwave Filter Applications, IEEE Trans. MTT, vol. 47, no.1, 1999, pp.111-114. 6. H.Heuermann, Calibration Procedures with Series Impedance and Unknown Lines Simplifies on-Wafer Measurements, IEEE Trans. MTT, vol. 47, no.1, 1999, , pp.15. 7. D.Kajifez, S.Chebolu, M.R..Abdul-Gaffoor, and A.A.Kishk, Uncertainty Analysis of the Transmission-Type Measurement of Q-factor, IEEE Trans. MTT, vol. 47, no.5, 2001, pp.998-1000. 8. A.J.Lord, Comparing On-Wafer Calibration Techniques to 100GHz, Microwaves & Rf, vol.39, no.1, 2000, pp.114-118. 9. R.K.Mongia and R.K.Arora, Equivalent Circuit Parameters of an Aperture Coupled Open Resonator Cavity, IEEE Trans. MTT, vol. 41, no.8, 1993, pp.1245-1250. 10. D.Kajfez, Linear Fractional Curve Fitting for Measurement of High Q factors, IEEE Trans. MTT, vol. 42, no.7, 1994, pp.1149-1153 11. P.A.Rizzi, Microwave Engineering, Prentice Hall, 1988. 12. B. Kapilevich, A. Faingersh, A. Gover, Accurate determination of Q factors of a quasioptical resonator, Microwave and Optical Technology Letters, Volume 36, Issue 4, pp. 303-306, 2003

Development of Models 13. B.Kapilevich, A. Faingersh, A. Gover Modelling and Measurements of the Parameters of a Quasi-optical mm-Wave Resonator by Means of a Tunable Grid Coupler, European Microwave Week, 33 European Microwave Conf. – 2003, Germany, pp.85-88 14. A.A.M. Saleh, An adjustable quasi-optical bandpass filter – part 1: theory and design formulas, IEEE Trans. MTT, vol. 22, no.7, pp.728-734, 1974.

39

THE MODE-MATCHING TECHNIQUE AND FAST NUMERICAL MODELS OF ARBITRARY COORDINATE WAVEGUIDE OBJECTS

Anatoly A. Kirilenko, Vladimir I. Tkachenko, Leonid A. Rud, Dmitrij Yu. Kulik Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Proskura St., Kharkov, 61085

Abstract:

A new algorithm based on two versions of mode-matching (MMT) approaches is proposed for solving the boundary value problems associated with arbitrary waveguides or cavities having piece-wise coordinate surfaces. The solutions are initially based on a pre-processing procedure aimed for automatic recognition of an object’s structure and forming the matrix operators taking part in the mode bases search, or in the calculation of step junction S-matrixes. The new code has been tested by the relatively simple objects considered earlier, and by new objects that were not previously considered for MMT modelling because of the laboriousness of an algorithm elaboration. It was shown that the new MMT electromagnetic solver was also applicable in the cases of smooth boundary objects at step-wise approximated surfaces.

Key words:

complicated waveguides, mode-matching technique, automatic recognition, coordinate boundaries, arbitrary structures.

1.

INTRODUCTION

The mode-matching technique (MMT) continues to be a very powerful tool for the analysis, design and optimization of the microwave devices among several numerical methods of computational electromagnetics. Due to its simple nature, it appeared at the early stages of microwave technique development and provided exact solution of many boundary value problems in the analysis of the waveguides, resonant cavities and gratings. This power modelling technology remains the tool for the solution of actual problems of microwave communication technique1, power microwave transmission lines2, etc.


42

Kirilenko, Tkachenko, Rud, Kulik

MMT is noted for three important features: relative universality (within the wide class of geometries), good convergence, and high accuracy. Being a leader in the calculation speed and accuracy, and providing the fast solution of very complicated minimax problems, MMT does not loose its position with wide-spread expansion of the mesh methods. Perhaps, a single negative feature of MMT is the necessity of individual consideration of each new problem arising in practice. Moreover, an appropriate qualification of a microwave designer in analytical treatment of the boundary-value problem is required. Up to this point, even bounded by a definite class, there were no mode-matching based tools providing consideration of arbitrary geometries. Therefore, to solve the actual problem, one must spend more time for the mathematical treatment and the development of corresponding algorithm and program code than for the calculations themselves. The milestones of a new generalized approach to the implementation of mode-matching procedures are presented below. Such solutions may be named as those based on the generalized mode matching technique (GMMT). First of all, the generalization consists in a possibility to obtain the solution of the boundary-value problems with an “unpredetermined” topology of boundaries. In other words the case-in-point is an arbitrary configuration within a wide class of the objects with piecewise coordinate boundaries. Secondly, the generalization consists in an automatic generation of all required structural data for the creation of a corresponding set of the GMMT matrix operators. Thirdly, all structural peculiarities of the specified geometry must be taken into account: longitudinal and transversal symmetry of the device; symmetry of excited fields; symmetry of separate complicated waveguide lines and their regular parts, arising at and dividing into the parts with a perfectly electric (magnetic) wall in the plane of symmetry; the connectivity of the waveguide cross-sections, symmetry of the plane junctions of separate waveguides, etc. Finally, the implementation of a unified criterion of the accuracy control, both for algorithms of full mode bases search and for the procedures of an automatic electromagnetic assembling by S-matrix technique, can be treated as a generalization.

2. PRE-PROCESSING PROCEDURE It is clear that an automatic MMT approach must be based on two milestones, namely, on a pre-processing procedure (A), aiming to recognize the internal structure of the object under consideration and to prepare the data for numerical algorithm, and on a solver as itself (B), destined to calculate a

Technique and Models of Waveguide Objects

43

given-size mode bases of the complicated WGs specified by pre-processor and the S-matrices of plane junctions of these WGs. The flowchart of Procedure "A" is presented in Fig.1. Purports of its steps are clear from the captioning data. The object under consideration must be specified by its edge points and, correspondingly, a cross-section of the generalized piecewise-coordinate WG line may be presented as the set of rectangular subregions assigned, for example, by the edge point ( x ( j ) , y ( j ) ) , height h ( j ) , and width w( j ) . The preprocessor must find a corresponding matrix of ( x ( j ) , y ( j ) , a ( j ) , h( j ) ), j 1, 2,...J which completely defines the crosssection of WG line. This data permits further recognition of the connectivity of WG line boundary to form the structure of a determinant matrix equation according to rectangles’ common boundaries and other geometry peculiarities required for fast mode basis calculation. Specification of the object geometry by means of project-file Longitudinal segmentation of the object into regular fragments Transversal dissection of the fragments and separation of individual waveguides Segmentation of the cross-sections into the sets of “canonical” subregions

No

Is the object uniform along the transversal axes?

Analysis of the connectivity of the individual cross-sections (the number of TEM-modes) Analysis of the possible symmetry of the generalized crosssections, individual lines cross-sections and transversal symmetryof the object as a whole

Yes

Analysis of the transversal symmetry of the object as a whole

Analysis of the longitudinal symmetryof the object Separation of waveguide plane junctions and introduction of virtual waveguides, if necessary Determination of the matrices of the subregion overlappings for each of plane junctions Forming the structural scheme of the microwave circuit or its bond graph

Figure 1. A flow-chart of the pre-processing procedure.

3. MODE BASES CALCULATION The determinant structure depends on the version of the technique used for the field matching (see remarks below) and on the cross-section topology which can be rather complicated. For example, the cross section of the WG lineshownin Fig.2 is the simplest of the cross-sections of WG lines arising as

44


the result of IC (Fig.2) decomposition and described by nine subregions. Such a line has the connectivity degree equalling four and is described by nine rectangles. When using the conventional approach1, 3, 4, the subregions’ fields are directly matched on the common boundaries at projecting the E field on the “wide” parallel-plate WG basis and the H -field on the “narrow” parallel-plate WG basis that leads to the determinant equation of the tentative structure shown in Fig. 3.

6

2

7 1

5

3

8

10

9

4

Figure 2. Dissection of the shielded third order IC low—pass filter by a plane and the crosssection of arisen WG line to be calculated.

E

1,2,3,4

H ! 1,2

E

5,2,3,4

H

5,2

! E

5,6,7,8,9

H

5,6

! E

10,6,7,8,9

H !

10, 6

1

2

!

5

5

!

6

6

! 10

I

M

EM !

2

0

0

!

0

0

!

0

ȟM !

ȟ !

ȟE !

! !

0 !

0 !

! !

0 !

0 !

! !

0 !

0

EM

M

!

I

E

!

0

0

!

0

0

ȟE

ȟ

!

ȟM

ȟEM !

0

0

!

0

!

!

!

!

!

!

!

!

!

!

!

0

0

0

!

E

I

!

M

EM !

0

0

0

0

! ȟEM

ȟM

!

ȟ

ȟE

!

0

!

!

!

!

!

!

!

!

!

!

!

0

0

0

!

0

0

! EM

M

!

I

0 !

0 !

0 !

! !

0 !

0 !

! !

ȟ !

! ȟM ! !

ȟE !

0

Figure 3. The tentative structure of determinant equation corresponding to the WG line sketched in Fig.2.

The labels over columns designate the vector of unknowns which correspond to a column. For example, 2 and 2 describe the vector of unknown amplitudes of parallel-plate WG modes of the 2nd subregion that propagate along the axis OY in the positive and negative directions, correspondingly. The labels on the left rows describe the origin of a row


45

equation. For example, the row E 5,2,3,4 is the result of E-field matching at the common boundary of the 5th sub-region with the 2nd, 3rd and 4th. Here, we used the following tentative designations: The block matrices M and conjugated M are the matrices of coupling integrals between modes of adjacent parallel-plate WG's. I, ȟ and E are the diagonal matrices of units, propagation constants and propagation phase or attenuation coefficients (along the distance h ( j ) ). The total order of determinant is defined by the number of space harmonics m( j ) taken into account in each sub-domain. Naturally, at the numerical solution, the subdomain expansion sizes must be chosen according to Mittra’s rule, namely, m( j ) must be proportional to a ( j ) . Taking into account the availability of so many zero block matrices, several schemes of determinant calculations can be proposed. Generally speaking, the investigation of various calculation schemes showed the case of arbitrary geometry, the most straightforward way of operating with the whole matrix, turns out to be the best one. Firstly, this way provides the lowest probability of blanks in large-sized mode bases and, secondly, it is characterized by the best behaviour of determinant value facilitating the roots search. Omitting the procedure of dispersion equation solution for the set of cutoffs f c( n ) 20 dB

0 0

1

2

3

4

5

6

7

8

Frequency, GHz Figure 6. The frequency response of IC low-pass filter calculated by GMMT.

0 -5 -10

Loss, dB

-15 -20 -25 -30 -35

Experimental filter [1] Redesigned filter in 24x12 mm 2 housing 2 Double semi-ring filter in 16x8 mm housing

-40 -45 830

835

840

845

850

855

860

865

870

Frequency, MHz Figure 7. Responses of the single and double semi-ring filters.

An interesting result was obtained while attempting to update the specific configuration of a recently proposed8 small-sized filter. The minimax procedure incorporated into the developed GMMT solver was used for the reconstruction of filter geometry, having one semi-ring as a resonant cavity,

52


and for the optimization of a new, more complicated configuration with double- and triple-semi-rings (see Fig.7). Increasing the number of semirings allows reducing the filter dimensions8. The last example illustrates an unconventional application of MMT for calculating an iris in a circular WG basing. This involves the step-wise approximation of WG smooth boundaries in order to ascertain a capability of the developed GMMT to calculate objects with smooth boundaries. Such a test calculation was compared with exact results obtained by the conventional MMT (Fig.8). It rather unexpectedly achieved a qualitative coincidence of amplitude-phase characteristics even at N 5 (!), where N is the number of steps on a circle quarter, and the total coincidence at N 17 . It must be noted that the iris response calculation stipulates not only the search of full mode bases for the wide and narrow WGs but the calculation of the plane junction of these WG's, and further application of the S-matrix technique as well. S thin iris required exact calculation of the fringing field interaction by higher modes. 60

Return Loss, dB

50

40

Exact MMT solution and stepwise approximation at N=17 N=5 HFSS

30

20

10

0 6

8

10

12

14

16

18

20

Frequency, GHz Figure 8. Frequency response of the iris in circular WG calculated by MMT, HFSS and by GMMT with stepwise approximation of smooth boundaries.


53

6. CONCLUSIONS The algorithms that generalize the application of mode-matching technique to the structures having the piece-wise Cartesian coordinate surfaces have been developed. This automatic approach to the field matching concerns not only recognizing the internal structure of a waveguide line and forming dispersion equation, but calculating the S-matrices of the plane-junctions as well. Saving the high speed and accuracy of calculations inherent to the mode-matching based solutions, the developed program code moves them close to the mesh methods in general. The research described in this publication was made possible in part by Award No. UE25004-KH-03 of the U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF) and INTAS Award No 01-0373.

7. REFERENCES 1. F. Arndt, R. Beyer, J. Reiter, T. Sieverding, and T. Wolf, Automated Design of Waveguide Components Using Hybrid Mode-Matching/ Numerical EM Building Blocks in Optimization Oriented CAD Frameworks—State-of-the-Art and Recent Advances, IEEE Trans. Microwave Theory Tech. 45(5), 747-760 (1997). 2. M. K. Thumm and W. Kasparek, Passive High-Power Microwave Components, IEEE Trans. Plasma Science 30(3), 755-786 (2002) 3. G.V. Kisunko, Electrodynamics of Hollow Systems, VKAS Publ., Leningrad (1949) (in Russian). 4. A. Wexler, Solution of Waveguide Discontinuities by Modal Analysis, IEEE Trans. Microwave Theory Tech., 15, 508-517 (1967). 5. G. Veselov, N. Platonov, and E. Slesarev, About taking into account the field singularities in the mode-matching technique, Radiotekhnika 35(5), 27-34 (1980) (in Russian). 6. V.P. Lyapin, V.S. Mikhalevsky, and G.P. Sinyavsky, Taking into account the edge condition in the problem of diffraction of waves on step discontinuity in plate waveguide, IEEE Trans. Microwave Theory Tech.. 30(7), 1107-1109 (1982). 7. A. Kirilenko, D. Kulik, L. Rud, V. Tkachenko, and P. Pramanick, Electromagnetic modeling of multilayer microwave circuits by the longitudinal decomposition approach, 2001 IEEE MTT-S Int. Microwave Symp. Dig., Phoenix, 1257-1260 (2001). 8. A. Kirilenko, D. Kulik, V. Tkachenko, The automatic mode-matching solver application by the example of complicated shape cavities design, Proc. NUMELEC-03, Toulouse, rep. PO2.25, (2003).

ELECTRIC FIELD INTEGRAL EQUATION ANALYSIS AND ADVANCED OPTIMIZATION OF QUASI-OPTICAL LAUNCHERS USED IN HIGH POWER GYROTRONS Jeff Neilson Calabazas Creek Research, Saratoga, CA 95070, USA

Abstract

Modern high-power gyrotrons typically use a mode converter and launcher to convert the high order cavity mode to a Gaussian like output mode. Total efficiencies (cavity power to usable Gaussian power) of the conversion are usually 85-95%. The analysis codes used to design these systems are based on approximate techniques that are not sufficiently accurate to allow design of higher efficiency converters. We have developed an analysis code based on the electric field integral equation, which provides very accurate calculations for the radiated fields. An advanced surface synthesis technique was developed to improve the converter efficiency.

Key Words

Quasi-optical launcher, integral equation, gyrotron

1

INTRODUCTION

A typical method for accomplishing beam/RF separation in modern high power gyrotrons uses a combination of an internal mode converter and stepcut launcher [1]. The internal converter uses perturbations of the waveguide surface to convert the output mode from the cavity into a set of modes whose combined fields have a Gaussian-like profile. This Gaussian-like profile can then be efficiently launched, focused and guided by small mirrors inside the vacuum envelope of the gyrotron. Figure 1 depicts such a launcher and guide system. The current analysis method for these converter/launcher systems is performed in two steps. First, the waveguide mode converter is analyzed using coupled mode theory. Then the radiated fields are calculated from the waveguide cut using the Stratton-Chu formulation [2]. This is, in principle, an exact calculation if the true fields on the waveguide wall are known; however, the act of cutting open the waveguide can perturb the fields from those calculated using the closed waveguide solution.For the fields produced by the waveguide converter, this approach has given good results because the [


56

J. Neilson

converter waveguide cut is done in regions where the field intensity is low, resulting in small perturbations to the waveguide fields. The combination of the mode converter analysis with the Stratton-Chu formulation has been a useful design tool. Experience has shown, however, that launcher systems designed for high average power gyrotrons using this analysis have typically shown significant diffraction losses not predicted by the codes and less than efficiencies. It is thought that this less-than-optimal performance may come from code analysis inaccuracies. Measurements of the radiated fields from the converter/launcher systems differ from those predicted by theory [3]. As average gyrotron power is increased, the internal loss due to this calculation error will grow and further increase the construction complexity and expense of the gyrotron. An exact analysis of the launcher system, in addition to eliminating design uncertainties due to analysis approximations, would allow for arbitrary wall deformation in the launcher surface. Such flexibility would give tube engineers a way to explore alternative designs for achieving higher efficiencies and for designing improved converters that are more easily manufactured or more compact. For an analysis code to be a useful design tool, the code must do its calculations without exorbitant amounts of CPU time or expensive super-computers.

Window RF Launcher and Mode Converter

Reflector

RF

Electron Beam

Electron Beam

Cavity

Reflector

Figure 1. Typical configuration for whispering gallery mode to Gaussian mode converter system used in modern high power gyrotrons.

Electric Field Analysis

57

When the original work on this problem was done, it was known that, in principle, an exact formulation of the problem could be stated through the use of surface integral formulations of Maxwell’s equations. This approach was not taken because of the CPU and memory requirements made such an approach intractable. However, the integral equation approach has now become viable because of several factors. In the short period of time since the original analysis was done, calculation speed in engineering workstation computers has increased more than an order of magnitude. In addition, new techniques for solving integral equation formulations of large body scattering have been introduced. These new techniques, such as the fast multipole method [4], greatly reduce the computational requirements. In this paper, we show the application of the electric field integral equation (EFIE) for calculation of the radiation from the converter and launcher system. Using the multi-level fast-multipole algorithm, we have performed calculations for a converter/launcher system and compared the calculations to measurements. Results from this code have shown the feasibility and accuracy of the integral equation approach. Using a more generalized surface formulation, numerical synthesis of a converter surface has been performed. This optimization approach has resulted in designs of significantly shorter length and reduced diffraction losses than designs using the current designs methodology.

2

EFIE FORMULATION

For observation points lying on a conducting surface S which, forms the waveguide converter and launcher, the electric field integral equation (EFIE) is given by

S

i G ( r, r' ) ⋅ J ( r' ) dS' = 4π ------E ( r ) kη

(1)

for r on surface S, where J(r) is the unknown surface current, Ei(r) is the incident waveguide source field and

1- ∇∇′ g ( r, r' ) G ( r, r' ) = I – ---2 k

(2)

58

J. Neilson

This equation is applied to the launcher surface and the unknown surface current J(r) is discretized for numerical solution using the method of ik R

e g ( r, r' ) = -------------r – r'

(3)

moments (MOM) [5]. The solution time and memory requirements for the MOM solution are dramatically decreased by use of the multi-level fast multipole algorithm. The GMRES algorithm is used for iterative solution of the surface currents. The excitation field is the mode emanating from the gyrotron cavity. The incident electric field on the surface S induced from this field is calculated using the vector Huygens principle and is given by – ikR

i 1 - ∇' ⋅ J ( r' ) 1----------------+ ikR-R ˆ e –ik R dS' E ( r ) = jωµ --------- J( r' ) e------------ dS' – ------------2 R 4π 4πωε R S

S

1- 1----------------+ ikR-e – ikR R ˆ × M ( r' ) dS' + ----2 4π R s

(4)

where the magnetic and electric surface currents are given as i

M ( r ) = – nˆ × E ( r )

(5)

i J ( r ) = nˆ × H ( r )

(6)

and Ei, Hi are the electric and magnetic field of the incident mode. Use of Eq. for calculation of the incident field is not an exact formulation of the problem. Ideally, the surface current at aperture would consist of the incident field of the excitation mode and an unknown surface current, which represents the field resulting from multiple reflections between the waveguide ends and surface S. Inclusion of an unknown surface current on the aperture was not done as it substantially increases both solution complexity [6] and the number of unknowns. Since the structure to be modeled is much larger than the free space wavelength, the reflected field will be significantly smaller than the excitation field and its neglect will not impact the calculation.


3

59

EXAMPLE CALCULATION

The radiated field of a 110 GHz, TE22,6 converter and launcher was calculated using the EFIE formulation. The cylinder wall variation for this launcher has the form of

r ( φ, z ) = r o + α z + ε 1 cos ( H 1 ( z ) + 3φ ) + ε 2 cos ( H 2 ( z ) + φ )

(7)

with a total length of 150mm and a spiral cut length of 5mm. The mesh used to model the converter and launcher had a density of approximately 7 triangles wavelength for a total of 160K unknowns. Sixty iterations were used to calculate the unknown surface currents for a normalized residual (a)

(b)

22

22

-5

20

-5

20

-10

18

-10

18

-15

16

-15

16

-20

14

-25

12

-1

0

1

2

Azimuth (radians)

3

4

-20

14

-25

12

-1

0

1

2

Azimuth (radians)

3

4

Figure 2. Radiated field intensity in dB on cylinder (R=5.6 cm) surrounding launcher. Cylinder axis is offset 1.16 cm (towards launcher cut) from launcher axis. (a) Calculated intensity. (b) Measured intensity.

error of the surface current less than 0.01. The error in energy conservation was 1.5%. The total run time and memory requirements were 45 minutes and 500MB on a 1.5GHz Pentium IV The calculated and measured intensity of the radiated phi component of electric field is shown in Figure 2. This calculation was done for the field on a cylinder of radius 5.6 cm surrounding the launcher. The measured and calculated field contours are remarkably similar, especially considering the difficulty in obtaining this measurement accurately, requiring generation of a high purity TE22,6 mode, and measurement in the near field zone of the launcher The design length was constrained to be shorter than the optimal length so therewere significant amounts of surface current along the spiral cut .

[

60

J. Neilson

of the launcher.The radiated field from the edge surface currents gives rise to the large amount of sidelobes seen in both the calculations and measured fields. The calculated result using the EFIE analysis is considerably closer to the measured result than that obtained by the Stratton-Chu (S-C) calculations, which is shown in Figure 3. Significant differences exist between this calculation and the measurement. Since the S-C calculation does not model the large edge currents that are present in this launcher, the lack of good agreement is not surprising.

22 -5

20 -10

18 -15

16 -20

14

-25

12

-1

0

1

2

3

4

Figure 3. Stratton-Chu calculation for the radiated field intensity in dB on cylinder (R=5.6 cm) surrounding launcher.

4

ADVANCED OPTIMIZATION OF Q-O LAUNCHER MODE CONVERTER

Launcher converter designs have been based on the Denisov type design approach using two azimuthal variations (Eq. 7). The amplitudes H and H(z)have been typically modeled as constants to linearvariation.For constant diameter launchers that are not much above cutoff this approach can be used to generate a beam with high Gaussian content and low diffraction losses.However,fortapered launchers there is increased coupling to unwanted


61

parasitic modes which reduce the beam quality and increase diffraction losses. By generalizing the surface model as

z

N

r ( φ, z ) = r o + αz +

a n ( z ) cos n=1

β n ( z ) dz ± l n φ 0

and using numerically optimized functions for an and En, significantly more compact designs with less diffraction loss can be achieved. The most successful launcher design tested in a gyrotron to date (140 GHz TE28,8 launcher designed at FZK and tested in a 1MW CW Thales tube[7]) was shown to have very low diffraction losses (1.5%) and high Gaussian content. Using the new design approach, a redesign of this launcher was undertaken. A new design using the azimuthal variations L=1,2,3 and 6 was generated that was 20% shorter than the existing design with virtually no diffraction losses and higher Gaussian content. Plots of the calculated azimuthal component of the electric field intensity on a cylinder for the original and improved design are shown in Figure 4.

(b)

(a) 28

32

26

30

-5

-5

24

28

-10

-10

22 ) m c( 20 -15 si x A 18 -20

26

) m c( si x A

24 22

-20

16

20 -25

18 16

-15

0

1

2

3 4 Azimuth (Radians)

5

Azimuth (radians)

6

-25

14 12

0

1

2

3 4 Azimuth (Radians)

5

6

Azimuth (radians)

Figure 4. Radiated field intensity in dB on cylinder (R=10 cm) surrounding launcher. (a) Original design. (b) Optimized design using generalized surface form.

62

5

J. Neilson

CONCLUSIONS

The feasibility and accuracy of the EFIE approach has been demonstrated by the close agreement between measurement and calculation. The results of the EFIE calculation are also better than what can be achieved using the Stratton-Chu calculation in conjunction with the coupled mode analysis. Using the calculations provided by the EFIE analysis, the diffracted power losses can now be determined. The optimization technique developed has been shown to give significant improvements in performance of QO converters while reducing the length. These improvements can result in cost reductions for gyrotron manufacturing; the result of reduced magnet size and lowered processing times.

6.

ACKNOWLEDGEMENT

The authors would like to thank Prof. Ron Vernon and Mike Perkins at University of Wisconsin who performed the test launcher measurements. This research is supported by DOE Small Business Innovative Research grant number DE G.G. Denisov, A.N. Kuftin, V.I. Malygin, N.P. Venediftov, D.V. Vinogradov and -FG03-00ER82965.

REFERENCES [1] [2]

[3]

[4]

[5]

V.E. Zapevalov, “110 GHz gyrotron with built-in high-efficiency converter,". J. Electronics, vol. 72, nos. 5 and 6, pp. 1079-1091, 1992. M. Blank, K. Kreischer, and R.J. Temkin, “Theoretical and Experimental Investigation of a Quasi-Optical Mode Converter for a 110-GHz Gyrotron,” IEEE Trans. Plasma Science, vol. 24, No. 3, pp. 1058-1066, June 1996. D. Denison, T. Chu, M. Shapiro and R.J. Temkin, “Gyrotron Internal Mode Converter Reflector Shaping from Measured Field Intensity,” IEEE Trans. Plasma Science, vol. 27, No. 2, pp. 512-519, April 1999. W. Chew, J. Jin, C. Lu, E. Michielssen and J.Song, “Fast Solution Methods in Electromagnetics,” IEEE Trans. on Ant. and Prop., vol. 45, no. 3, pp. 533-543, Mar 1997. R.F. Harrington, “Matrix Methods for Field Problems,” Proc. IEEE, vol. 55, pp. 136-148, 1967.

Electric Field Analysis [6]

[7]

63

R. Bunger and F. Arndt, “Moment-Method Analysis of Arbitrary 3-D Metallic NPort Waveguide Structures,” IEEE Trans. on Microwave Theory and Tech., vol. 48, no. 4, pp. 531-537, April 2000. G. Dammertz,et.al,”Prototype of a 1 MW, CW Gyrotron at 140 GHz for Wendelstein 7- X,”,28th Intl Conf IRMMW, Sep 2003, pg121.

COMPARISON OF TWO OPTIMIZATION CRITERIA FOR QUASI-OPTICAL POWER TRANSMISSION LINES

N. N. Voitovich2, B. Z. Katsenelenbaum1, O.V. Kusyi2, 2

Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine 1 Institute of Radioengineering and Electronics, Russian Academy of Science, Moscow, Russia;

Abstract:

Key words:

1.

Two optimization criteria for antenna-rectenna power transmission lines are compared. The criteria describe the energy transmission coefficient and the mean-square residual of obtained and desired fields in the rectenna plane. The behavior of each criterion on functions optimal for another is studied. Numerical results for rectangular and circular apertures are shown and analyzed (a part of results is published in [1]; a mistype in [2] is corrected). microwave power transmission, paraxial optics, phase front optimization.

INTRODUCTION.

PROBLEM FORMULATION

Problems connected with long beams of electromagnetic field arise while transmitting the power between two antennas (i.e. from a solar power station onto the Earth) [3 – 6]. Field U ( x, y ) generated on transmitting antenna, creates field V ([ ,K ) in the plane of receiving antenna (rectenna). In the paraxial approximation, the field V is expressed (with accuracy to a constant factor) by U as

V ([ ,K )

ñ U ( x, y ) exp[ic ( x[ yK )]dxdy , 2S ³D

(1)

where D is the antenna domain in the dimensionless coordinates, ' is therectennadomain, n~ kaD d istheFresnelparameter, a , D are characteristic 65 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 65–72. © 2005 Springer. Printed in the Netherlands.

66

Voitovich, Katzenelenbaum, Kusyi

linear sizes of the antenna and rectenna, respectively, d is a distance between the antenna and rectenna (see Figure 1), and ka 2 d S .

Figure 1. Transmit and receive antennas.

The following two criteria are usually formulated for power transmitting lines: a) the energy transmission coefficient

L(U )

V

2 '

/U

2 D

;

(2)

b) the mean-square difference between a given field in the rectenna plane and a received one

V (U )

V0 V

2 f

f f

³ ³ V ([ ,K ) V ([ ,K ) 0

2

d [ dK .

(3)

f f

Here V0 is a desired field distribution in the rectenna plane which is zero outside the rectenna and constant on modulus on it and U D and V ' are usual mean-square norms on the antenna and rectenna apertures respectively and V f is such a norm in the whole rectenna plane and V0 is assumed to be normalized as V0

'

1.

In this paper, the question of how one of the criteria behaves on the functions optimizing another, is considered. Of course, the field on the antenna, being optimal for one criterion, is not optimal for the other. Field

Two Optimization Criteria for Power Transmission Line

67

U L ( x, y ) , providing the optimal transmission coefficient, creates the field in the rectenna plane, for which the value of functional (3) is much larger than its minimal value V (U V ) . However, it turns out that the function U V which provides the minimum to functional (3), gives almost optimal value of functional (2). The investigation is carried out in cases when variables are separable, namely, for rectangular and circular apertures.

2.

RECTANGULAR APERTURES Let the antenna and rectenna be equi-oriented rectangles of sizes bE . Then

2a u 2b , 2D u 2 E , respectively, and (for simplicity) aD U ( x, y ) u ( x)u (ay / b) , V ([ ,K ) v([ )v(DK / E ) , 1

c 2S ³ u ( x)e icx[ dx .

v([ )

(4)

1

Functional (2) becomes of the form

L(U ) l 2 (u ) ,

(5)

where

l (u ) v

D

³

1 1

_ v([ ) _2 d[ ,

v u

a

2

2

u a,

D

³

1 1

_ u ( x ) _2 dx

(6) are one-dimensional mean-

square norms on the antenna and rectenna apertures. The function ul , which provides the maximum to the functional l , is the first eigenfunction u1 of the integral equation

Onun ( x)

2

S³

sin( x x ') un ( x ')dx ' 1 x x' 1

corresponding to the maximal eigenvalue

,

(7)

O1 l (ul ) . The functional (3)

68


V 1 (u )

relates to its one-dimensional analogue

v ([ ) v0 ([ )

2 f

V (UV ) 2V 1 (uV ) V 12 (uV ) . We assume that

vV

D

as (8)

1 . The function uV is calculated by the

formula

uV ( x)

3.

1

c 2S ³ v0 ([ )eicx[ d[ .

(9)

1

CIRCULAR APERTURES

In the case of circular antenna and rectenna of radii a and D , 1 2 respectively, the azimuth-independent fields are U ( r M ) (2S ) u (r ) , 1 2 V ( U T ) (2S ) v( U ) , 1

v( U ) c ³ u (r ) J 0 (crU ) rdr .

(10)

0

We give the main formulas analogous to those for the rectangular apertures:

L(U ) l (u ) , l (u )

where

vD

1

is 2

³ _ v( U ) _ 0

expressed

Ud U , u

1

a

by

³ _ u (r ) _ 0

(11) the 2

same

formula

(6)

with

rdr . The homogeneous equation

for the function ul maximizing the functional has the form

Onun (r ) c ³

1 0

rJ 0 (cr ') J1 (cr ) r ' J 0 (cr ) J1 (cr ') un (r ')r ' dr ' . (12) r 2 r '2


69

The following relation is valid for the second functional

V (U ) V 1 (u )

2

v v0 f .

(13)

The function uV is calculated by the formula 1

uV (r ) c ³ v0 ( U ) J 0 (kr U ) U dU . 0

4.

(14)

NUMERICAL RESULTS In Figs. 2, 3 the values of the functionals on U V , uV and ul are shown.

At small c the values of each functional on both functions ul , uV are almost the same, because the functions themselves are close.

Figure 2. The behavior of the functionals.

At larger ñ the behavior of l (uV ) seems rather surprising: it is close to

l (ul ) at any ñ . This fact can be explained by the following arguments. It is easily seen

70


Figure 3. The behavior of the functionals.

2

l (u ) 1

V (u ) v0 v D u

(15)

2 a

for any c and u . Since, obviously, at u of (15) tends to be zero as c o f , then

uV the numerator in the fraction

lim l (uV ) 1, c of

(16)

is what explains the asymptotical behavior of l (uV ) . According to (4), (9) (and, analogously, (10),(14)), vV Kv0 , where K is an integral operator in the homogeneous equation (7) or (12). It is the first iteration of the initial function v0 in the power method for calculating the maximal eigenvalue

O1 of the equation K *vn

Onvn

(17)


71

with the same kernel (see, f. e. [7]). Express v0 in the form f

v0

¦C v

n n

(18)

n 1

then f

vV

On Cn vn ) . 2 O1

O1 (C1v1 ¦ n

At small c we have

(19)

On O1 , n 2,3... , thus, vV is proportional to

vl and l (uV ) is close to l (ul ) , as noted above. At intermediate c , only several eigenvalues On are notably smaller than 1 and larger than 0 . Only the eigenfunctions vn corresponding to these intermediate eigenvalues in the expansion (18) makes the value l (uV ) smaller than l (ul ) . The range of values c , at which their relative contribution is noticeable, is not too wide.

Figure 4. Erroneous and valid curves in comparison and the ratio of losses.

For the case of rectangular apertures a part of the above results is presented in [2]. In particular, in Figure 6.4 from [2] the relations l (uV ) / l (ul ) and V 1/ 2 (uV ) / V 1/ 2 (ul ) are shown. They are copied in Figure 4 above as the lowest and dashed lines.Note that the higher curve in Figure 6.4

72


from [2] (dashed line in Figure 4) is erroneous. The valid curve (and its description) obtained from the results of this paper, is presented in Figure 4. In this figure, we also show the ratio of losses 1 L(UV ) / 1 L(U l ) for two solutions considered here.

5.

REFERENCES

1. Katsenelenbaum B. Z., Kusyi O. V., Voitovich N. N., “Comparison of two Optimization Criteria for Power Transmission Lines.” in Proc. of Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2003), 131-135, Lviv, 2003. 2. Katsenelenbaum B. Z., Electromagnetic Fields - Restrictions and Approximation. WILEYVCH, Berlin, 2003. 3. Fadeev V. G., Vanke V. A., “Optimization of the transmitting antenna of solar space power system,”. J. of Communications Technology and Electronics 1999; 44; 775-779 (Russian). 4. Katsenelenbaum B. Z., Microwave power transmission by a long beam. Proc. of Seminar/Workshop DIPED-99, 17-21, Lviv, 1999. 5. Korshunova E., Shaposhnikov S. S., Vaganov R. B., “Focal Spot without the nearest diffraction sidelobes,” Proc. of Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2001), 126-131, Lviv, 2001. 6. Kusyi O. V., Shaposhnikov S. S., Vaganov R. B., Voitovich, N. N., “Bicriterion optimization problems for power transmitting line,” Proc. of Seminar/Workshop DIPED{2002), 127-130, Lviv-Tbilisi, 2002. 7. Fox A. G., Li T., “Resonant modes in a maser interferometer,” Bell Sys. Tech. J. 1961; 40; 453-458.

A GENERAL PURPOSE ELECTROMAGNETIC CODE FOR DESIGNING MICROWAVE COMPONENTS W. Bruns [email protected]

H. Henke Technische Universitaet Berlin [email protected]

Abstract

A general purpose electromagnetic code has been developed based on the finite difference method. The code computes resonant fields and arbitrary time dependent fields. The objects may contain linear dielectric and magnetic materials as well as lossy materials, open boundaries, and may be periodic in three dimensions. Scattering parameters are computed via an FFT of the impulse response. In the time domain, the excitation is by port modes, by relativistic charges or through free moving charges (particle in cell). Different measures have been taken in order to speed up the code. Symmetries are used whenever possible, gridcells are only allocated to field regions and parallel computing is possible. The code is well suited for designing travelling and standing wave structures in the millimeter wave range and in particular millimeter wave tubes.

Keywords:

FDTD, Parallel Computation, PIC

1.

INTRODUCTION

The code, called GdfidL, is based on the finite difference method. The coefficients of the difference equation are derived by the finite integration method. In the first sections, the underlying approximations of Maxwells equations are described, then, some efficiency improvements are scetched. It follows a description of the implemented parallel computations. At the end the treatment of free moving charges is described.

1.1

Principle: Time stepping the fields

The basic approach is time stepping of the fields. It is the famous FDTDalgorithm introduced by Kane S. Yee in 1966 [1]. With a suitable small time step, one can compute the new fields simply by performing curl-operations on 73 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 73–91. © 2005 Springer. Printed in the Netherlands.

74

W. Bruns, H. Henke

the fields, and adding the result, scaled by a material depended factor, to the old fields. The electromagnetic field at a time t is given by the field at an earlier time, and by the excitation, e.g. currents. = t0 ) + [µ]−1 H(t) = H(t = t0 ) + [ε]−1 E(t) = E(t

t τ =t0 t

τ =t0

    

dτ −∇×E

− κE −G dτ ∇×H

   

(1)

Computing the new H. The magnetic field at the time t + ∆t/2 is computed from the fields at earlier times, by replacing the time integration by a multiplication of the integrand at the center of the integration interval with the width of the timestep. + ∆t/2) = H(t − ∆t/2) − [µ]−1 H(t − ∆t/2) − ∆t ≈ H(t

t+∆t/2

dτ ∇×E

τ =t−∆t/2 [µ]−1 ∇×E t

(2)

The algorithm is time reversible when the electric field is taken in the middle of the integration interval.

Computing the new E. + ∆t) = E(t) E(t + [ε]−1

t+∆t

τ =t

− κE −G dτ ∇×H

− [ε]−1 κE ≈ E(t) + ∆t [ε]−1 ∇×H −[ε]−1

t+∆t τ =t

t+∆t/2

(3)

dτ G

+ ∆t/2) is computed by linear interpolation beThe dependent current κE(t tween the values of E(t + ∆t) and E(t). The integration of the current dependent terms can be carried out exactly, when the time dependence of the currents is known.

2.

SPACE DISCRETIZATION

For every practical computation, one must restrict oneself to a finite number of degrees of freedom. For example, when performing a mode matching computation, one only computes with a finite number of mode amplitudes, assuming that the ignored amplitudes are so small that their effect can be ignored. The finite difference algorithm does not attempt to compute the electromagnetic field everywhere, but only at selected points in space.

A General Purpose Electromagnetic Code for Designing

75

The finite integration algorithm, which in free space is equivalent to the finite difference algorithm, attempts to compute integral values of the electromagnetic field over small integration areas. The Finite Integration algorithm substitutes curl equations by difference equations for the line in Maxwell’s · ds and H · ds along discrete edges ∆s. The unknowns are tegrals E electric and magnetic voltages between the points of a primary and a dual grid, fig. 1.

H

E Figure 1.

Primary grid (dark) for the electric field and dual grid (light) for the magnetic field.

The derivation of the finite difference coefficients starts from Faradays and Amperes law: −

d dt d dt

· dA = µH

A

· ds E

(4)

· ds H

(5)

δA

· dA = εE

A

δA

In the Finite Integration Algorithm, the areas we integrate over are the faces of the primary grid A and the faces of the dual grid A . When the material boundaries are just tangential or normal to these faces, we assume a constant average field strength over these faces: −

µdA A

A

d H · nA ≈ dt

d · nA ≈ εdA E dt

· ds E

(6)

· ds H

(7)

δA

δA

The line integrals on the right sides of the above equations are sums of four line integrals along the edges of the primary and dual grid, respectively. In order

76

W. Bruns, H. Henke

to get line integrals also on the left sides, we integrate the equations over the edges of the primary or dual grid. −

· ds ds µdA ∆s ∆s A s d H · d δA · ds ≈ E ds dt ∆s ∆s A εdA

d dt

· ds ≈ H

E δA

(8) (9)

Assuming that the contour integrals on the right sides stay constant, we arrive at: −

d 1 · ds ≈ · ds H E ds dt ∆s ∆s A µdA δA

d 1 · ds ≈ · ds E H ds dt ∆s ∆s A εdA δA

(10) (11)

Our unknowns are now the line integrals of the fields along the edges of the · ds and h ≈ H · ds, we can drop the primary and dual cells. With e ≈ E approximation signs and write −

The values

∆s

d 1 h = ds (e1 + e2 − e3 − e4 ) dt ∆s A µdA 1 d ds (h1 + h2 − h3 − h4 ) e = dt ∆s A εdA

1 A

εdA

ds and

∆s

1 A

µdA

(12) (13)

ds are the coefficients of the differ-

ence equations. The values hi and ei are the line integrals of the field strengths surrounding the element under consideration.

2.1

Computing the FD-Coefficients

GdfidLfurther approximates the FD-coefficients by assuming for the co efficients 1εdA ds that the value A εdA is constant over the integration A

path ∆s. Therefore GdfidL uses an FD-coefficient of

A

ds εdA

. The area over

which the permittivity has to be integrated is the vicinity of an edge of the primary grid. Four cells belong to this vicinity, each cell may be filled with up to two different materials. Figure 2 illustrates the situation where the material boundaries in the four cells touch the edge. The integral A εdA in the FD-coefficient now is A

εdA =

1 8

(ε1,1 + ε2,1 )A1 + (ε1,2 + ε2,2 )A2

+(ε1,3 + ε2,3 )A3 + (ε1,4 + ε2,4 )A4

(14)


77

Figure 2. Left: The FD-coefficients to compute an electric component from the surrounding magnetic components depend on up to eight different permittivities. The marker indicates the location of the electric component. The areas A1 , A2 , A3 , A4 are the areas of faces of the primary grid cells touching the edge where the electric component is defined on. The thick lines indicate edges of the primary grid, the thin lines indicate edges of the dual grid. Right: The marker indicates the location of the magnetic component. The FD-coefficients to compute a magnetic component from the surrounding electric components depend on up to four different permeabilities. Two of the permeabilities are the permeabilities in the shown cell, the other two belong to the cell above the paper plane. The thick lines indicate edges of the primary grid, the thin lines indicate edges of the dual grid.

The value ds of course is the length of the edge of the primary grid. To evaluate the coefficient of a magnetic component 1µdA ds , we inA

tegrate the permeability in the vicinity of a dual edge. Since a dual edge is the connection of the two centers of two primary cells, the dual edge lies within two primary cells. GdfidL assumes that in each primary cell the integral A µdA is constant. Then, with up to two different materials in each primary cell, the FD-coefficient for a magnetic component is

1 1 ds = 2 A µdA

∆1 ∆2 + (µ1,1 + µ2,1 )A1 /2 (µ1,2 + µ2,2 )A1 /2

(15)

Figure 2 illustrates the material distribution in one of the two primary cells involved.

78

W. Bruns, H. Henke

EIGENVALUE COMPUTATION, PERIODIC BOUNDARY CONDITIONS

3.

Equations 12 and 13 may be written as matrix equations for arithmetic vectors e and h with the unknown integrated electric and magnetic field strengths over the primary and dual edges: −

Here the elements of (C)e are ± ±

1 A

εdA

d e = (C)hh dt

d h = (C)ee dt

1 A

µdA

(16)

ds and the elements of the (C)h are

ds. The matrices are extremely sparse, with only up to 4 nonzero

entries per row. In case of resonant fields we substitute jω for from equations 16 (C)h (C)ee = ω 2e

d dt

and obtain (17)

If the boundary conditions at the outer boundaries of the computational volume are simple ones, ie. if the outer boundaries can be assumed perfectly electric conducting or perfect magnetic conducting, then the matrix of the eigenvalue problem (C)h (C)e is real. For periodic boundary conditions at the outer surface of our computational volume, some of the matrix elements become complex, because the periodicity requires that eg. the electric field at a lower boundary has to be the same as the field at the corresponding upper boundary, multiplied with a complex factor e−jϕ . GdfidL uses subspace iteration as implemented in an algorithm of Tueckmantel [4] to search for the lowest nonzero eigenvalues of 17. This algorithm needs some hundred to some thousand iterations of the form: (18) yi+1 = (C)h (C)e yi − γi yi where the γi are the zeroes of some polynomial. Since the algorithm requires only matrix times vector operations, and not the matrix itself, it is not necessary to really construct and store the matrix. GdfidL implements the matrix times vector operation in a four step process, without performing a complex matrix times vector operation. Two steps are very similiar to the operations needed to perform a single time step in a FDTD algorithm. The grid is extended such, that above the last gridplane of the computational volume an auxiliary plane with the same material distribution as the very first plane is placed. Below the lowest plane of the computational volume, an auxiliary plane with the same material distribution as the last plane is placed. This is done for all cartesian directions where periodic boundary conditions are to be enforced. In the first step, a complex auxiliary vector x is computed. x := (C )e yi

(19)


79

e Here the entries of the real matrix (C ) are the real valued FD-coefficients ± 1 ds in the artificially enlarged volume. If the vector yi would contain µdA

the integrated electric field strengths of a resonant field with frequency ωn , then this auxiliary vector x would be the integrated magnetic field strengths of jωnh. This step is similiar to the computation of the H-field update in an FDTD-algorithm. To compute the auxiliary vector, it is not necessary to store the matrix (C )e , but only to be able to perform a H-field update. In the second step, the periodic boundary conditions for the H-fields are applied to the complex auxiliary vector x. This is: The components of x that lie at the lower boundaries of the computational volume are multiplied by a complex factor ψ = exp(jϕ) and the result is copied to the corresponding components at the upper planes. ϕ is the wanted phase shift. Figure 3 illustrates this procedure for a 2-dimensional grid, when periodic boundary conditions in a single direction are to be enforced.

Figure 3. Left: The periodic boundary conditions for the magnetic field are enforced by taking the values at the lower plane, multiplying them by a complex factor and assigning the result to the magnetic field components at the upper plane. Right: The periodic boundary conditions for the electric field are enforced by taking the values at the upper plane, multiplying them by a complex factor and assigning the result to the electric field components at the lower plane. The thick lines indicate edges of the primary grid, the thin lines indicate edges of the dual grid.

In the third step, the vector update yi+1 := (C )h x − γi xi

(20)

is performed. The elements of (C )h are the real valued FD-coefficients in the artificially enlarged volume. This step is similiar to the E-field update in a FDTD-algorithm. Again, the matrix (C )h is not needed explicitly. In the fourth step, the periodic boundary conditions for the electric field are applied to the vector yi+1 . This is: The components of yi+1 that lie at the upper boundaries of the computational volumes are multiplied by a complex factor ψ = exp(−jϕ) and the results are copied to the components at the lower planes.

80

3.1

W. Bruns, H. Henke

Example for Periodic Boundary Conditions

The periodic boundary conditions are applied to compute the dispersion relation in a periodic arrangement of spheres connected by round rods. Figure 4 shows an elementary cell and the computed dispersion diagram.

Figure 4. Above: Elementary cell of a 3D array of conducting spheres, connected by round conducting rods. The lattice constant a is the same in all three directions, the radius of the spheres is 0.375 a, the radius of the rods is a/10. Shown is the real part of the eletric field of π the fundamental mode with k = (1, 1, 1) 4a . Below: The band structure for the first few modes in the 3D array.


81

FASTER FD-IMPLEMENTATION

4.

In additionto the commonly known FD-optimization that computes with

· ds and E · ds instead of H and E [3] two algorithmic improvements H have been found and implemented.

4.1

Single sweep through memory

Normally the H- and E-update in FDTD-codes are performed as follows: For all Timesteps: DO Update all H-components, Update all E-components, ENDDO For all Timesteps The above algorithm in every timestep reads all the E components to update all H-components, then reads all the H-components to update all E components. In every timestep, all field-components are touched twice, but with a long CPU-time distance between. Careful inspection of the update process reveals that it is possible to update the H components of a cell, and immediately after that the E-components can be updated, since they are no longer needed to update other H-components. The second use of the field components will be much faster on cache-based computers, since the field components will already be in the cache. The old E-components can be overwritten while stepping through the mesh. E.g. for lossfree problems it might look like: REAL, DIMENSION(1:3,0:nx+1,0:ny+1,0:nz+1) :: & Eds, Hds, dsoEpsA, dsoMueA DO iz= 1, nz, 1 DO iy= 1, ny, 1 DO ix= 1, nx, 1 Hds(1,ix,iy,iz)= Hds(1,ix,iy,iz) - dt*dsoMueA(1,ix,iy,iz) & * ( Eds(2,ix ,iy ,iz )-Eds(2,ix ,iy ,iz+1) & + Eds(3,ix ,iy ,iz )-Eds(3,ix ,iy+1,iz ) ) Hds(2,ix,iy,iz)= Hds(2,ix,iy,iz) - dt*dsoMueA(2,ix,iy,iz) & * (-(Eds(1,ix ,iy ,iz )-Eds(1,ix ,iy ,iz+1)) & + Eds(3,ix ,iy ,iz )-Eds(3,ix+1,iy ,iz ) ) Hds(3,ix,iy,iz)= Hds(3,ix,iy,iz) - dt*dsoMueA(3,ix,iy,iz) & * ( Eds(1,ix ,iy ,iz )-Eds(1,ix ,iy+1,iz ) & -(Eds(2,ix ,iy ,iz )-Eds(2,ix+1,iy ,iz ))) !! !! Now we can update the Eds-components of the cell since !! they are no longer needed for the remaining H-updates. !! All used H-components have already been updated:

82

W. Bruns, H. Henke !! Eds(1,ix,iy,iz)= Eds(1,ix,iy,iz) + dt*dsoEpsA(1,ix,iy,iz) & * (-(Hds(2,ix ,iy ,iz ) - Hds(2,ix ,iy ,iz-1)) & + Hds(3,ix ,iy ,iz ) - Hds(3,ix ,iy-1,iz ) ) Eds(2,ix,iy,iz)= Eds(2,ix,iy,iz) + dt*dsoEpsA(2,ix,iy,iz) & * ( Hds(1,ix ,iy ,iz ) - Hds(1,ix ,iy ,iz-1) & -(Hds(3,ix ,iy ,iz ) - Hds(3,ix-1,iy ,iz ))) Eds(3,ix,iy,iz)= Eds(3,ix,iy,iz) + dt*dsoEpsA(3,ix,iy,iz) & * (-(Hds(1,ix ,iy ,iz ) - Hds(1,ix ,iy-1,iz )) & + Hds(2,ix ,iy ,iz ) - Hds(2,ix-1,iy ,iz ) ) ENDDO ENDDO ENDDO

A similiar optimization can be applied in the discretized curl-curl operator that is used for eigenvalue computation. The optimization saves about 30 % CPU-time on typical desktop computers.

4.2

Computing only in field carrying Gridcells

The Finite Difference algorithm can be easily implemented if one represents the fields as 4-D arrays. An example of how simple the FDTD-update procedure might look was shown in the previous section. This approach has the disadvantage that memory (and CPU) is also used for cells that are totally inside perfect electric or magnetic materials. But for many realistic geometries, the volume carrying fields is only a fraction of the total rectangular volume. Then it would be advantageous to deal only with the cells which have a nonzero field. Figure 5 shows such a geometry, where less than 10% of the computational volume really needs to be considered for the field computation. One possible scheme could be the use of linked lists, where every field carrying cell has the information about its neighbours. This needs 6 indices per field cell in addition to the 12 floating point words for the field components and their coefficients. This approach was used in the former ”GdfidL” [5] [6]. The ”GdfidL” of today has a grid organization that needs only a single index per cell. The fields itself are stored in 2D-arrays, where the second index is the number of the cell. An INTEGER array ”NrofCell” is used to extract the topology information. The FDTD-update with the single index per cell might look like: REAL,DIMENSION(1:3,0:*) :: Eds, Hds, dsoEpsA, dsoMueA INTEGER, DIMENSION(0:nx+1,0:ny+1,0:nz+1) :: NrofCell DO iz= 1, nz, 1 DO iy= 1, ny, 1 DO ix= 1, nx, 1


83

Figure 5. A model of the BESSY cavity with attached waveguides and tuning plungers. The three large damping waveguides are attached to the cavity at different heights, such that no symmetry plane is left. Because of the large waveguides, most of the enclosing box is filled with electric conducting cells. Only 8 % of the computational volume is filled with interesting gridcells. 92 % of the gridcells can be ignored.

i= NrofCell(ix,iy,iz) IF (i .LT. 1) CYCLE !! skip when no field possible !! !! indices of neighbour cells in positive directions !! ipx= NrofCell(ix+1,iy ,iz ) ipy= NrofCell(ix ,iy+1,iz ) ipz= NrofCell(ix ,iy ,iz+1) Hds(1,i)= Hds(1,i) - dt*dsoMueA(1,i) & * ( Eds(2,i)-Eds(2,ipz) + Eds(3,i)-Eds(3,ipy) ) Hds(2,i)= Hds(2,i) - dt*dsoMueA(2,l) & * (-(Eds(1,i)-Eds(1,ipz)) + Eds(3,i)-Eds(3,ipx) ) Hds(3,i)= Hds(3,i) - dt*dsoMueA(3,i) & * ( Eds(1,i)-Eds(1,ipy) -(Eds(2,i)-Eds(2,ipx))) !! !! indices of neighbour cells in negative directions !! imx= NrofCell(ix-1,iy ,iz ) imy= NrofCell(ix ,iy-1,iz ) imz= NrofCell(ix ,iy ,iz-1) Eds(1,i)= Eds(1,i) + dt*dsoEpsA(1,i) & * (-(Hds(2,i) - Hds(2,imz)) + Hds(3,i) - Hds(3,imy) ) Eds(2,i)= Eds(2,i) + dt*dsoEpsA(2,l) &

84

W. Bruns, H. Henke * ( Hds(1,i) - Hds(1,imz) -(Hds(3,i) - Hds(3,imx))) Eds(3,i)= Eds(3,i) + dt*dsoEpsA(3,i) & * (-(Hds(1,i) - Hds(1,imy)) + Hds(2,i) - Hds(2,imx) ) ENDDO ENDDO ENDDO

5.

PARALLEL COMPUTATION: LOCAL FIELD UPDATE

The core of the Finite Difference Method is the discretisation of the curloperators. With these discretised curl operators, one computes time dependent fields (FDTD) via the discretised form of 1 H((n + 1/2)∆t) = H((n − 1/2)∆t) − ∆t ∇×E(n∆t) µ

(21)

1 + 1/2)∆t) (22) E((n + 1)∆t) = E(n∆t) + ∆t ∇×H((n ε and one finds resonant fields in lossfree structures by searching for eigenvalues of the discretised form of 1 1 = ω2E ∇× ∇×E ε µ

(23)

Most of the CPU-time is spent in applying these discretised curl operators. However, they are quite easily parallelised by using subvolumes. For example, when performing a FDTD calculation, the algorithm for each subvolume is: For all Timesteps: DO Compute local H by applying the local curl operator to the local E For all Directions: DO Send tangential H to the neighbour Receive tangential H from neighbour ENDDO For all Directions Compute local E For all Directions: DO Send tangential E to the neighbour Receive tangential E from neighbour ENDDO For all Directions ENDDO For all Timesteps Figure 6 scetches a local subvolume. The tangential H-components at the lower boundaries of the local volumes must be sent to the neighbour volumes in negative directions. Correspondingly, the tangential E-components at the upper


85

boundaries must be sent to the neighbour volumes in positive directions. For correct results, the tangential components from a neighbour in eg. x-direction must be received before data can be sent in eg. y-direction.

Figure 6. The dark lines and circles represent the electric field components in a local volume. The light ones represent the magnetic field components. The tangential E field components at the upper boundaries of the local volume (thick dark) and the tangential H field components at the lower boundaries (thick light) can be computed from the local information. These components are sent to the neighbour volumes. The tangential E field at the lower boundaries (dashed dark) and the tangential H field at the upper boundaries (dashed light) cannot be computed from the local information. These components are received from the neighbour volumes.

5.1

Parallel computation: Excluding unneeded gridcells

The Finite Difference Method in cartesian coordinates is easily parallelised, since the subdivision of the total rectangular computational volume is easily done, if one restricts oneself to rectangular subvolumes. One just has to partition the grid such, that each processor has about the same number of gridcells. This approach works well, when electromagnetic fields can exist in a large fraction of the volume. However, most realistic RF-devices, if computed in a rectangular volume, do not lead to a grid where most gridcells are filled with vacuum or a dielectric. The opposite is the case: Complicated devices, for which the computation inherently is time consuming, have an enclosing rectangular box of which 90% or more is filled with electric conducting material. If one subdivides such a volume into as many subvolumes as there are processors, most processors will work on parts of the volume where the fields are known to be zero a priori. What a horrible waste of resources. Finite Element based codes do not have that problem. Since they anyway have to deal with their complicated mesh-topology, dealing with nonrectangular sub-volumes is their daily bread. But if one wants to stick with

86

W. Bruns, H. Henke

the inherently easier implementation and cheaper execution of classical Finite Differences, one has to stick to rectangular subvolumes. There is a way out: Each processor works on more than one subvolume. If we subdivide the total volume in many more subvolumes than we have processors, then we can discard the subvolumes where no fields can exist, and spread the remaining ones evenly over the available processors. This approach is halfway between classical Finite Difference and the complicated topology of Finite Element Meshes. As a typical example,figure 7, we take the cavity of figure 5.

Figure 7. A model of the BESSY cavity with attached waveguides and tuning plungers. This is the same cavity as shown in figure 5. In this figure, the different colours indicate the used subvolumes. The total volume is subdivided in 8x24=192 subvolumes, of which 122 can be discarded. The total number of gridcells is about 16 millions. GdfidL needs about 3 GBytes of RAM and six hours wall clock time on an eight processor PC Cluster (total cost 8.000 EUR) to accurately compute the first 120 resonant fields in that structure.

Local field computation. When performing a FDTD calculation, the algorithm for a single subvolume per processor is: For all Timesteps: DO Compute local H by applying the local curl operator to the local E For all Directions: DO Send tangential H to the neighbour volumes Receive tangential H from the neighbour volumes ENDDO For all Directions Compute local E For all Directions: DO


87

Send tangential E to the neighbour volumes Receive tangential E from the neighbour volumes ENDDO For all Directions ENDDO For all Timesteps However, if one wants to have only a single thread of execution, the field update for more than one subvolume per processor must be done slightly more complicated, since otherwise deadlocks will occur: For all Timesteps: DO For all Subvolumes: DO Compute local H by applying the local curl operator to the local E ENDDO For all Subvolumes For all Subvolumes: DO For all Directions: DO Send tangential H to the neighbour volumes Receive tangential H from the neighbour volumes ENDDO For all Directions ENDDO For all Subvolumes For all Subvolumes: DO Compute local E ENDDO For all Subvolumes For all Subvolumes: DO For all Directions: DO Send tangential E to the neighbour volumes Receive tangential E from the neighbour volumes ENDDO For all Directions ENDDO For all Subvolumes ENDDO For all Timesteps

5.2

Grid Generation

It is crucial that the grid generation is parallelised as well, otherwise that step would be the most time consuming part. The generation of the grid and the FDcoefficients is made in two steps: In the first step, each processor gets assigned the same number of subvolumes to generate the coefficients for. Subsequently, each subvolume is inspected, how many gridcells can carry a nonzero field. The subvolumes with only zero field are discarded, and the remaining ones are spread over the available processors such, that a: each processor has about the same number of interesting grid-cells to deal with, and b: that the communication between subvolumes on different processors is minimised. This spreading over the available processors is implemented via a call of the METIS [9] pack-

88

W. Bruns, H. Henke

age. In the second step, each processor generates the mesh and the coefficients for the assigned subvolumes.

6.

SIMULATING FREE MOVING CHARGES

Free moving charges are simulated by the ’Particle in Cell’-algorithm. The algorithm uses a large number of charges of finite size and fixed shape, fig. 8. Free moving charges show up in Maxwells equations as a current density. To compute the electric field at the next timestep, the charge which has traversed a face of the dual grid must be computed. This is done with an algorithm similiar as the one described by Villasenor [7], extended for a grid with uneven spacings. That charge amount, multiplied bya factor of dsoEpsA · ds changes, in = ∆s , is the amount by which the electric unknown E εdA addition to the change due to the curl of H. The charge is accelerated by the electric field, and rotated by the magnetic field at its actual position. Therefore, the electric and magnetic field must be known at the same time. The normal FDTD-algorithm does not compute the magnetic field at the same times as the electric field. Instead, the magnetic field is only known half a timestep away. The natural assumption, that the magnetic field at the time where the electric field is known, would be the average of the magnetic field before and after, leads to the computation of the magnetic field in two half steps. One step, to compute the magnetic field at the time when it is needed to compute the Lorentz-force on the charges, and the other half step to compute the magnetic field at the time t = (n + 1/2)∆t. The computation of the acceleration and rotation is performed by an algorithm invented by Boris [2]. The optimised implementation of Buneman, as can be found in the TRISTAN [8] code, is used.

6.1

Parallel Computation

Moving charges change the electric field in their immediate vicinity, and their velocity is changed by the electric and magnetic field in their immediate velocity. Therefore it is natural to perform all the charge related computations on the processor who is responsible for computing the electromagnetic field within the volume where also the charge is in. While the charges are drifting through the computational volume, they will leave the domain of one processor and enter the domain of another processor. Since the computation of the magnetic field in two halfsteps is only required in the vicinity of charges, the algorithm with the two half steps is only needed for subvolumes where charges are in. The charge free subvolumes can be treated with the standard FDTD algorithm.


89

Figure 8. The dark arrows represent the electric field components. The light ones represent the magnetic field components. For integrating the Lorentz-force, the force due to the magnetic field must be known at the same time as the force due to the electric field. The fields at the center of mass of the charge (black circle) is computed by linear interpolation of the fieldcomponents nearest to the position of the center of mass. The circles are at the positions of the fieldcomponents which are involved in computing the x- and y-components.

6.2

Use of symmetries for Particle Pushing

The force on a particle is computed by an interpolation of 2 x 3 x 8 nearby field components, see figure 8. This interpolation must be modified for particles which are near to a plane of symmetry, figure 9. GdfidL uses an auxiliary gridplane. The fieldcomponents in this auxiliary gridplane are computed such, that the fields near the plane of symmetry obey the wanted symmetry. For a magnetic wall: The normal electric field component in the auxiliary plane is the negative one of the normal component inside of the computational volume. The normal magnetic voltage is doubled. Since no current may traverse a magnetic wall, it must be enshured that no net charge traverses the magnetic wall. When, due to the particle pushing, the particle has traversed the symmetry plane, the position of the particle is reflected back into the computational volume. The sign of the normal component of the particles velocity is changed. This is scetched in figure 10.

90

W. Bruns, H. Henke

Figure 9. The dark arrows represent the electric field components. The light ones represent the magnetic field components. The shaded area is outside of the computational volume. At the border of the computational volume, magnetic boundary conditions shall be applied. For interpolating the Lorentz-force, the magnetic voltages whose paths cross the magnetic boundary condition, have to be multiplied by two (thick light arrows). The tangential magnetic components outside of the computational volume must be set to the negative value of the corresponding magnetic components just inside (dashed light arrows). The normal electric components outside must be set to the negative value of the corresponding electric components inside (dashed dark arrows).

Figure 10. The dark arrows represent the electric field components, or convection currents. The shaded area is outside of the computational volume. The two quadratic patches are a charge cloud before and after the particle pushing. At the border of the computational volume, magnetic boundary conditions shall be applied. When a charge cloud would traverse the magnetic wall due to the particle pushing, its convection current outside of the computational volume must be reflected back into. The normal components outside (dashed dark arrows) must be subtracted from the corresponding normal components inside. The tangential convection currents must be doubled (thick dark arrows).


7.

91

REFERENCES

[1] K. S. Yee, “Numerical Solution of initial boundary value problems involving maxwell’s equations in isotropic media”, IEEE Transaction of Antennas and Propagtion 14 (1966) 302 [2] Boris, J. P., “Relativistic plasma simulation-optimization of a hybrid code”, in Proceedings of the Fourth Conference on the Numerical Simulation of Plasmas Naval Res. Lab., Wash. D.C., 1970. [3] Th. Weiland, “Ein Verfahren zur Berechnung von Wirbelstroemen in massiven, dreidimensionalen, beliebig geformten Eisenkoerpern”, etz Archiv, H. 9 (1979), pp. 263-267 [4] J. Tueckmantel, “An improved version of the eigenvector processor SAP applied in URMEL”, CERN/EF/RF 85-4, 4 July 1985 [5] W. Bruns, “GdfidL: A Finite Difference Program for Arbitrarily Small Perturbations in Rectangular Geometries”, IEEE Transactions on Magnetics, vol. 32, no. 3, May 1996, pp. 1453-1456 [6] W. Bruns, “GdfidL: A Finite Difference Program with Reduced Memory and CPU Usage”, Proceedings of the PAC-97, Vancouver, vol. 2, pp. 2651-2653, http://www.triumf.ca/pac97/papers/pdf/9P118.PDF [7] J. Villasenor, O. Bunemann, “Rigorous charge conservation for local electromagnetic field solvers”, Computer Physics Communications 69 (1992) 306 [8] http://webserv.gsfc.nasa.gov/ESS/exchange/contrib/macneice/pic-tristan.html [9] George Karypis, Vipin Kumar, “A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs”, University of Minnesota, Department of Computer Science, Minneapolis, MN 55455, Technical Report: 95-035, http://wwwusers.cs.umn.edu/∼karypis/metis/

CHAPTER 2

QUASI-OPTICAL DEVICES AND SYSTEMS

AMPLIFICATION AND GENERATION OF HIGHPOWER MICROWAVE BY RELATIVISTIC ELECTRON BEAMS IN SECTIONED SYSTEMS Edward Abubakirov1, Nikolay Kovalev1, Victor Tulpakov2 1 2

Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia Moscow Radiotechnical Institute, Moscow, Russia

Abstract:

The highest powers of microwave radiation produced with devices driven by high-current relativistic electron beams amount to 109-1010 W in pulses of 1100 ns duration. As the high-frequency electric fields in the devices are limited with microwave breakdowns, further enhancement of microwave pulse energy requires broader interaction space. The main problem with such oversized and, accordingly, multi-mode structures, is keeping coherence of output radiation. Because of this problem, special means for mode selection must be applied. In the paper, methods of mode selection based on sectioning of the operating space are discussed and examples of their experimental realization are presented.

Key words:

high-power microwaves, multi-mode systems, mode selection.

1.

INTRODUCTION

The main problem of powerful microwave electronics is preventing breakdowns in electron devices and their output elements. Note that surface processing gives only a limited effect because even the pure metal is disrupted with high electric fields. So, at pre-breakdown fields the only opportunity to enhance the RF power is to increase the cross-section of microwave devices. However, in the oversized system the intense electron beam can excite several modes with different frequencies and spatial structures, which means loss of coherence. Some methods to suppress parasitic excitation can be borrowed, with a proper adaptation, from the “classic” microwave electronics, but most of mode selection methods in microwave devices driven by intensive relativistic electron beam need a specialized approach [1, 2]. The paper is devoted to principles, peculiarities and realizations of mode selection methods based on sectioning the interaction space of a relativistic electron microwave generators and amplifiers. The method uses longitudinal 95 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 95–103. © 2005 Springer. Printed in the Netherlands.

96

Abubakirov, Kovalev, Tulpakov

separation of the interaction space into several parts, so that coupling of these parts would depend on partial rf field structures and the device performance would be realized only at a definite set of modes in sections. The main attention in the paper is paid to devices, whose operation is based on the Cherenkov mechanism of stimulated radiation. In such a system, a rectilinear electron beam formed with the simplest guns interacts with an electromagnetic wave which phase velocity is close to the velocity of electrons. Cherenkov devices are especially attractive for centimeter and long millimeter wave bands.

2.

SCHEMES OF SECTIONED DEVICES

The principle of sectioning can be applied to a wide variety of microwave sources. The simplest versions are following (Fig.1 and 2): (a) a sectioned amplifier, which consists of a sequence of amplifying sections, pierced with a common electron beam; (b) a resonant traveling wave tube (TWT), that is an amplifier with a selective feedback provided with narrowband reflectors (along with passive reflectors, the active ones can be used as well); (c) a cascaded oscillator representing a selective though low efficient oscillator followed with an efficient amplifier not coupled to the upstream oscillator electromagnetically, but excited with the modulated electron beam.

e-beam

Mode2

Mode3 Microwave output

Microwave input

Mode1

Figure 1. Sectioned amplifier.

Application and Generation of H-P Microwaves FEEDBACK Mode2

Reflection Mode 2 Mode 1

AMPLIFYING Mode1

97

EM-wave

Reflection Mode 1 Mode 2

e-beam

Modulation Mode 1

AMPLIFYING Mode 2 EM-wave

Figure 2. Sectioned oscillators: resonant TWT (top) and cascaded oscillator (bottom).

3.

ELEMENTS OF SECTIONED MICROWAVE SOURCES

Mode selective sectioned devices can be composed of forward and backward wave sections, Bragg reflectors, mode converters, etc.

3.1 Forward-wave amplifiers In traditional TWTs, to avoid self-excitation of the slow wave structure, rf absorbers are widely used. However, in the HPM electronics, SWS are oversized in order to avoid breakdown and the absorbers are not efficient. Electrodynamic decoupling between sections (see Fig.1) seems to be the most promising opportunity to prevent the spurious self-excitation.

3.2

Reflectors

Passive reflectors. Reflectors made on a base of hollow metallic waveguides with smooth corrugated sidewalls [3] are widely used in highpower microwave electronics. Selective properties of such reflectors are provided with resonant coupling of operating electromagnetic waves which

98


parameters must satisfy Bragg conditions. For the helically corrugated waveguide r ( z , M ) R a cos(h z m M ) , the condition is

h1 h2 h , m1 m2 m (1) where h1, h2 are propagation constants and m1, m2 and azimuth indexes of operating waves. To enhance the selectivity, more than two modes can be coupled in double corrugated structures [4] and multi-channel feed-back systems [5]. Active reflectors. A backward wave amplifier (BWA), operating below its excitation threshold, can be regarded as reflector or converter, which couples electromagnetic wave and space charge waves of the electron beam. In such sections, the electromagnetic wave modulates the electron beam or, modulated electron beam excites electromagnetic wave. The beam as an active medium provides simultaneous transformation and amplification of waves. The advantages of the active reflector are:

a high gain G ~ (1 − J J st ) at the electron current J approaching the start current Jst of the section (Fig.3) ; a narrow amplification frequency band ∆f f ~ (1 − J J st ) that can provide an additional mode selection and reduce an interference of the electron beam noise; an electrodynamic decoupling between sections since the amplified electromagnetic signal accompanying the modulation of the electron beam is extracted from BWA in the direction of the cathode, whereas the modulated electron beam proceeds in the opposite direction. A strong dependence of the BWA gain on amplitudes of coupled waves makes the active reflector analogous to a saturated mirror that favors to fast transient time and high efficiency of the device [6]. −1

Application and Generation of H-P Microwaves

Gain

150

99

0.99

100

0.97 0.95

50

0.90

0 2,6

2,8

3,0

3,2

3,4

3,6

(k||-Z/v)L Figure 3. Amplification in a BWA at various ratios of operating and start current.

3.2

Self-exciting sections

The cascaded oscillator (Fig.2) is featured with operation of two or more sections in the non-linear regime. The main problem is combining stability of self-exciting in the first section with efficient microwave radiation in the second one. An analysis [7] shows that the simplest version of cascaded oscillator can be realized only as a trade-off between efficiency and stability relative to fluctuations of electron beam parameters. The reason is an unsuitable phase correlation between energy and density modulation of particles in the beam on the output of the section. So, adding of remodulating or phase-correction sections can improve the situation.

4.

EXPERIMENTAL SECTIONED DEVICES

4.1 Resonant TWTs Anexperimental version of the resonant TWT was made as a combination of an amplifier with two Bragg reflectors. The operating mode of the amplifying section was the lowest slow non-symmetric hybrid wave (HE11) with rotating transverse structure. This mode can be easily transformed into

100


11,4

100

11,3

80

11,2

P,arb. units

frequency, GHz

Gaussian wave beam by a simple horn antenna. The selective feedback was realized by 5-entry helically corrugated Bragg reflectors which coupled the rotating HE11 mode to counter-rotating modes TE41. The cathode reflector consisted of two identical parts; a mechanical rotation of one part resulted in a tunable phase shift and, so, in a frequency tuning of the oscillator. The X-band oscillator was driven with a 1.3MeV, 10 kA, 150 ns electron beam formed with a cold emission gun. The electron beam was guided with a pulsed (quasi-static) magnetic field. The microwave power was radiated through a horn antenna and polyethylene window and registered with semiconductor “hot carriers” sensors [8]. The peak power was about 1.5 GW and the pulse duration was 30-40 ns. Rotation of parts of the cathode reflector allowed tuning the frequency of the oscillator within 10.9-11.4 GHz 3 dB band (Fig.4) [2, 9].

11,1 11,0

60 40 20

10,9

0 10,8

-30 -20 -10

0

10

20

30

40

50

M, degree

10,8

10,9

11,0

11,1

11,2

11,3

11,4

frequency, GHz

Figure 4. Frequency tuning and output power of resonant TWT.

4.2 Cascaded Oscillators In a cascaded oscillator, the simplest self-exciting section is the orotron that is a Cherenkov oscillator with an open high-selective cavity. The cavity cannot withstand high rf fields and, so, is appropriate only for low-efficient part of the sectioned oscillator. Such a cascaded oscillator [2] was realized with an orotron operating at TE312 mode of a circular cross section cavity. The orotron provided axissymmetric rf modulation of the electron beam, which, in its turn, excited a traveling wave section operated at slow TM01 mode of a circular corrugated waveguide. The cascaded oscillator was realized with the same electron beam as for the resonant TWT; it produced pulsed power about 2 GW at 9.1 GHz, and the pulse duration reached 100 ns.


4.3

101

Sectioned Amplifiers

The simplest version of the sectioned amplifier stable in the absence of input signal represents a combination of a narrowband BWA modulating the electron beam and an output wideband TWT power amplifying section. The first, proof of principle, X-band amplifier of the sort produced 100 MW [10]. Later, a GW power amplifier of extended cross section was designed [11]. The amplifier (Figs. 5 and 6) driven with 0.8-0.9 MeV, 6 kA, 0.2 µs electron beam consisted of: quasi-optical mode converter (5) transforming the input signal produced with a 100 kW pulsed 9.1 - 9.6 GHz tunable magnetron to the rotating TE41 mode of the circular waveguide; backward wave amplifier (4) operating in a whispering gallery TE41 mode and serving as a pre-amplifier; horn (3) matched the BWA to the electron gun space; output traveling wave section (6) operating in the slow hybrid HE11 mode of the corrugated circular waveguide; horn antenna (8), simultaneously serving as the electron beam collector; input (9) and output (10) vacuum windows; electron beam guidance pulsed solenoid (11) combined with the vacuum case (2); diode with a field emission cathode (1). Maximum output power of the amplifier was about 1100 MW (Fig.7) at 47 dB gain and 20% efficiency. Amplification bandwidth was about 1%. The measured output wave pattern was close to Gaussian.

Figure 5. Block diagram of the gigawatt amplifier.

102


Figure 6. Design of the amplifier system.

Figure 7. Waveforms of (a) accelerating voltage, (b) heterodyned signal, (c) output power, and (d) spectrum of radiation S(f), which is shifted down with the local oscillator operating at the frequency 8.98 GHz.

4.4

Pulse-periodic operation of sectioned devices

Subsequent to the above mentioned single pulse devices, sectioned microwave oscillators operating at high pulse repetition rates were developed recently. A “super-radiation” BWO with selective pre-modulating section delivered 2 GW, 1 ns pulses at 700 pps with 2.5 kW average power [12]. Similar results were demonstrated in experiments with sectioned BWO made


103

recently by IAP and MRTI: the device produced 600 MW/15 ns pulses at 500 pps during 3s bursts.

5.

CONCLUSION

Driven with high-current relativistic-electron accelerators, generators and amplifiers with sectioned interaction space are capable of delivering gigawatt-nanosecond microwave pulses, ~103 pulses per second being available.

6. 1.

2.

3. 4. 5.

6.

7. 8. 9. 10. 11. 12.

REFERENCES Kovalev N., Petelin M., Mode selection in microwave relativistic electron generators with distributed interaction, in Relativistic microwave electronics, IAP AS USSR, Gorky, (1981). Abubakirov E., Fuchs M., Gintsburg V. et al, Cherenkov relativistic oscillators of coherent electromagnetic radiation with multimode sectioned electrodynamic systems. Proc. of 8th Int. Conf. on High-Power Electron Beams. World Scientific, 2, 1105-1110, (1991). Kovalev N., Orlova I., Petelin M., Wave transformation in a muti-mode waveguide with corrugated walls, Izv.vuzov. Radiofizika, 11: 783-786, (1968). Ginzburg N., Peskov N., Sergeev A., Two-dimensional double-periodic Bragg resonators for free electron lasers, Optics Commun., 96, 254-258, (1993). Abubakirov E., Fuchs M., Kovalev N., High-selectivity resonator for powerful microwave sources, Proc. 11th Int. Conf. on High Power Particle Beams, Prague, 1, 410413, (1996). Abubakirov E., Kovalev N. Relativistic BWO as a part of sectioned generators and amplifiers, Proc. of 2-d Int. Workshop on Strong Microwaves in Plasmas, IAP, Nizhny Novgorod, 2, 788-793, (1993). Abubakirov E., Smorgonsky A., On an achievement of stable operation in a relativistic sectioned oscillator, Radiotekhnika i electronika, 35: 133-139, (1990).. Denis B., Pozhela Yu. Hot electrons. Vilnus: Mintis, 1971. Abubakirov E., Denisenko A., Savelyev A. et al., Frequency tunable relativistic resonant TWT, Pisma ZhTF, 26: issue 4, 14-18, (2000). Volkov A., Zaitsev N., Ilyakov E. et al., Realization of high gain in power microwave pulse amplifier with explosive emission gun, Pisma ZhTF, 18: issue 12, 6-10, ( 1992). Abubakirov E., Denisenko A., Fuchs M. et al. X-Band Gigawatt Amplifier, IEEE Trans. on Plasma Science, 30: no.3, 1041-1051, (2002). Korovin S., Lubutin S., Mesyats G. et al., Generation of sub nanosecond pulses in 10 GHz band with high peak and average power, Pisma ZhTF, 30, issue17, 23-31, (2004).

MICROWAVE DEVICES WITH HELICALLY CORRUGATED WAVEGUIDES

V. L. Bratman1, A.W. Cross2, G. G. Denisov1, A. D. R. Phelps2, S.V. Samsonov1 1

Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia Department of Physics, University of Strathclyde, Glasgow, UK

2

Abstract:

Helical corrugation of the inner surface of an oversized circular waveguide provides very flexible dispersion characteristic of an eigenwave. Under certain corrugation parameters, the eigenwave can possess a sufficiently high and almost constant group velocity over a wide frequency band in the region of close-to-zero axial wavenumber. This makes it attractive for broadband gyroTWTs and gyro-BWOs with reduced sensitivity to electron velocity spread. Another set of parameters ensures an operating wave with a strong frequency dependant group velocity over a frequency band, which is sufficiently separated from any cutoffs. Such wave dispersion is favourable for frequencychirped pulse compression at very high power levels. An overview of experiments on the helical-waveguide gyro-devices and the pulse compressor is presented.

Key words:

gyrotron-type devices; gyro-TWT; gyro-BWO; waveguide with helical corrugation; microwave pulse compression.

1.

INTRODUCTION

Metal hollow waveguides with various types of periodic corrugation are used widely in high-power microwave electronics. One such structure consists of a helical corrugation in the wall of a circular cylindrical waveguide, which involves both an axial and azimuthal periodicity. The surface of a helically corrugated waveguide can be represented in a cylindrical coordinate system (r, M, z) as follows: r(M, z) = r0 + l cos(mB M + kB z) .

(1)

Here r0 is mean radius of the waveguide, l is amplitude of the corrugation, mB and kB=2S/d define the azimuthal number and axial component of the 105 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 105–114. © 2005 Springer. Printed in the Netherlands.

106

Bratman, Cross, Denisov, Phelps, Samsonov

Bragg periodicity vector, respectively, and d is the corrugation period (Fig.1). Such a corrugation provides asymmetry of the wave dispersion for circularly polarized modes resulting in additional mode selection and control of their dispersion characteristics. These properties make waveguides with a helical corrugation attractive for a large number of applications 1, 2. In particular, they have recently been successfully used as interaction regions in gyro-TWTs 3, 4, gyro-BWOs 4, 5 and as a dispersive medium for passive microwave pulse compression 6.

Figure 1. Schematic view of a waveguide with a three-fold right-handed (mB=-3) helical corrugation.

It is important to note that the latter applications rely on significantly different mode dispersion for their operation. For a gyro-TWT the most favourable operating wave is that which has a constant and sufficiently high group velocity over a wide frequency band in the region of close-to-zero axial wavenumber. In contrast, the operating wave for a pulse compressor should have a strongly frequency dependant group velocity over a frequency band which is separated from the cutoff frequency of the waveguide. These very different requirements can be satisfied by waveguides with quite similar geometry. In both cases, the parameters of the helical corrugation are chosen such that two partial modes, one close to cutoff and one propagating, are resonantly coupled (Fig.2). In experiments with the use of the helical waveguides in gyro-devices and for pulse compression, a three-fold (|mB|=3) helical corrugation (Fig.1) was used that coupled the TE2,1 (mode 2) and the TE1,1 (mode 1) circularly polarized modes of opposite rotation. The frequency band of main interest is mostly situated below the cutoff frequency of the TE2,1 mode, and therefore by having a sufficiently smooth down-tapering of the corrugation amplitude, the operating eigenmode totally transforms into the TE1,1 mode which was used to inject and extract the microwave energy from the helical structure.

Microwave Devices with Helically Corrugated Waveguides

107

Figure 2. Schematic dispersion diagram for a helically corrugated waveguide: k=Z/c is the wave vector, kz is its axial component, k0 corresponds to the frequency of exact Bragg resonance, c and d are unperturbed (partial) modes of the smooth waveguide; W1 and W2 are Floquet harmonics of the operating eigenmode; Wu1 and Wu2 are Floquet harmonics of the upper eigenmode.

2.

HELICAL-WAVEGUIDE GYRO-DEVICES

Depending on the direction of the guiding magnetic field, and with respect to the sign of the azimuthal number of the profile mB., the most selective configuration for gyro-devices with helically-rippled waveguides is when an axis-encircling electron beam resonantly interacts at the second cyclotron harmonic with a co-rotating TE2,1 component of the operating eigenmode, which is scattered on the corrugation into forward (for TWT) or backward (for BWO) propagating TE1,1 mode The operating waveguide for a Ka-band gyro-TWT 4, 7 has been designed to provide wave dispersion (Fig.3), which is matched within the maximum frequency band to an 80-keV electron beam having a pitch ratio of 1.2. In this experiment, an axis-encircling electron beam was formed in a thermionic gun with a reversed magnetic field near the cathode (cusp) 7, 8. A magnetic field of up to 0.7T at the interaction region was produced by a pulsed (3 ms) solenoid. A high-voltage power supply was capable to generate pulses of voltage up to 80kV and current up to 20A with a flat-top duration of up to 10Ps. The highvoltage and magnetic systems operated at a pulse repetition rate of up to 1Hz. A driving microwave pulse of duration up to 3Ps was produced by one of two

108


magnetrons with mechanical tuning of the radiation frequency covering the range between 33.4GHz and 36.8GHz at power of about 10kW.

Figure 3. Properties of the gyro-TWT operating eigenmode: a) dispersion diagram (dashed line corresponds to unperturbed electron-cyclotron wave); b) group velocity as a function of frequency.

In the regime of zero-drive stable amplification, the gyro-TWT electron efficiency was measured to be 27-28% for beam voltages from 50 to 80kV and beam current in the range of 4–8 A. The saturated gain of 23-25dB was measured at an input power of about 0.5kW. The linear gain of 30-35dB was obtained when the input power was less than 0.1-0.3kW. The maximum output power amounted to 180kW when the voltage was 80kV and beam current was 8.5-9A. The most broadband operation of the gyro-TWT (Fig.4) was demonstrated at a beam voltage of 80kV, which agreed well with the theoretical predictions. As was clear from the measurements, the maximum –3dB bandwidth of the gyro-TWT exceeds 3.2GHz, or 9% (upper frequency boundary of the amplification lies beyond the frequency bandwidth provided by the RF driving sources that were available). Along with the gyro-TWT the use of a helically corrugated waveguide is advantageous for realization of a smooth-frequency-tunable gyro-BWO where the operating eigenmode has a negative group velocity. Analysis of the helical-waveguide gyro-BWO capabilities showed that this device may be attractive for a number of technological applications, for which CW kilowatt-power gyrotrons are actively used [9]. This was the motivation of a project aimed at realizing a CW tunable gyro-BWO with a power of several kilowatts at a frequency of about 24GHz 5.


109

Figure 4. Instantaneous bandwidth of the gyro-TWT at various parameters.

Specific features of the CW helical-waveguide gyro-BWO as compared to our previous experiments were the use of a magnetron-injection gun (MIG) typical for conventional gyrotrons and a low-voltage (20kV) electron beam. It should be noted that an electron beam produced by a MIG is not an axis-encircling beam, which may affect the selectivity of the configuration discussed above, namely, a possibility of the spurious TE1,1 mode excitation at the second cyclotron harmonic also appears in the regime of the gyroBWO (Fig.5). Correspondingly, the MIG was designed to produce an electron beam with a radius of about 1.5mm at which the starting current of the parasitic gyro-BWO oscillations slightly exceeded that of the operating mode. The experiments demonstrated the selective second harmonic operation of the gyro-BWO at the desired mode for the designed values of the magnetic field, beam voltage and current in the CW (several hours) regime. The measured maximum output power, frequency range and tuning band (Fig.6a) were in reasonable agreement with the design. Rather large variations in the output power (oscillating behavior of power vs. B-field) can be explained by the improperly matched output window. The tuning characteristic of the gyro-BWO can be smoothed by the use of a broadband multiple-disc lowreflection window whose operation has been successfully tested in gyro-TWT experiments 4. At a beam current of 2A, gyro-BWO operation was tested in the regime with a single-stage energy recovery (depressed collector). When the collector potentialincreased from zero to almost 10 kV the tube efficiency grew from 15% to 23% (Fig.6b). Along with a substantial increase in the device efficiency, the use of the depressed collector allows reduction of the

110


voltage of the main power supply down to almost 10kV, which makes the gyro-BWO significantly more attractive for technological applications.

Figure 5. Dispersion diagram for the CW gyro-BWO (the dashed lines correspond to the partial modes.

a)

b)

Figure 6. Experimental results for the gyro-BWO at accelerating voltage of 20 kV and beam current of 2 A: a) the tuning characteristic (the dashed line corresponds to doubled cyclotron frequency); b) the energy recovery results.


3.

111

HELICAL-WAVEGUIDE PULSE COMPRESSOR

A phenomenon of compression of smoothly frequency modulated (chirped) electromagnetic pulses in a dispersive medium is well known and actively used in microwave electronics (radars) and laser physics 10. Hollow metal waveguides representing dispersive media (group velocity of an eigenmode is a function of frequency) are attractive for the microwave pulse compression 11 because of their capabilities of handling very high power, relative compactness and simplicity. Analysis of possibilities to increase the power of frequency-swept radiation using copper (the losses are important) waveguides at lower-order modes shows that X-band pulses of 50-200 ns in duration with a frequency modulation of 2-15% can be compressed in the waveguides with reasonable (less than 10 m) lengths into 0.5-3 ns pulses with 10-100 times higher peak power containing 30-60% of the input pulse energy. This set of parameters makes the proposed type of pulse compression attractive to increase the power from non-resonant relativistic Cherenkov devices, such as TWT and BWO, resulting in microwave sources of multi-gigawatt peak power. However, for this application, the use of a conventional (smooth-bore) waveguide, has serious limitations due to its being operated very close to cut-off. In optimum cases, the frequency at the beginning of an input pulse should be only 0.5-1% above the cutoff frequency. If a TWT is used to drive the compressor then it is inevitable that the low-frequency part of the amplification band is below the cutoff which will then be reflected from the compressor back to the amplifier resulting in its possible parasitic selfoscillation (RF isolation using unidirectional elements is problematic at very high power). If a relativistic BWO is used as a source of frequencymodulated pulses for a smooth-waveguide compressor, then the necessary frequency sweep can be produced only by using a difficult-to-realize accelerating voltage modulation. The two problems of wave reflection from a compressor and optimum frequency modulation can be simultaneously solved using a waveguide with a special helical corrugation of its inner surface 6. As was mentioned in the introduction, the geometry of the waveguide can be similar to that used for the gyro-devices but the parameters of the corrugation should be chosen in a way such that the eigenwave group velocity is a rapidly varying function of frequency (Fig.7). The helical symmetry allows the frequency regions with zero or negative group velocity of the eigenwave to be avoided, which ensures good rf matching of the compressor with the input source over a sufficiently wide frequency band. In addition, the flexibility of the wave dispersion allows its optimisation for a given frequency modulation of an input pulse by varying the corrugation parameters.

112

a)


b)

Figure 7. Eigenmode properties of a helically corrugated waveguide for pulse compression: a) dispersion diagram; b) group velocity and losses for a 2.08 m long waveguide.

The operation of a helical-waveguide compressor was studied theoretically and confirmed in an experiment where a 70-ns 1-kW pulse from a conventional TWT was compressed in a 2.08 meter long helical waveguide. The output pulse had a peak power of 10.9 times higher than the input pulse and duration of about 3 ns (Fig.8). The experimental results were in very good agreement with the simulations which also predicted that with two times faster frequency sweep at the end of the pulse (which was beyond the capabilities of the input source used) the power compression ratio and efficiency can be increased to 18.7 and 65%, respectively.

a)

b)

Figure 8. Pulse compression in the helically corrugated waveguide: a) experimental results; b) simulation results.


113

For a helical compressor the optimum negative frequency sweep can quite naturally be realized at the falling edge of a relativistic BWO pulse. For example, if a BWO generates hundreds of MW during 50 ns over a voltage drop from 700 kV to 400 kV, this frequency modulated radiation can be compressed up to 10-20 times in power with efficiency higher than 50%. In addition, because of its reflection-less properties a helical compressor can be used effectively at the output of a powerful amplifier. A favourable wave dispersion can be also synthesized for higher-order modes resulting in an increase of the helical waveguide diameter by 1.5-2 times (without significant overlapping of the coupling bands) and correspondingly in an enhancement of its rf breakdown strength. A combination of a moderately relativistic BWO or TWT with a helical waveguide compressor may result in a multi-gigawatt short-pulse microwave source which is attractive for a number of applications including radars and plasma chemistry. A design based on detailed numerical simulations of a relativistic BWO capable of generating a frequency-modulated pulse to be compressed is currently under development.

4.

CONCLUSION

The helical corrugation of the inner surface of an oversized circular waveguide that resonantly couples two circularly polarized partial modes having significantly different group velocities provides an eigenwave with a very flexible dispersion characteristic. This eigenwave is advantageous for use both in broadband gyrotron-type devices and in frequency-modulated pulse compressors.

5.

ACKNOWLEDGEMENTS

This work was supported by the Presidium of Russian Academy of Sciences and the Russian Foundation for Basic Research under grants 01-0216780 and 04-02-16698 and EPSRC, UK.

114

6.


REFERENCES

1. Kovalev N. F., Orlova I. M., Petelin M. I. Wave transformation in multimode waveguide with corrugated walls, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11 (5), 783-786 (1968). 2. Thumm M. Modes and Mode Conversion in Microwave Devices, in Generation and Application of High Power Microwaves, Proc. of 48th Scottish Universities Summer School in Physics, St Andrews, R. A. Cairns and A.D.R. Phelps Eds.: Institute of Physics Publishing, 1996. 3. Bratman V.L., Cross A.W., Denisov G.G., He W., Phelps A.D.R., Ronald K., Samsonov S.V., Whyte C.G. and Young A.R., High-Gain Wide-Band Gyrotron Traveling Wave Amplifier with a Helically Corrugated Waveguide, Phys. Rev. Letts., 84 (12) 2746-2749 (2000). 4. Bratman V.L., Cross A.W., Denisov G.G., Glyavin M.Yu., He W., Luchinin A.G., Lygin V.K., Manuilov V.N., Phelps A.D.R., Samsonov S.V., Thumm M., Volkov A.B. Broadband Gyro-TWTs and Gyro-BWOs with Helically Rippled Waveguides. Proc. 5th Int. Workshop Strong Microwaves in Plasmas, A.G. Litvak Ed., Nizhny Novgorod, Russia, 2002, pp. 46-57. 5. Samsonov S.V., Denisov G.G., Bratman V.L., Bogdashov A.A., Glyavin M.Yu., Luchinin G.A., Lygin V.K., Thumm M., Frequency-Tunable CW Gyro-BWO with a Helically Rippled Operating Waveguide, IEEE Trans. on Plasma Sci. (Special Issue on High Power Microwave Generation), June 2004 (to be published). 6. Samsonov S.V., Phelps A.D.R., Bratman V.L., Burt G., Denisov G.G., Cross A.W., Ronald K., He W. and Yin H. Compression of frequency modulated pulses using helically corrugated waveguides and its potential for generating multi-gigawatt RF radiation, Phys. Rev. Letts., 92, 118301 (2004). 7. Samsonov S.V., Bratman V.L., Denisov G.G., Kolganov N.G., Manuilov V.N., Ofitserov M.M., Volkov A.B., Cross A.W., He W., Phelps A.D.R., Ronald K., Whyte C.G., Young A.R. Frequency-broadband gyro-devices operating with eigenwaves of helically grooved waveguides, Proc. 12th Symp. on High Current electronics, Tomsk, Russia, 24-29 Sept. 2000, G. Mesyats, B. Kovalchuk, and G.Remnev Eds., pp. 403-407. 8. Rhee M.J., Destler W.W. Relativistic electron dynamics in a cusped magnetic field. Phys. of Fluids, 17 (8) 1574-1581 (1974). 9. Bykov Yu., Eremeev A., Glyavin M., Kholoptsev V., Luchinin A., Plotnikov I., Denisov G., Bogdashev A., Kalynova G., Semenov V., and Zharova 24 - 84 GHz Gyrotron Systems for Technological Microwave Applications, IEEE Trans. on Plasma Science, 32 (1) 67-72 (2004). 10. E. Hecht, Optics. New York: Benjamin Cummings, 2002, 4th Ed. 11. R.A. Bromley, B.E. Callan, Use of waveguide dispersive line in an f.m. pulse-compression system, Proc. IEE 114 (9) 1213-1218, (1967).

QUASI-OPTICAL TRANSMISSION LINES AT CIEMAT AND AT GPI

Á. Fernández1, K. Likin2, G. Batanov3, L Kolik3, A. Petrov3, K. Sarksyan3, N. Kharchev3, W. Kasparek4, R. Martín1 1

EURATOM-Ciemat Association for Fusion, Avda. Complutense, 22, 28040 Madrid (Spain) Present address. University of Wisconsin, Madison, Wisconsin (USA) Institute of General Physics, Russian Academy of Sciences, Moscow (Russia) 4 Institute of Plasma Research, University of Stuttgart, Stuttgart (Germany) 2 3

1. INTRODUCTION The Electron Cyclotron Resonance Heating (ECRH) method has proven to be a highly efficient tool for plasma breakdown, localized heating, current drive, MHD activity control, stabilization of Neoclassical Tearing Modes (NTM), etc, in plasmas confined by a strong magnetic field. Moreover, the relative simplicity of the launching systems and the big progress in the development of powerful microwave sources and high power transmission systems made this heating method very attractive for many fusion experiments [1, 2]. To get the maximum efficiency in the absorption of the electron cyclotron (EC) waves, the microwave beam must conform to the following. (1) be launched into a plasma in the right direction with respect to the magnetic field; (2) have an appropriate wave polarization; (3) have a wave pattern with a maximum along its axis and low side lobes; and (4) be focused on a plasma axis. The output wave beam parameters and the total efficiency strongly depend on the launching antenna and on the transmission line. At a high power level (hundred’s of kW), oversized waveguides, and/or large mirrors must be used in order to avoid arcing inside a line and on an antenna. This entails some general requirements in the transmission systems: - the main mode must have low ohmic losses along the line and, in the case of a mirror line, low diffraction losses; - high mode purity: small conversions of the main mode into other modes, i.e. the conservation of wave polarization and intensity distribution;


116

Á. Fernández, et. al.

-

the microwave power should not cause any arcing inside the transmission line; - the beam must have a fixed polarization at the output of the transmission line; and - elements for measuring and monitoring the forward and reverse power should be compatible with operation at high power. All of these requirements are easily fulfilled using quasi-optical transmission lines. Quasi-optical lines operating with the main mode (TEM00) have the following advantages: - the wave pattern has one central lobe along the beam axis; - the wave beam can be easily focused in the plasma center, and focusing is important in the cases of small and medium cross-section sizes of the plasma column; - the incident angle of the beam can easily be varied; and - the wave polarization can be changed, and any polarization of the wave can be achieved, by means of two corrugated mirrors with different corrugation depths. As compared to corrugated oversized waveguides, quasi-optical lines have some disadvantages; one of them is the relative large cross-section that implies more occupied room. Hybrid lines, i.e. a combination of waveguides and mirrors, can be a solution when there is not enough room available around the launching port. This paper describes the main parameters of the components of the quasi-optical and hybrid transmission lines, which are used for ECRH and Electron Cyclotron Current Drive (ECCD) experiments in the TJ-II stellarator at CIEMAT in Madrid (Spain) and in the L-2M stellarator at the General Physics Institute (GPI) in Moscow (Russia).

2. QUASI-OPTICAL TRANSMISSION LINES AT CIEMAT The TJ-II stellarator is a mid-size four-period heliac axis device, with a major radius of R = 1.5 m and a magnetic field B |1T. It has been in operation since 1997 [3]. The magnetic field is obtained using a set of helically positioned toroidal coils, two central conductors, and two vertical field coils. By changing the currents that flow through the central conductors, a wide range of magnetic configurations can be achieved. In each configuration the plasma position, size and shape change and the ECRH system must heat in every configuration on- and off-axis without inducing any current by ECCD. In addition, it should induce currents on- and off-axis when it is required.

Q-O Transmission Lines at CIEMAT and GPI

117

In order to fulfill all the requirements two quasi-optical transmission lines have been designed to launch the millimeter wave power into the plasmas. The lines are located at two toroidal stellarator symmetric positions [4,5]. Each transmission line is fed by a gyrotron of 300 kW, 1 s pulse length at 53.2 GHz (as it corresponds to the second harmonic of the electron cyclotron frequency in the TJ-II plasmas). The tubes were designed and manufactured by GYCOM Ltd. (Nizhny Novgorod, Russia). Both lines use a set of 9 mirrors plus one movable elliptical launcher located inside the vacuum vessel. The first quasi-optical transmission line (QTL1) has 8 curved mirrors and 2 grooved plane reflectors to transmit the power from the gyrotron to the plasmas. The beam is focused by the internal mirror at plasma center with a beam waist of 9.5 mm. The beam diameter is 100 mm at the barrier window. The mirrors are aluminum, except for the internal one, which is made of stainless steel. The mirrors are fixed on mounts, which allow the alignment of the mirror orientation in two planes with micrometers. A schematic of the side view of this line can be seen in Figure 1.

TJ-II

A

B 2020mm

2495 mm 2495 mm 30º 30º

Figure 1. Side view of the first transmission line.

The gyrotron output radiation is Gaussian-like with a purity of 96%, but it is astigmatic, i.e. the wave beam cross-section is elliptical. With the first two matching mirrors, this astigmatism is corrected. This is important, on one

118


hand because the beam is axisymmetric through the rest of the line and, on the other hand, if the gyrotron must be changed, the same beam parameters can be achieved by changing only these two mirrors. The main parameters of the mirrors are summarized in the following table (Table 1). Table 1. Parameters of the first two mirrors. Dimensions in mm Mirror Focal distance in incidence plane Focal distance in perpendicular plane Mirror size in the incidence plane Mirror size in perpendicular plane

1 Hyperbolic -1904.4 1075.2 411.0 186.0

2 Ellipsoidal 714.7 1626.1 478.0 338.0

The distance between mirrors, the beam waists position, and the beam size on the mirrors are shown in Table 2. The gyrotron window is the reference plane and the distance between the window and the first mirror is 700 mm. The beam waists in vertical and horizontal planes are not located at the window: as Table 1 shows, in vertical plane the waist is wo=18.14 mm placed 12.3 mm inside the gyrotron, and in horizontal plane wo=23.15 mm placed 179.6 mm outside the gyrotron. After the second mirror, the beam cross-section is circular. Table 2. Distances between mirrors, beam waists position and beam size on the mirrors. All the dimensions are in mm. The distances are positive in the propagation direction

Nr.

1

Distance between mirrors 700.0

2

400.0

3 4 5 6 7 8 9 10 P

3188.4 800.0 3188.4 800.0 3988.4 1249.0 2020.0 1535.0 272.0

w0in

18.14 23.15 48.0 18.0 59.8 59.8 59.8 59.8 59.8 83.9 27.6 30.1 9.5

Distance w0inmirror

712.3 520.4 1861.7 831.1 1196.1 1993.5 1194.9 1992.4 1996.0 729.4 777.4 711.8

wmirror

w0out

72.7 46.5 84.5

48.0 18.0 59.8

Distance w0outmirror -1461.7 -431.1 1992.3

69.7 84.6 69.7 84.5 84.6 85.3 57.6 52.0

59.8 59.8 59.8 59.8 83.9 27.6 30.1 9.5

-1193.5 1993.5 -1192.4 1992.4 519.6 1242.6 823.2 272.0


119

In general, to heat the plasmas by EC waves at the second harmonic, an elliptical polarization is required. Since the output radiation of the gyrotron has a linear polarization, it is necessary to incorporate polarizers for choosing the optimal polarization. Two corrugated mirrors, an elliptical polarizer, and a twister are set in positions 3 and 5. The first receives the required elliptical polarization and the second one rotates the polarization plane. To avoid arcing at high-power level, the corrugations have a sinusoidal shape. This groove shape is very important in determining the polarizer’s performance. The groove profile of each mirror is given in Table 3. Table 3. Groove shape. Dimensions in mm

Polarizer Elliptical polarizer (3) Twister (5)

Amplitude 0.738 1.065

Period 3.381 3.381

It is very important to be aware of the power being delivered into the plasma in each discharge. To measure a fraction of the forward and reverse power, two mirrors with an integrated directional coupler have been designed. One of these mirrors is installed at the beginning of the line to measure the output power from the gyrotron. The other mirror, the 9th, i.e. the nearest mirror to the vacuum vessel, measures the power at the end of the line. Thus, the transmission losses can be estimated. In Figure 2, a schematic drawing of the structure can be seen.

T=1.5 mm

Mirror surface

Array of holes

Rectangular waveguide

a=3.98 mm

a=4.78 mm WR-19 Figure 2. Schematic drawing of the mirror with coupling holes.

120


A small amount of the microwave power impinging on the mirror is coupled into a rectangular waveguide. The width of the rectangular waveguide is chosen so that the propagation constant is equal to the wave vector for the incidence angle [6]. Using a taper, the dimension is increased until it reaches the standard WR-19. To improve the radiation pattern, i.e. to get low side lobes and a narrow antenna pattern, the diameter of the holes is varied to produce a truncated Gaussian taper of the coupling efficiency. Owing to the symmetric design the device works as bi-directional coupler, i.e. it is also possible to detect and measure the radiation reflected from the plasma. Once calibrated, the power during each shot can be measured. Calorimetric measurements with a cylindrical water load are also carried out in both lines. With a movable mirror placed after the second mirror and with an additional fixed mirror, the beam is diverted to the load. In Figure 3, the position of the load and the mirrors are shown. The load is 2 m long and its internal diameter is 80 mm. The beam waist diameter at the aperture is 26.3 mm. In a single pulse operation, the maximum gyrotron pulse length is 100 ms. T o co n trol u nit

W ater lo ad

G yro tro n

Figure 3. Cylindrical water load and movable mirror.

The losses along the first transmission line are quite reasonable-approximately 8%, and the beam distortion is negligible. Table 4 shows the second transmission line has 10 mirrors and includes a movable mirror inside the vacuum vessel. The power is launched through the lateral port A6. The beam is focused at plasma center and in the absence of any plasma, the waist is about 9.5 mm, as in QTL1. The polarization is linear along the line and the polarization plane can be changed by means of the first corrugated mirror.


121

Table 4. Parameters of the second line. All values are given in mm

Distance between Nr mirrors 1 2 3 4 5 6 7 8 9 10

700 400 4200 400 4200 400 4200 2865 3000 1535

Mirror Mirror size Curvature Curvature size in in radius in radius in vertical horizontal vertical horizontal plane plane plane plane 329 172 f f 294 376 1682 1430 527 304 4383 f 462 360 1730 f 397 348 1781 f 460 296 4060 f 281 432 1515 2469 456 323 2821 1301 261 185 1965 982 188 168 504 393

wo_vert wo_hor 18.08 43.0 45.41

25.03 38.0 35.8 41.6

45.6 28.5 39.9 30.2 9.5

26.2 40.3 29.3 9.5

The layout of Mirror 10 inside the vacuum vessel in the QTL1 sector is shown in Figure 4. In QTL2, the mirror is located in the upper port due to the helical axis of the TJ-II plasmas. The parameters of both internal mirrors are identical and at a fixed launching angle, both beams have the same waist (9.5 mm) on the magnetic axis. The launching angle can be changed in both toroidal and poloidal directions with a flexibility of M=r20º in the toroidal direction, and 0º

@

exp>i( T 0 r cos T 0 )@, r 1, T 0 >0 ,2S @, a W c 0 0 Wc 0 ˆ Here E exp( iZc t )( E xc iE yc ) / E Ac 0 is the normalised electron velocity, a 2eAc mcZc E Ac 30 J m 1 R0 Z c c , ] c z cE Ac 0 Z c c , W c t cE Ac 20 Z c 2 ,

E

' 2( Z Hc Z c ) Z c E Ac 20 is the detuning of the cyclotron frequency in the commoving frame from the cut-off frequency and G is the parameter proportional to electron current, R0 is injection radius of the hollow electron beam. The function f ( ] c ) describes the axial distribution of the electron

134

Ginzburg, Yalandin, Korovin, Rostov, Phelps

density. The initial conditions are written under the assumption that in the initial state the electrons are distributed uniformly in cyclotron rotation phases, aside from small fluctuations assigned by parameter r. 0.010

P

'

'

0.005

'

0.000 0

10

20

30

W

Figure 1. Pulses of cyclotron SR for different parameter ' that characterizes detuning from group synchronism regime.

Temporal evolution of the radiation power P Re a wa* w] for different values of the detuning parameter ' is presented in Fig. 1 for the parameters corresponding to the experimental values6: operating mode TE21, waveguide radius R=0.5cm, beam injection radius R0=0.2cm, pitch factor g E A E|| ~ 1 , total current I=200A, particle energy 200 keV, pulse length b b c J || 7 cm. The radi5ated field has the form of a short pulse with typical duration about several reciprocal gains. The maximum growth rate and maximum pulse amplitude are achieved at the grazing condition ' 0 . The estimated duration of SR pulse amounts to 300 ps for the peak power level of about 8 MW. Detuning from the group synchronism regime leads to the gain and the SR pulse peak power decreasing. The experiments on the observation of cyclotron SR6 were carried out based on the sub-nanosecond high current accelerator RADAN 30315 , which generated a single 200 keV, 200A electron bunch with duration 300-500 ps. The transverse velocity was imparted to the electrons by the kicker (system with strongly inhomogeneous magnetic field). SR pulses were observed in the two regions corresponding to the grazing regime with TE21 and TE11 modes. An oscilloscope trace of the cyclotron SR pulses in group synchronism with TE21 mode is presented in Fig. 2a. In the experiments, the maximal peak power of the 40 GHz SR pulses was 400 kW for a pulse duration of about 400ps (i.e. of the order of 10 cyclotron oscillations). We should emphasise the dramatic reduction of the peak power and gain for the detuning from group synchronism regime by the varying of the guide magnetic field (Fig. 2b). It is connected with the longitudinal dynamics of the

Superadiance of Intense Electron Bunches

135

real electron bunch caused by the Coulomb repulsion and dispersion of the initial electrons’ velocities. In the exact group synchronism regime, when in the moving frame the radiation frequency tends to the cut-off frequency, with waveguide wavelength O c tending to infinity, this results in the longitudinal displacement of the electrons being less significant. As we increase the magnetic field and go away from the cut-off frequency O c falls and the same displacement can strongly reduce the radiation. Practically the entire microwave signal disappeared when the magnetic field detuned from the group synchronism condition. 1.0

a)

P/Pmax

b)

0.8 0.6 0.4

1 ns 0.2

400 kW 0.0 11

12

13

H, kOe

Figure 2. (a) An Oscilloscope trace of cyclotron SR pulse. (b) Experimental dependence of peak power on guide magnetic field.

3.

CHERENKOV SUPERRADIANCE

The Cherenkov SR pulses can be produced by a bunch of electrons moving along rectilinear trajectories in slow wave structures (SWS). Two varieties of Cherenkov SR have been studied. The first one is associated with the interaction with the forward propagating wave under synchronism (4) Z hV||0 . where Z and h are the frequency and longitudinal wave number respectively. Such an interaction can be realized in the dielectric loaded waveguide. The second type of Cherenkov SR studied occurs in the case of interaction with the slow spatial harmonic of the backward wave in periodically corrugated waveguide under synchronism condition (4), where h h0 h , h0 is the longitudinal wave number of the fundamental harmonic, h 2S d , d is the corrugation period. For the both cases the longitudinal component of the electric field of the synchronous wave can be presented in the form E z Re>E A rA A z ,t expiZt ihz @ ,

136

Ginzburg, Yalandin, Korovin, Rostov, Phelps

where E A rA is the transverse profile of synchronous field component,

A z ,t is the slow varied complex amplitude. Under the assumption of a small variation of particles’ velocity the radiation of the electron bunch can be described by the equations 3/ 2 ° ª wT º ½° iT ® «1 Q ¾ F ] Re a e w] »¼ ° °¯ ¬ ¿ , 1 2S iT wa wa r B F ] f W ³ e dT 0 S 0 wW w]

w 2T w] 2

>

@

(5)

where the upper and lower signs correspond to the interaction with the forward and backward wave, respectively. Here we use the following dimensionless variables ZC( t z / V||0 ) eAEA rb ZCz , a W , , ] V C 2 J 03V0 mZ0 1 r V||0 / Vgr 0

T Zt hz is the phase of an individual particle with respect to the field of the synchronous harmonic, V gr is the group velocity of electromagnetic wave,

J0

1 E

1 / 2

||0

,Q

2J 02 C . C

§ eI b Z ¨ ¨ 2 mc 2J 3 0 ©

· ¸ ¸ ¹

1/ 3

,

2 is the Pierce parameter, Z { 2 E A rb k 2 N is the coupling impedance, N

is the waveguide norm, I b is the electron bunch current, rb is the electron injection radius. The function F ] defines the longitudinal profile of the wave coupling impedance (tapered, for example, by varying the corrugation L

depth). This function is normalised as 1 L ³ F ] d]

1 , where L

ZCl V0

0

is the dimensionless length of the interaction space. The function f ( W ) describes the current pulse profile. Below we assume that electron density is constant ( f W 1, W >0 ,T @ ) within dimensionless bunch duration Tbunch

Z0 C 1 r V0 / V gr

't b

apart from small initial density perturbations at the system entrance:

Superadiance of Intense Electron Bunches

T]

~

0

137

~

T 0 J cos T 0 , J 1, T 0 >0 , 2S , wT / w]

] 0

0.

(6)

These perturbations initiate the development of SR emission. For uniform SWS: F ] 1 formation of a short superradiance pulse is shown in Fig.3a and Fig.3b for forward and backward wave propagation respectively. This process is caused by electron bunching and slippage of the wave with respect to the electrons due to the difference between the wave group velocity and the electron longitudinal velocity.

Figure 3. Formation of a short superradiance pulse for forward (a) and backward (b) wave propagation.

The distinctive feature of superradiance is the linear dependence of peak power on the square of the number of radiating particles1, 2. For backward wave interaction the dependence of the SR pulse amplitude on the electron pulse duration is shown in Fig.4 for the constant beam current, Q 0.2 . The peak amplitude is proportional to the electron pulse duration until this duration is rather short T6, and electron pulse becomes too long to provide coherent radiation from all particles over the pulse length. A similar dependence takes place for SR in the forward wave. For a rather long electron bunch, the “multi-spikes” generation regime is realised because the various parts of a bunch radiate almost independently. In the case of the backward wave interaction, such a regime is similar to the self-modulation regime in the BWO driven by the quasi-stationary electron beam16. In the case of interaction with the forward wave such a regime is refereed to as self-amplified spontaneous emission (SASE)2 .

138

Ginzburg, Yalandin, Korovin, Rostov, Phelps 4

|a|

2

T bunch

0

0

2

4

6

8

Figure 4. Dependence of SR pulse amplitude on the electron pulse duration for the constant beam current.

It is important to note that in certain conditions the SR pulse peak power can substantially exceed the power of the electron beam because a short SR pulse that forms in the initial stage of the interaction can accumulate energy from different fractions of the extended electron bunch. This fact does not contradict the energy conservation law because the SR pulse total energy is still smaller than the total beam kinetic energy. Let us introduce the power conversion factor as the ratio of the SR pulse peak power to the electron beam power:

Ȁ

J 0 1

2

Q a max

. 8 In the case of “forward” Cherenkov SR in the uniform SWS, the conversion coefficient can essentially exceed a factor of one if the interaction distance is rather long L !! 1 and normalised electron bunch duration: Tbunch | L . The evolution of SR pulse in this case is shown in Fig.5. After formation of a SR pulse at the initial stage of interaction, its trailing edge is fed by the subsequent fresh electron fractions with small (noise level) modulation. In the given case, conversion factor achieves 3 and can increase further with increasing interaction distance. In the case of “backward” Cherenkov SR in a uniform SWS the conversion factor KEr, t W u H r, t @ zˆ dx dy` d t

R EH z ,W

(7)

f

Note that for finite energy signals, the total energy carried by the electromagnetic field is given by W z R EH z ,0 . According to the Wiener-Khinchine theorem, the spectral density function of the electromagnetic signal energy S EH z , f is related to the Fourier transform of the cross-correlation function R EH z ,W through the Fourier transformation: S EH z , f

f

j 2S f W d W ³ R EH z ,W e

f

>

@

³³ Er , f u H r , f zˆ dx dy (8) ~ 1 ~ ˆ u ! E r , f H r , f z dx dy f 0 °° 4 ³³ ®1 ~

~ ° ³³ Er , f u H r , f zˆ dx dy f 0 ¯° 4 Following Parseval theorem, the total energy carried by the electromagnetic field can also be calculated by integrating the spectral density S EH z, f over the entire frequency domain:

>

>

W z

f

³ S EH z, f d f

f

f ª 1

^~

@ @

~

`

@

`

º

³ « ³³ Re Er, f u H r, f zˆ dx dy » df ¼ 0 ¬2

(9)

We identify:

^>

d W z 1 ~ ~ Re ³³ Er, f u H r, f zˆ dx dy (10) 2 df as the spectral energy distribution of the electromagnetic field (over positive frequencies).

258

4.

Y.Pinhasi, Yu.Lurie,A.Yahalom

MODAL PRESENTATION OF ELECTROMAGNETIC FIELD IN THE FREQUENCY DOMAIN

The “phasor like” quantities defined in (4) can be expanded in terms of transverse eigenmodes of the medium in which the field is excited and propagates [3]-[5]. The perpendicular component of the electric and magnetic fields are given in any cross-section as a linear superposition of a complete set of transverse eigenmodes: j k zq z j k zq z º ~ ~ ª E A r , f ¦ «C q z , f e C q z , f e »¼ Eq A x, y q¬ (11) j k zq z j k zq z º ~ ~ ª H A r , f ¦ «C q z , f e H x , y C q z, f e q A »¼ q¬ C q z , f and C q z , f are scalar amplitudes of the qth forward and ~ backward modes respectively with electric field Eq A x, y and magnetic ~ field H q A x, y profiles and axial wavenumber: 2 2 k ! k A q (propagating modes) ° k kA q k zq ® (12) ° j kA q 2 k 2 k k A q (cut - off modes) ¯ Expressions for the longitudinal component of the electric and magnetic fields are obtained after substituting the modal representation (11) of the fields into Maxwell's equations, where source of electric current density ~ J r, f is introduced: j k zq z j k zq z º ~ ~ ª E z r , f ¦ «C q z , f e C q z , f e »¼ Eq z x, y ¬ q

1 ~ J z r, f j 2S f H 0

(13)

j k zq z j k zq z º ~ ~ ª H z r, f ¦ «C q z, f e C q z, f e »¼ H q z x, y ¬ q

The evolution of the amplitudes of the excited modes is described by a set of coupled differential equations:

259

Space-frequency model of ultra wide-band interactions d C r q z , f dz

(14) º ·~ 1 B j k zq z ª«§¨ Z q ¸ J r, f r zˆ J~ r, f » E~ x, y dx dy e ³³ ¨ z q A Nq » « Z q ¸¹ ¼ ¬© The normalization of the field amplitudes of each mode is made via each mode's complex Poynting vector power: ~ ~ N q ³³ Eq A x, y u H q A x, y zˆ dx dy (15) B

>

@

and the mode impedance is given by: P0 k 2S f P 0 ° k zq ° H k Zq ® 0 zq k zq ° P0 k z q ° H0 k 2S f H 0 ¯

for TE modes

(16) for TM modes

Substituting the expansion (11) in (10) results in an expression for the spectral energy distribution of the electromagnetic field (over positive frequencies) as a sum of energy spectrum of the excited modes: 2 2º d W z 1ª C q z, f C q z , f » Re N q ¦ « df 2¬ ¼ q

^ `

Propagating

¦ q Cut - off

5.

^

` ^ `

Im C q z, f C q z , f Im N q

(17)

THE ELECTRON BEAM DYNAMICS

The state of the particle i is described by a six-component vector, which consists of the particle's position coordinates ri xi , yi , z i and velocity vector v i . The velocity of each particle, in the presence of electric Er, t and magnetic Br , t P 0 H r , t fields, is found from the Lorentz force equation: ½ d vi 1 ° e 1 >Eri , t v i u Bri , t @ v i d J i °¾ (18) ® J i °¯ m v z i dz ° dz ¿ where e and m are the electron charge and mass respectively. The fields represent the total (DC and AC) forces operating on the particle, and include


260

also the self-field due to space-charge. The Lorentz relativistic factor J i of each particle is found from the equation for kinetic energy: dJi 1 e v i Eri , t (19) 2 dz m c v zi where c is the velocity of light. The time it takes a particle to arrive at a position z, is a function of the time t0i when the particle entered at z=0, and its instantaneous longitudinal velocity v z i z along the path of motion: z

ti z t 0i ³

1

0 v z i z '

d z'

(20)

The current distribution is determined by the position and the velocity of the particles in the beam: Q N§ v · J r, t ¦ ¨ i ¸ G x xi G y yi G >t ti z @ (21) N i 1¨ v zi ¸ ¹ © Here Q I 0 T is the total charge of the e-beam pulse with DC current I 0 and temporal duration T. The “phasor like” current density is given by: f ~ J r, f 2 u f ³ J r, t e j 2S f t d t f

Q N § v 2 u f ¦ ¨ i N i 1¨ v z i ©

6.

· ¸ G x x G y y e j 2S f t i z i i ¸ ¹

(22)

SPONTANEOUS EMISSION

Random electron distribution in the e-beam cause fluctuations in current density, identified as shot noise in the beam current [6]-[11]. Electrons passing through a magnetic undulator emit a partially coherent radiation, which is called undulator synchrotron radiation. The electromagnetic fields excited by each electron add incoherently, resulting in a spontaneous emission with generated power spectral density [12]: d Psp Lw §1 · W sp Psp Lw sinc 2 ¨ T Lw ¸ (23) df ©2 ¹

261

Space-frequency model of ultra wide-band interactions

where Psp Lw is the expected value of the spontaneous emission power, Lw Lw is the slippage time and: vz0 vg

W sp

T

Z vz0

k z k w

(24)

is the detuning parameter. The spontaneous emission null-to-null bandwidth is approximately 2 W sp | 2 f 0 N w . In a FEL, utilizing a magneto-static planar wiggler, the total power of the spontaneous emission is given by [12]: Psp Lw

where a w

1 e I0 8 W sp

2

§ aw · Z ¨¨ ¸¸ Lw 2 © J E z 0 ¹ Aem

(25)

e Bw is the wiggler parameter and kw m c 2

Aem

~ ³³ Eq x, y dx dy

(26)

2 ~ Eq 0,0

is the effective area of the excited mode. The spontaneous emission power is proportional to e I 0 , where I 0 is the DC beam current. In the low gain limit, the spontaneous emission power grows as the square of interaction length Lw . Analytical and numerical calculations of the spontaneous emission power spectral density of the FEM are shown in Fig.3. (b) dPsp(Lw) / d f [PW/GHz]

dPsp(Lw) / d f [PW/GHz]

(a) 15

8

6

10

4

2

0

20

40

60

80

f [GHz]

100

120

5

0 20

30

40

50

60

70

80

f [GHz]

Figure 3. Spectrum of spontaneous emission for beam energy of: (a) Ek=1.375 MeV and (b) Ek|1.066 MeV (grazing). Analytical calculations (solid line) and numerical simulation (dashed line).


262

Figure 4. Evolution of spontaneous emission: (a) spectrum and (b) power along the wiggler. The beam energy is Ek=1.375 MeV.

In high-gain FELs, utilizing sufficiently long undulators, the spontaneous emission radiation excited in the first part of the undulator is amplified along the reminder of the interaction region resulting in synchrotron-amplified spontaneous emission (SASE). The evolution of SASE power along the wiggler when the beam energy is set to Ek=1.375 MeV is shown in Fig.4. Lowering the energy to Ek=1.066 MeV (grazing case) results in the SASE power shown in Fig.5.

7.

SUPER-RADIANCE

When the electron beam is modulated or pre-bunched, the fields excited by the electrons become correlated, and coherent summation of radiation fields from

Figure 5. Evolution of spontaneous emission: (a) spectrum and (b) power along the wiggler at grazing Ek|1.066 MeV).


263

individual particles occurs. If all electrons radiate in phase with each other, the generated radiation becomes coherent and is termed super-radiant emission [13]-[24]. The power spectrum of the super-radiant emission is related to the spontaneous emission spectrum by [12]: 2 ~ d Psr Lw I f d Psp Lw (27) ~ df df e I 0 ~ where I f is the Fourier transform of the electron-beam current. The energy spectral density of the super-radiant power radiated by a single bunch with a temporal Gaussian shape is: 2 d Wsr Lw · §1 k W sp T Psp Lw e 2S T f sinc 2 ¨ T Lw ¸ (28) df ¹ ©2 where k Q is the expected number of electrons in the bunch of total e charge Q I 0 T . In the case of an ultra short bunch, with duration much shorter than the period of the radiation field ( T f 1 ), the total energy of the super-radiant emission is: 1 Q2 8 W sp

2

§ aw · Z 2 ¸ ¨ (29) ¨ J E ¸ A Lw z0 ¹ em © The super-radiance energy is proportional to the square of the total charge Q of the bunch and to the square of the interaction length Lw. The calculated spectral density of energy flux in the case of two wellseparated solutions is shown in Fig.6a. The spectrum peaks at the two synchronism frequencies with main lobe bandwidths of ' f1,2 | 1 , Wsr Lw

W sp1,2

where W sp1, 2 are the slippage times. The corresponding temporal wavepacket (shown in Fig.6b) consists of two “slow” and “fast” pulses with durations equal to the slippage times that modulate carriers at their respective synchronism frequencies. The spectral bandwidth in the case of grazing shown in Fig.7a, is determined by dispersive effects of the waveguide taking into account by the simulation. The corresponding temporal wavepacket is shown in Fig.7b. In the case of a continuous sinusoidal modulated current (pre-bunched beam): i t I 0 >1 m cos2S f 0 t @ (30) at frequency f 0 and modulation depth m, the power of the super-radiant emission:


264 (a)

(b)

10

f = 100 GHz f = 29 GHz

5

Ex [kV/m]

dW(Lw) / df [pJ/GHz]

60

40

0

20 -5

0 20

40

60

80

100

-10

120

2.9

3.1

3.3

f [GHz]

3.5

3.7

3.9

t [nS]

Figure 6. Super-radiant emission from a short T=1 pS electron bunch (T f0=0.1 at Ek=1.375 MeV): (a) Energy spectrum (analytic calculation and numerical simulation results are shown by solid and dashed lines, respectively) and (b) temporal wave packet.

m2 I0 §1 · (31) W sp Psp Lw sinc 2 ¨ T f 0 Lw ¸ 4 e 2 © ¹ Fig.8 shows the super-radiant power as a function of prebunching frequency f0 for various modulation levels. A comparison is made with simulation results. Super-radiant power emitted by an infinite series of ultra short bunches (impulses) is also shown. In this case the current can be expanded in a Fourier series: f f ª § 2S ·º i t ¦ I 0 T G t n T I 0 «1 2 ¦ cos¨ n t ¸» (32) © T ¹¼» n f n f ¬« Psr Lw

The resulting spectrum of super-radiant emission contains all harmonics of the prebunching frequency f 0 1 each having a sinusoidal current T modulation with modulation index m=2. Fig.8 shows a curve of the superradiant power (a)

(b)

20

60

10

Ex [kV/m]

dW(Lw) / df [pJ/GHz]

80

40

20

0

-10

0

20

30

40

50

f [GHz]

60

70

80

-20

2.9

3.0

3.1

3.2

t [nS]

Figure 7. That of Fig.6, but at grazing (Ek|1.066 MeV).

3.3

3.4

3.5


265

Figure 8. Power spectral density of super-radiant emission from a sinusoidally modulated current and from an infinite series of ultra short bunches (impulses). Analytical calculations (solid lines) and numerical simulation results (dashed lines).

emitted by a series of impulses as a function of the fundamental modulation frequency f 0 . The discrepancy between analytical calculations and numerical simulations at high modulation levels is due to stimulated emission effects that arise in the simulations, but not taken into account in the analytical calculations (where the effect of the radiation on electrons in not considered).

8.

SPACE-FREQUENCY MODEL FOR FEL OSCILLATORS

In laser oscillators, part of the radiation excited in the gain medium is coupled-out, while the remainder is circulated by a feedback mechanism, as shown schematically in Fig.9. Assuming a uniform cross-section resonator (usually a waveguide), the total electromagnetic field at every plane z, can be expressed in the frequency domain as a sum of a set of transverse ~ (orthogonal) eigenfunctions with profiles Eq x, y and related axial wavenumber k z q f . At the beginning of a round-trip n, each of the modes is assumed to have an initial amplitude C q n 0, f and the total field at z=0 is given by: ~ ~ E n x, y , z 0; f ¦ C q n 0, f Eq x, y (33) q

The field obtained at the end of the interaction (wiggler) region z = Lw can be


266

Figure 9. Schematic illustration of FEL oscillator.

written as: ~ E n x, y, z

j k zq f L w ~ Lw ; f ¦ C q n Lw , f Eq x, y e q

(34)

Here the amplitude of the qth mode excited by a driving current density of ~ the electron beam J n x, y, z; f is found by integration of the excitation equation (14): C q n Lw , f C q n 0, f

j k zq f z 1 Lw ~ n ~ dx dy dz ³ ³³ J x, y, z; f Eq x, y e 2N q 0

(35)

The spectral density of the energy flow after the interaction with the electron beam at the nth round-trip is: d W n Lw df

¦ Cq q

n L , f 2 1 Re^N ` q w 2

(36)

After a round-trip in the resonator of length Lc, the field fed back into the entrance (z=0) of the interaction region is:

Space-frequency model of ultra wide-band interactions ~ E n1 x, y, z

267

~ 0; f ¦ C q'n 0, f Eq' x, y q'

(37) º~ ª j k zq ' f Lc n ¦ « ¦ U q' q" C q" Lw , f » Eq' x, y e »¼ q ' «¬ q" U q ' q" is a complex coefficient, expressing the intermode field reflectivity of transverse mode q" to mode q', due to scattering of the resonator mirrors or any other passive elements in the entire feedback loop. Scalar multiplication ~ of both sides of Eq. (37) by Eq x, y , results in the initial mode amplitude: Cq n1 0, f ¦ U q q" Cq"n Lw , f e

j k zq" f Lc

q"

(38)

which is required in equation (35) to solve the field excited in the consecutive round-trip. In the frequency domain, the total out-coupled radiation obtained at the oscillator output after N round-trips is composed of a summation of the circulated fields (34) inside the resonator: N j k zq f Lw ~ ~ E out f ¦ ƶ q ¦ C q n Lw , f Eq x, y e q

(39)

n 0

where ƶ q is qth mode field transmission of the out-coupler. The energy spectrum of the electromagnetic radiation obtained at the output after N round-trips is given by: d Wout N df

where T q

Yq

2

N

n ¦ T q ¦ Cq Lw , f q

2

n 0

^ `

1 Re N q 2

(40)

is the power transmission coefficient of mode q.

To simplify the analysis, we assume excitation of a single transverse mode. The power spectral density of the spontaneous emission out-coupled power is described by [26]: out d Psp

df

T

1- R 2 4

§1 · R sin 2 ¨ k z Lc ¸ 2 © ¹

d Psp Lw df 2

(41)

where Lc is the resonator (round-trip) length, R U is the total round-trip power reflectivity and T is the power transmission of the out-coupler. The maximum transmission of the Fabry-Perot resonator [25] occurs when


268

k z Lc 2mS (where m is an integer), which defines the resonant frequencies of the longitudinal modes. The free-spectral range (FSR) is the inter-mode frequency separation given by: vg 1 dZ 1 >k z f m1 k z f m @ FSR (42) Lc t r 2S d k z

where v g

dZ d kz

is the group velocity of the radiation and tr is its round-

trip time. The transmission peak is

T

1- R 2

with full-width half-

maximum (FWHM) bandwidth of: FWHM

where F

FSR F

(43)

S4R

is the Finesse of the resonator. 1 R The noise equivalent bandwidth is the bandwidth of an ideal band-pass filter producing the same noise power at its output. The spectral line-shape of the power density of the equivalent band-limited noise at the system's output is uniform within the noise equivalent bandwidth. The noise equivalent bandwidth of a single resonant longitudinal mode is B

S

S

FWHM

FSR . Consequently, the spontaneous emission power 2 2F of longitudinal mode m is: d Psp Lw T out m Psp B (44) 2 df 1- R fm

Since the typical bandwidth of sinc 2 W sp f

is

1

W sp , the number of

longitudinal modes within the spontaneous emission bandwidth is

1

1

W sp FSR

.

Thus the total spontaneous emission measured at the output of the resonator will be: 1 1 1 d Psp Lw T out out S Psp m # Psp 2F 1- R 2 W sp W sp FSR df fm (45) 1 T 1 T S Psp Lw Psp Lw 2F 1- R 2 2 4 R 1- R 2

269


9.

RADIATION BUILDUP IN A FEL OSCILLATOR

In the presence of electron beam, the radiation circulating in the resonator is re-amplified in the interaction region at each round-trip. At the first stage of the oscillator self-excitation, the synchrotron undulator radiation emitted by the individual electrons entering the interaction region at random, interferes and combines coherently with the circulating field in the resonator. If the single-pass gain is higher than the total resonator losses (transmission and internal losses), the radiation intensity inside the resonator increases and becomes more coherent. After several round-trips the radiation power is built-up in the linear regime until the oscillator arrives to its nonlinear stage of operation and to saturation. The space-frequency numerical simulation WB3D was employed to demonstrate the development of the radiation, generated in a millimeter wave FEM oscillator. The spectrum of the output power after several radiation round-trips is shown in Fig.10a and the total energy buildup is described in Fig.10b for beam energy of Ek=1.375 MeV. The grazing case is described in Fig.11. 0.8

0.6

0.6

Pout [W]

dPout / df (Lw) [kW/GHz]

(a) 0.8

0.4

0.2

(b)

0.4

0.2

0.0

92

94

96

98

100

102

104

0.0

106

0

50

f [GHz]

100

150

200

Round-trip number

Figure 10. (a) Oscillator output power spectra and (b) total energy buildup in the FEM oscillator when Ek=1.375 MeV. (b)

(a) 8

6

1.5

Pout [W]

dPout / df (Lw) [kW/GHz]

2.0

1.0

4

2

0.5

0.0

0 42

44

46

f [GHz]

48

50

52

0

20

40

Round-trip number

Figure 11. That of Fig.10, but at grazing (Ek | 1.066 MeV).

60

80

270


Acknowledgments The research was supposed by the Israel Science Foundation and the Israel Ministry of Science.

References [1] Y. Pinhasi, Yu. Lurie and A. Yahalom, Nucl. Instr. and Meth. in Phys. Res. A 475 (2001), p.147. [2] Y. Pinhasi, Yu. Lurie, A. Yahalom, and A. Abramovich, Nucl. Instr. Meth. Phys. Res. A 483 (2002), p.510. [3] N. Markuvitz and J. Schwinger, J. Appl. Phys. 22 (1951), 806. [4] L. B. Felsen, Radiation and scattering of waves (Prentice Hall, New Jerzy, 1973). [5] L. A. Vaynshteyn, Electromagnetic waves (Sovietskoye Radio, Moscow, 1957). [6] W. Schottky, Ann. Physik 57 (1918), 541. [7] S. O. Rice, Bell System Tech. J. 23 (1944), 282. [8] S. O. Rice, Bell System. Tech. J. 24 (1945), 46. [9] L. D. Smulin and H. A. Haus, Noise in Electron Devices (The Technology Press of Massachusetts Institute of Technology, 1959). [10] H. Motz, J. Applied Phys. 22 (1951), 527. [11] H. A. Haus and M. N. Islam, J. Applied Phys. 54 (1983), 4784. [12] Y. Pinhasi, and Yu. Lurie, Phys. Rev. E 65 (2002), p.026501. [13] R.H. Dicke, Phys. Rev. 93 (1954), 99. [14] R. Bonifacio, C. Pellegrini, L.M. Narducei, Optics Comm. 50 (1984), 373. [15] K.J. Kim, Phys. Rev. Lett. 57 (1986), 1871. [16] S. Krinsky, L.H. Yu, Phys. Rev. A 35 (1987), 3406. [17] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Optics Comm. 148 (1998), 383. [18] R. Bonifacio, B. W. J. McNeil, and P. Pierini, Phys. Rev. A 40 (1989), 4467. [19] N. S. Ginzburg and A. S. Sergeev, Optics Comm. 91 (1992), 140. [20] A. Gover et al., Phys. Rev. Lett. 72 (1994), 1192. [21] Y. Pinhasi and A. Gover, Nucl. Inst. and Meth. in Phys. Res. A 393 (1997), 393. [22] I. Schnitzer and A. Gover, Nucl. Inst. and Meth. in Phys. Res. A 237 (1985), 124. [23] A. Doria, R. Bartolini, J. Feinstein, G. P. Gallerano, and R. H. Pantell, IEEE J. Quantum Electron. QE-29 (1993), 1428. [24] M. Arbel, A. Abramovich, A. L. Eichenbaum, A. Gover, H. Kleinman, Y. Pinhasi, Y.Yakover, Phys. Rev. Lett. 86 (2001), 2561. [25] A. Yariv, Optical Electronics (Holt Rinehart and Winston, 1991). [26] Y. Pinhasi, Y. Lurie, A. Yahalom, Nucl. Instr. Meth. Phys. Res. A 528, (2004), p.62.

CHAPTER 3

APPLICATIONS OF QUASI-OPTICAL SYSTEMS

BI-STATIC FORWARD-SCATTER RADAR WITH SPACE-BASED TRANSMITTER

A.B. Blyakhman Nizhny Novgorod Research Radio Technical Institute

Abstract:

Keywords:

1.

A multi-positional forward-scatter radar complex is proposed, with the transmitter based on a satellite and the receiving network distributed on the ground. Such a global system would be capable to detect, track and recognize air and space objects, in particular, stealthy ones. detection of stealthy targets, global security.

INTRODUCTION

Recent works on the forward-scatter radar [1 -3] have convincingly demonstrated its main advantages: x When a target enters a zone between the transmit and receive positions, the target radar cross section (RCS) increases by factor of 103 – 104; x the target RCS in the forward-scatter zone does not depend upon the target coating (for instance, absorbing one). These advantages, compared to the conventional monostatic radar, provide much improved opportunities to detect track and identify low flying light aircrafts and helicopters, “Stealth” aircrafts, cruise missiles, hanggliders etc. However, the operation zone of the forward-scatter radar is relatively narrow. Capabilities of the radar can be expanded by using a multipositional system: a chain of bistatic links, each link forming a detection zone stretched between receiving and transmitting posts. A further upgrade of the forward-scatter radar would be using a transmitter placed in space.


274

2.

A. Blyakhman

BISTATIC SPACE-BORNE FORWARD-SCATTER RADAR

The idea of satellite-borne bistatic radar has been discussed beginning in the 80’s [4, 5]. However, recent experimental results give a firmer ground for such projects.

2.1

System Geometry

The transmitting system can be located on satellites with different orbit height. Low orbit location, evidently, will require less radiating power, but a greater number of satellites [4]. However, the organization of continuous observation over the selected territory and its prompt change gets more complicated. So, the continuous global coverage is provided for the orbits of medium height (10 000 km) with 12 satellites, and for the low heights (1 100 km) with 50 satellites. The placement on geostationary orbit provides tactical advantages and enables one to permanently observe the chosen territory. Three satellites provide global coverage, however, it requires greater radiated power. The satellites located on the geostationary orbit enjoy better survivability and can receive navigation information by an easier way than low orbit satellites. In case of geostationary deployment, the interference exerts smaller influence in comparison with lower orbits. There are other factors, which determine advantages and disadvantages of different transmitter siting heights. Simple estimations make it clear that, when a beam width of the transmitting antenna in the main orthogonal section is about 4q, the earth surface with a characteristic dimension of about 3 000 km is radiated. It helps to provide operation in the mode of forward scattering radiolocation simultaneously, with a significantly large group of ground-based receiving stations. Such beam width allows relaxing the requirements for the accurate pointing of the satellite and receiver antenna; and a narrower beam requires greater antenna dimensions and weight. From a military point of view, the most important thing is that the receiving stations are not radiating ones. In other words, they are “invisible”.

2.2

Detection Zone

The main design principles have been developed and approved for bistatic forward scattering radars [1-3]. These principles make it possible to detect, track and identify air targets. These radars use continuous quasiharmonic

Bistatic Forward-Scatter Radar….

275

radiation of the transmitter and measurement of the Doppler frequency bias and determination of the arrival direction of the wave scattered by the target at the receiving position. These principles can be used fully to develop the space-borne forward scattering system. The choice of the frequency range is determined by two factors: dependence of the target’s RCS upon diffraction angle [1] and the loss value on propagation path. Comparative analysis reveals that it is advisable to choose operating wavelength in the range of O = 0,3 – 0,4 m. We know from scientific literature (see for example [6, 7]) that at a frequency of 850 MHz (O = 35 cm) total absorption in the troposphere and in hydrometeors is from 2.5 dB to 0.2 dB, when the satellite elevation angle changes from 0q to 10q respectively. As noted above, the structure of the receiving position can be understood from the previous investigation. In particular, the receiving position may have a multibeam antenna system with the beam length of 5q – 7q and circular polarization due to the Faraday effect. To create a detection zone of the bistatic space-borne radar, we use radar equation for the two-positional system:

Q

PT GT G R O2KFT2 ( E , H )FR2 ( E , H )

4S 3 P0 rT2 rR2

u V (D v , D h ),

where: Q – signal/noise ratio PT – average power of the transmitter P0 – self-noise power of the receiver in the band of optimal processing GT ,GR – gain factors of the transmitting and receiving antennas K – generalized losses (transmission, reception, processing) V(Dv , Dh ) – bistatic RCS of the target, as a function of diffraction angle in the vertical (Dv) and horizontal (Dh) planes FT2 ( E , H ), FT2 ( E , H ) power directional pattern of the transmitting and receiving antenna rT, rf – distance from the transmitting and from the receiving systems to the target The most important features of the system in question are conditioned by bistatic RCS – V(Dv, Dh) function. Figures 1, 2 show bistatic RCS (calculated according to [1]) for a ballistic missile and its warhead as well as a “Stealth” fighter. The validity of the RCS calculation has also been demonstrated

276

A. Blyakhman

experimentally. Independence of the RCS upon the material of the object is explained in [8, 9]. The calculation proves that bistatic RCS of missiles

and “Stealth” aircraft exceeds 104m2 as a maximum and as for the warheads, this value exceeds 103m2 Estimation of the detection zones was conducted for the detection probability D t 0.9 and PT = 500 kW. Figures 3, 4 demonstrate detection zones of “Stealth” fighter (F-117A) and ballistic targets flying along a normal line to a vertical plane that pass over transmitter-receiver line. Thus, calculations demonstrate that forward scattering radar barrier has a very high power potential and provides detection of not only missiles but their warheads at the altitudes maximum possible for these targets (below radio horizon). Air objects including those produced according to “Stealth” technology may be detected simultaneously with the ballistic objects. As explained above, applying this technology to space objects will not change their detection characteristics by forward scattering barrier.

2.3

Detection and Identification Principles

Measurement of the trajectory parameters by the bistatic system with a space-borne transmitter can be carried out in a similar manner as by groundbased systems, [2, 10] since all the main principles of creating these systems are identical. Air objects tracking by ground-based forward scattering system were used in full-scale experiments [1,2]. Features connected with essentially long base-line distance and very far speed of objects can be taken into consideration. Figure 5 demonstrates results of experimental tracking of air objects. Rather high rate of data renewal (1 second and less) makes it possible to form the trajectory of the target in 3-4 seconds after it enters the area covered by the radar barrier. It is certainly, the most important advantage of the system. The bistatic forward scattering radars with quasiharmonic probing signal identify targets by the Doppler spectrum analysis of the returned signal when targets pass the barrier [3]. A two-level classification system was developed and approved in the ground-based systems, in course of the full-scale experiments. It provided identification of the 4 classes of targets with a probability of 0.7-0.8. Thus, the experiments clearly proved the possibility in principle to identify classes of targets by bistatic forward scattering radars.


277

Figure 1. RCS of an aircraft target (F-117A).

Figure 2. 1 - RCS Intercontinental Ballistic Missile (ICBM) Tepkhodon-2 as an assembly. 2- RCS of a warhead of the ICBM Tepkhodon-2.

278

A. Blyakhman

Figure 3. Detection zone of an air target (F-117A). a) Vertical section. b) Horizontal section (flight altitude - 1000m)


279

Figure 4. Detection zone of a space target (vertical section). 1 - RCS ICBM Tepkhon-2 as an assembly. 2 - RCS of a warhead of the ICBM Tepkhon-2.

3.

APPLICATIONS

As an early detection and warning boundary, the radar barrier must function uninterruptedly. The quasi-harmonic probing signal determines rather high efficiency (60-70%) of the transmitter generator. Thus, the power consumed by the transmitting system does not exceed 1 MW. Today, sources of such power may be created on the basis of a nuclear power plant with a life cycle of 7 years. Weight and dimensions of such a plant allow the whole transmitting system to be put into geostationary orbit by domestic space vehicles. It is not a problem to make a mobile ground system, which would be similar to one already tested [1]. As is shown above, a chain of sea and ground-based posts, together with one transmitting system, make it possible to form a surface radar barrier of required configuration with the range of 3 000 km. Each receiving system is able to detect, track, and identify ballistic missiles at a range of more than 6000 km, and it covers all the possible heights of missiles flying. The

280

A. Blyakhman

reduced equipment volume of the receiving post limits its power consumption to several kilowatts. The “Stealth”-technology does not limit the effectiveness of such barriers. It is fairly obvious that beam control of the transmitting system makes it possible to quickly change the area of forward scattering barriers.

Figure 5. Flight tests results of the air targets tracking. Mi-8 helicopter, flight altitude H=200m, target velocity v=44m/s. L-29 jet airplane, flight altitude H=200m, target velocity v=148m/s.


4.

281

CONCLUSION

The forward-scatter radar system with transmitter located on an artificial earth satellite on the geostationary orbit would provide a unique opportunity to detect, track, and identify both large space objects (ballistic missiles and their warheads) and small-RCS (e.g. “stealthy”) ones. Such a collective global security system might be an ideal project for international cooperation.

5.

REFERENCES

1. A.B. Blyakhman, I.A. Runova, Forward Scatter Radar: Bistatic RCS and Target Detection, Proc. IEEE Radar Conf., Waltham, USA, April 20-22, 1999, pp. 203-208. 2. A.B. Blyakhman, A.G. Ryndyk, S.B. Sidorov, Forward Scatter Radar: Moving Object Coordinate Measurement, Proc. of IEEE Int. Radar Conf., Alexandria, USA, May 7-12, 2000, pp. 678-682 3. A.B. Blyakhman, S.N. Matyuguin, Target recognition at forward scatter radar, Radio technique and Electronics, 46(11), 1356-1360, (2001), in Russian. 4. Y. S. Hsu, D. C. Lorti, Space-borne bistatic radar on overview, IEEE Proc., 1986, F133, ʋ 7, pp. 642-648 5. P.K. Lee, T.F. Coffey, Space-Based Bistatic Radar: Opportunity for Future Tactical Air Surveillance, Proc. IEEE Inter. Radar Conf., May 1985, pp. 322-329. 6. Handbook on satellite communications & broadcasting, edited by L. Kantor (Radio & Comm., Moscow, 1984), p. 272, in Russian. 7. Handbook on radar, ed. by M Scolnik 8. P.Ya. Ufimtsev, Black bodies and shady radiation, Radio technique and Electronics, 35(12), 2519-2527, (1989), in Russian. 9. J.I. Glaser, Some results in determination of bistatic RCS of complicated targets; IEEE Trans., 77(5), pp. 8-18, (1989). 10. A.B. Blyakhman, F. N. Kovalev, A.G. Ryndyk, Method to determine coordinates of moving targets by bistatic radar, Radio technique, #1, pp.4-9, (2001), (in Russian).

ANALYSIS OF NANOSECOND GIGAWATT RADAR

A. Blyakhman 1 , D. Clunie 2 , G. Mesiats 3 , R.W. Harris 4 , M. Petelin 5 , G.Postoenko 5 , and B. Wardrop 6 P

P

P

P

P

P

P

P

P

P

P

P

P

P

1 NIIRT, Nizhny Novgorod, Russia; 2 High Power RF Faraday Partnership Lab, Oxon., UK; 3 IEP, Ekaterinburg, Russia; 4 BAE Systems, Chelmsford, UK; 5 IAP, Nizhny Novgorod, Russia; 6 Wylie Consulting, UK P

P

P

P

P

P

P

P

P

P

P

P

Abstract:

If a radar transmitter provides a sufficiently high energy in a short microwave pulse, efficient indication of moving targets among heavy clutter can be obtained by the simplest signal-processing algorithm. Such performance was demonstrated with an X-band 0.5 GW/6 ns/150 pps radar operating with a 3q beamwidth antenna.

Key words:

range resolution, moving target indication, clutter rejection.

1.

INTRODUCTION

During the mid-1990's the Russian Academy of Science and various entities from the UK established a cooperative agreement to investigate a novel radar concept. Eventually, this concept was called, in the UK, Nanosecond Gigawatt Radar, and it acquired the acronym NAGIRA. This system had a number of unique features; the concept has been described in a number of publications [1] & [2]. This paper is the first to describe some of the results obtained with this system. The components of this system have a number of unusual features and a number of key features that affect the overall system performance. These components are described and their associated measurements are shown. Finally, the radar performance characteristics are presented. A number of tests were performed against a variety of targets. Some interesting features of these tests are described and the high range resolution inherent within this system is demonstrated using the returns from a helicopter that show some unique characteristics. 283 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 283–296. © 2005 Springer. Printed in the Netherlands.

284

1.1

A. Blyakhman, et. al.

Organisations Involved

The design, manufacture, and testing of this system involved a number of organisations, including the following: x Russian Academy of Science x x x x x x

Institute of Electrophysics (Ekaterinburg) Scientific Instrument Special Design Bureau (Ekaterinburg) Institute of Applied Physics (Nizhny Novgorod) High Current Electronics Institute (Tomsk) Scientific Design Bureau “ALMAZ” (Moscow) GEC-Marconi Research Centre - Now BAE SYSTEMS Advanced Technology Centre (Great Baddow, Chelmsford, UK) x DERA (Defence Evaluation Research Agency) - Now split into two separate companies DSTL and QinetiQ (Malvern, UK) x UK Ministry of Defence

1.2

Specified & Measured Parameters

The original specification for the system are shown in Table 1. Table 1: NAGIRA System Specification & Measured Parameters

Frequency Frequency stability Pulse Duration Pulse Power Pulse Power stability PRF Pulse Forming Line Cathode Voltage (Vc) Cathode Current (Ic) RF generation Magnetic field Cathode life Transmitted Pulses Mode Converter Beamwidth Beam scan angle

SPECIFICATION 10GHz Wth), a study of the multipactor threshold Vth has been completed in terms of the dimensionless parameters O and VT VZ (see Figs. 4-5). Note that the results of the simple theory, as shown in Fig.3, gives Vth=1 within an infinite sequence of resonant bands of parameter O whereas V th o f beyond these

Figure 4. Comparisons between Monte-Carlo and statistical methods. Threshold value of s, solid areas correspond to the statistical method, and points to the Monte-Carlo method.

Vth

Figure 5. Comparisons between Monte-Carlo and Particle-In-Cell codes (the boundary of the solid area corresponds to that calculated with the Monte-Carlo algorithm, and points correspond to the results of calculations with the PIC code).

A Multipactor Threshold in Waveguides….

313

bands. This result is confirmed by numerical simulations with very low values of VT VZ . For finite velocity spread, the value of Vth increases within the resonant bands, but decreases outside of them. For higher values of the velocity spread, Vth becomes relatively small for any value of the parameter O . This indicates a possibility for the multipactor zones to overlap, provided that the secondary emission coefficient of the material exceeds the threshold value of Vth within a continuous region of O . At the second stage, realistic multipactor charts have been obtained using an approximation of the secondary emission coefficient according to Vaughan’s formula 21 with variable parameters: V m (maximum value of the secondary emission coefficient) and Wm (electron impact energy corresponding to V m ). It was found that depending on V m and the ratio mVT2 2Wm , the multipactor charts can contain some finite number of separated multipactor zones only, or a combination of separated and overlapping multipactor zones. Some results of these calculations with a fixed value mVT2 2Wm 10 2 are shown in Fig. 6.

Vm=1.2

Vm=2.0

Vm=1.5

Vm=1.7

Vm=2.5

Figure 6. Multipactor charts with different values of secondary emission coefficient.

314

J. Puech, et. al.

The parameter p

VZ

2W m m .

Some Monte-Carlo simulations were performed with real material data (Fig.7). Material: Copper etched surface Material: Alodine Thomson Treatment + Bake 4.5h in vacuum, Vaughan’s formula only, Vaughan’s formula is is used, V1 corresponds to 54 eV, Vmax used, V1 corresponds to 25 eV, Vmax corresponds to 225 eV, corresponds to 303 eV, electrons have electrons have Maxwellian Maxwellian distribution of initial distribution of initial velocities velocities with VT corresponding to 3 eV, with VT corresponding to 3 eV, Vmax = 1.75 Vmax=2.25

Log-log plot of breakdown voltage as a function of fL

Log-log plot of breakdown voltage as a function of fL

Figure 7. Plot of Multipactor charts: gap voltage versus f*d product.

To conclude the single carrier case, comparisons have been made between the Monte-Carlo method, the statistical method, and measurements performed at ESTEC. The squares represent ESTEC measurements. The light triangles correspond to the limits of the Multipactor zones obtained by the statistical code. The Monte-Carlo results, shown in black diamonds in Fig. 8, are computed at steps of the f*d product and of the power P:


315

aluminium

90 80 70

P (dB)

60 50

monte carlo mesures ESTEC

statistical mat code2 semenov

40 30 20 10 0 0,1

1

10

100

1000

f*d (GHz.mm)

Figure 8. Multipactor chart: comparisons between the Monte-Carlo code, the statistical code and measurements at ESTEC.

There is good agreement between the results of the Monte-Carlo code, the statistical code, and the ESTEC measurements for Aluminum.

4.

MULTIPACTOR IN MULTI-CARRIER OPERATION

4.1

ECSS: The 20 Cycles Rule 15

In the case of multi-carrier operation (which is the common situation in telecommunication systems), new parameters must be taken into account, such as amplitude, phase and frequency of the different carriers. A rule defined by the ECSS (European Cooperation for Space Standardisation) is aimed at helping designers handle the problem of Multipactor in multi-carrier operations: it is called the 20-cycle rule. According to this rule, Multipactor discharges can only occur if the time envelope of the signal is above the Multipactor threshold during a time corresponding to 20 gap-crossings of the electrons, for a given order. Consequently, when a frequency multiplex is given, it is necessary to find the worst-case phase distribution in order to have the highest level of the signal envelope, during the time corresponding to 20 cycles. Once this worst-case phase law has been determined, it is possible to

316

J. Puech, et. al.

compute the margin between the level of the signal envelope and the Multipactor threshold, as predicted by the chart. Software called WCAT has been developed in order to facilitate these calculations. The different parameters which can be taken into account are the number of carriers, amplitude of each carrier, number of gap crossings, the multipactor order to be considered, the “frequency” * “gap” size product, the material in question, and the model to be used for the secondary emission coefficient. The software finds the worst-case phase law of the frequency multiplex, which gives rise to the maximum value of the voltage during 20 cycles (the worst case from the Multipactor point-of-view). It can also compute the maximum voltage during an arbitrary number of cycles and the duration of the cycle depending on the order. The optimisation program is based on a genetic algorithm. Let’s consider the following example. 12 carriers of 130 W each are analysed. These carriers have frequencies between 10, 7 and 13 GHz. The metal is Alodine. The f*d product equals: f*d=13, 91 GHz. mm:

Figure 9. WCAT: optimisation of the phase law of the frequency multiplex.

The maximum of the signal envelope threshold is 390 V. The threshold computed by the Multipactor chart is at 1210 V. Thus, we can deduce the margin from the above computations: 20*log (1210/390) = 9,83 dB.


4.2

317

Computation of Electron Dynamics in Multi-Carrier Operation

The Multipactor effect is very sensitive to variations of the different parameters described above. To illustrate this point, the Multipactor effect can occur if all carriers have fixed frequencies and the same initial phases, but do not occur when frequencies and phases are different. 2D tests were performed to show the discharge’s dependence on initial phase and frequency ranges. Parameters corresponding to silver plated copper are used, secondary emission is approximated by Vaughan’s formula, V1 and Vm correspond to 30 eV and 215 eV respectively, Vm=1.99, electrons have a distribution of initial velocities, which depend on the emission angle and the initial velocity V0 corresponds to 3 eV. 4.2.1

Test Sets

The first test set was made by using carriers with different phases. The control parameter is the initial phase range between the first and the last carrier. The choice of phases for the other carriers is done randomly within the phase range. The initial phase sets are shown in Table 2. The results of the test are shown in Fig. 10. The second test set was made using different frequency ranges of the carriers. The control parameter is the frequency range between the first and the last carrier. Other carriers’ frequencies are equally spaced within this frequency range. The frequency ranges are shown in Table 3. The results of the test are shown in Fig.11. For both tests, the initial number of electrons was 105. The tests were executed until the number of electrons were greater than 106 or less than 1 and until time exceeded 3·10-8 sec. The time step was 10-13 sec. The amplitudes were chosen to obtain a total oscillatory velocity VZ (when all frequencies are the same) close to Vm. Even when all of the frequencies are fixed, and the initial phase range is differs from test to test, the electron number growth is hardly predictable (Fig.10). It shows that initial phases of carriers are very important parameters to take into account in order to obtain a reliable prediction of multipactor. A similar result is obtained for varying frequency range: even if initial phases of all carriers are the same (or fixed) but the frequency range is different from test to test, the results of multipactor development are also quite different (Fig.11). The fact that a variation in the carrier amplitudes can also lead to different types of possible electron dynamics, is even more obvious. To conclude, all the carrier parameters should be taken into account, together.

318

J. Puech, et. al.

Table 2. Parameters for the first and the second test sets 7

8

9

10

5.652

5.024

4.396

3.768

3.141

2.512

1.884

1.256

0

Frequencies set 2: 10.9 GHz, 10.92 GHz, 10.94 GHz, 10.96 GHz, 10.98 GHZ, 11.01 GHz Amplitudes: 281.17 V, 279.67 V, 278.25 V, 276.9 V, 275.62 V, 274.41 V

Figure 10. Multipactor effect in multi-carrier operation: influence of initial phases range.

4.2.2

Frequency set number Frequency range

1

2

3

4

5

6

0.55 GHz

6

0.44 GHz

5

0.33 GHz

4

0.22 GHz

3

0

2

0.628

Maximum difference between 2 initial phases

1

0.11 GHz

Initial phases set number

Initial phases: all phases are equal 0 Amplitudes:

281.17 V, 279.67 V, 278.25 V, 276.9 V, 275.62 V, 274.41 V

Figure 11. Multipactor effect in multicarrier operation: influence of frequency separation.

Conclusion

Multipactor in multi-carrier operation has been analysed with respect to the dependence on amplitude, frequency and phase separation. An example using six carriers between two parallel-plates with silver-plated copper has been analysed. The results have shown that all parameters must be taken into account in order to obtain a reliable prediction of multipactor. Consequently, it implies that Multipactor charts for the Multi-carrier case cannot be drawn without properly defined parameters.

5.

THE MULTIPACTOR EFFECT IN WAVEGUIDES16

In the previous studies, the only case considered was the two parallelplate model. When the case of a waveguide is analysed, the difficulty lies in the fact that two lateral metallic planes must be added in the analysis. In order to analyse this situation, a code based on the Monte-Carlo algorithm has been developed.


5.1

319

Algorithm used in the Waveguide Theory

When the electron collides with the metallic wall, the probability to give a reflected electron or to give secondaries is computed to have the number of electrons after the collision. If the primary electron creates secondary electrons, the number of secondary electrons emitted is computed depending on the energy and on the incidence angle of the primary electron. One single, randomly selected trajectory is followed after each impact. With this approach, many trials are computed to cover numerous cases. If, after one trial, the number of electrons is above 106, Multipactor may occur.

Emitted electron

e-

eProbability law of the secondary electrons

Reflected electron

Secondary electron

e-

D

D

Figure 12. Electron collision with the metallic wall: secondary and back-scattered electrons.

A back-scattered electron will leave the metallic wall with the same angle as the incident one (compared to the normal to the metallic wall). To be more precise, the electron will stay inside a probability cone whose main component is the symmetrical angle relative to the normal. If secondary electrons are emitted, they are emitted following a cosine probability law. Finally, we assume that all secondary or reflected electrons have the same behaviour as the chosen one. The Monte-Carlo algorithm is performed at each f*d product step, for a given power and for a given initial angle. The computation stops if the Multipactor effect occurs (i.e. if the number of created electron is larger than 106) or if the Multipactor effect will have not occur (i.e. if the number of created electrons is below 10-6) or if the number of trajectories, during which we follow the electron, has reached a limit. Four loops are considered: loop on the f*d product, on the power, on the initial phase, on the number of trajectories. Different formulas can be used for the secondary electron coefficient.

320

J. Puech, et. al.

In order to take into account the dependence on the angle of the incident electron, the above equations must be multiplied by the following coefficient: exp [1.55(1-cos D)] 17. The probability of reflection is given by: (1 cos D )

9 Z atom

and depends on the arrival angle of the incident electron, 17.

In the simulations, all three components of the TE10 electromagnetic field mode are considered. The variables linked with the electron are the position, the time and the velocity. Impact is possible with the four walls of the waveguide. It is important to notice that the magnetic field has a tendency to modify the trajectory of the electron--it moves toward the lateral walls.

5.2

Illustration for a Standard Waveguide

The waveguide used for the illustration is WR75 (19,05 x 9,525 mm). The frequency is 12 GHz and the metal considered is Aluminium. The result is shown in Fig.13:

No Multipactor for high fxd

Multipactor zones

Figure 13. Multipactor chart in the case of a waveguide.

6.

CONCLUSION AND PERSPECTIVES

The parallel plate model has been extensively studied during the research project performed by Chalmers, IAP and CNES. The main feature of the discharge is its resonance property, which is manifested in the Multipactor charts as resonant bands. The influence of parameters such as the initial velocity spread and the secondary emission coefficient has been evaluated.


321

An important point is that the effects of these parameters are not independent. As a matter of fact, depending on the value of the secondary emission yield, the resonant bands are narrower or wider. The existence of hybrid modes has made it possible to explain the continuous region in the multipactor charts in cases of high secondary emission coefficients. These modes can be found in the parameter space between the well-known resonant zones and can be considered as a combination of the classical resonant modes. In the multi-carrier case, the phenomenon is not very easy to describe, because the signal envelope has a very complex variation in time. The most accurate way to solve the problem is to couple the time evolution of the envelope with the electron trajectories between the metallic walls. Results coming from the code realising such a coupling have demonstrated that, as the multi-carrier character of the signal is taken into account, the Multipactor effect becomes very sensitive to parameters such as frequency separation between carriers, phase distribution and amplitude. In the case of the Multipactor effect in single carrier operation in a waveguide, the two lateral walls play an important role in the simulation. The two main phenomena are taken into account are secondary emission and reflection. The charts have shown that for high values of the f*d product, Multipactor does not occur. Concerning perspectives for the future, one of the main points is the simulation of the effect inside complex microwave components such as corrugated filters, cavity filters, etc. A first step towards solving such problems could be to predict the Multipactor effect in the presence of fringing fields, which occur in irises. Another interesting issue would be to use the Particle-In-Cell code for microwave geometries like waveguides. This could make it possible to evaluate the influence of a complex geometry also within the context of multi-carrier operation. Finally, it is important to be aware of the importance of e.g. Solid State Power Amplifiers (SSPA) in applications such as active antennas in new telecommunications systems. The power level at the output of such components increases more and more, and SSPAs are rapidly becoming competitive relative to the Travelling Wave Tube. As a consequence, new questions arise such as e.g. the Multipactor effect in the presence of dielectric walls. A project involving Chalmers University, IAP and CNES has been granted to study the Multipactor effect at or close to the walls of dielectric materials.

322

7. 1. 2.

3. 4. 5. 6. 7.

8. 9. 10.

11. 12. 13. 14.

15. 16. 17.

18. 19.

J. Puech, et. al.

REFERENCES P. T. Farnsworth, Television by electron image scanning, J. Franklin Inst., vol. 218, pp. 411-444, 1934 A. J. Hatch and H. B. Williams, The secondary electron resonance mechanism of lowpressure high-frequency gas breakdown, Journal of Applied Physics vol. 25 n°4, pp. 417-423, 1954. E. Chojnacki, Simulations of a multipactor-inhibited waveguide geometry, Physical Review, ST Accel. Beams vol. 3, 032001, 2000 V. D. Shemelin, Existence zones for Multipactor discharges, Sov. Phys. Tech. Phys. Vol. 31 (9), pp. 1029-1033 R. L. Geng, H. S. Padamsee, V. Shemelin, Multipacting in a rectangular waveguide, Proc. 2001, Particle Accelerator Conf., Chicago, pp. 1228-1230 V. Semenov, A. Kryazhev, D. Anderson, M. Lisak, Multipactor suppression in amplitude modulated radio frequency fields, Phys. Plasmas vol. 8, No. 11, pp. 5034-5039 C. Bourat, J.-M. Joly, On Multipactor effect in a 600 MHz RF cavity used in electron linear accelerator, IEEE Trans., Electrical Insulation, vol. 24, No. 6, pp. 10451048,1989 A. J. Hatch, H. B. Williams, Multipacting modes of high-frequency gaseous breakdown, Phys. Rev., v. 112, No. 3, pp. 681-685, 1958 A. Woode, J. Petit, Investigations into Multipactor Breakdown in satellite Microwave Payloads, ESA Journal, v. 14, No. 1, pp. 467-478, 1990. A. Kryazhev, M. Buyanova, V. Semenov, D. Anderson, M. Lisak, J. Puech, L. Lapierre, J. Sombrin, Hybrid resonant modes of two-sided Multipactor and transition to the polyphase regime, Phys. Plasmas vol. 9, No. 11, November 2002. G. Francis, A. von Engel, The growth of the High-Frequency Electrodeless discharge, Proc. Roy. Soc. London, Ser. A, V. 246, pp. 143-180, 1953 J. Sombrin, Effet Multipactor, CNES Report No. 83/DRT/TIT/HY/119/T A. L. Gilardini, Multipacting Discharges : constant –k theory and simulation results, J. Appl. Phys., v. 78, No. 2, pp. 783-795, 1995 D. Anderson, A. Sazontov, N. Vdovicheva, M. Buyanova, V.Semenov, J. Puech, M. Lisak, L. Lapierre, Simulations of Multipactor zones taking into account realistic properties of secondary emission, ESA Conference MULCOPIM 2003, September 2003 Space Engineering: Multipaction design and test, ECSS E-20-01, 5 May 2003 J. Sombrin, Claquage hyperfréquence et effet Multipactor dans les satellites, OHD conference, June 1993 F. Maurice, L. Meny, R. Tixier, Microanalyse et Microscopie Electronique à balayage, Ecole d’été de Saint-Martin d’Hères, Les éditions de Physique subventionnées par le CNRS, 11-16 September 1978 W. Henneburg, R. Orthuber, and E. Steudel, Z. Tech. Phys., vol. 17, p. 115, 1936. J.R.M. Vaughan. Multipactor. IEEE Trans. Electr. Dev., v. 35, No. 7, pp. 1172-1180, 1988.


323

20. A. J. Hatch and H. B. Williams, The secondary electron resonance mechanism of lowpressure high-frequency gas breakdown, J. Appl. Phys. V. 25, No. 4, pp. 417- 423, 1954. 21. J.R.M. Vaughan. A new formula for secondary emission yield.Trans. Electr. Dev., v. 36, No. 9, pp. 1963-1967, 1989.

QUASI-OPTICAL MODE CONVERTERS IN ADVANCED HIGH-POWER GYROTRONS FOR NUCLEAR FUSION PLASMA HEATING M. Thumm1,2, A. Arnold2, O. Drumm1, J. Jin1, G. Michel3, B. Piosczyk1, T. Rzesnicki1, D. Wagner4, X. Yang1 1

Karlsruhe Research Center, Association EURATOM-FZK, Institute for Pulsed Power and Microwave Technology, D-76021 Karlsruhe, Germany; 2University of Karlsruhe, Institute of High-Frequency Techniques and Electronics, D-76128 Karlsruhe, Germany; 3Max-PlanckInstitute for Plasma Physics, Ass. EURATOM-IPP, D-17491 Greifswald, Germany; 4MaxPlanck-Institute for Plasma Physics, Ass. EURATOM-IPP, D-85748 Garching, Germany Abstract:

Key words:

1.

The R&D activities at the Karlsruhe Research Center (FZK) on advanced highpower millimeter (mm)-wave gyrotrons for future use in electron cyclotron heating and current drive (EC H&CD) in magnetically confined fusion plasmas consist of: (1) Development of a 1 MW continuous wave (CW) gyrotron at 140 GHz for the stellarator W7-X, (2) Development of a coaxial cavity gyrotron capable of delivering 2 MW CW at 170 GHz for ITER, (3) Investigations on a 4 MW 170 GHz coaxial cavity gyrotron with a twobeam output (2x2 MW) for a future DEMO fusion reactor, and (4) Investigations on a tunable multi-frequency gyrotron (105 GHz to 140 GHz). The present paper discusses the different quasi-optical mode converter schemes employed in these various types of advanced gyrotrons. Conventional and coaxial high-power gyrotrons, quasi-optical mode converters, electron cyclotron plasma heating and current drive

INTRODUCTION

For increasing the collector’s electron beam interception area in long-pulse, high-power gyrotrons, an output coupler that separates the spent electron beam from the outgoing rf power, is required. It is the short wavelength, high output power and the rotating asymmetric high-order cavity mode of such tubes that have led to the need for novel mode conversion concepts [1]. The down-conversion of these high-order cavity modes with complicated field


326

M. Thumm, et. al.

structure by using conventional waveguide mode transducers with highly oversized waveguide diameter is practically impossible due to the extreme mode competition involved. The higher the operating mode is, the more it is appropriate to employ an asymptotic procedure for its description, namely the method of geometrical optics (g.o.) (see e.g. [2], [3]). In the framework of this method, the initial mode is represented as a system of rays successively reflected from the waveguide walls (Brillouin-Keller concept). To directly convert the complicated field structure of rotating high-order asymmetric gyrotron cavity modes into a linearly polarized Gaussian beam, i.e. to modify the configuration of rays, one can use quasi-optical (q.o.) devices, a proper combination of a specific mode converting waveguide slot radiator (launcher) together with a few curved mirrors [4], [5], often called a Vlasov converter. This method is universal, but diffraction effects limit its efficiency to approximately 80%, which cannot be accepted for high-power gyrotrons.

Figure 1. Different output coupling schemes for high-power, high-frequency gyrotrons [1].

The present section summarizes the principles and advantages of q.o. mode converters and discusses the design of improved launchers and beam shaping reflectors with higher efficiency

Q-O Mode Converters ….

327

1.1 Advantages of Quasi-Optical Mode Converters The q.o. mode converter is a part of the internal electrodynamic system of the gyrotron like the cavity and the uptaper (Figure 1b). Radial output coupling of the RF power into the fundamental Gaussian (TEM0, 0) freespace mode has three significant advantages for high-power operation: a. The linearly polarized TEM00 mode is directly usable for low-loss transmission as well as for effective antenna feeding and no further mode converters are needed. Therefore, q.o. mode converters are also used for relatively modestly overmoded systems when a very compact mode converter to the TEM00 mode is required [6], [7]. b. The converter separates the electron beam from the RF-wave path (Figure 1b) so that the electron collector is no longer part of the output waveguide as in the case of a tube with an axial output (Figure 1a). Hence, the collector can be designed especially for handling the high electron-beam power. In addition, energy recovery with a depressed collector becomes possible. c. The harmful effects of rf power reflected from the output window are expected to be significantly reduced, especially if the window disk is slightly tilted.

1.2. Principles of Quasi-Optical Mode Converters The principal schemes of q.o. mode converters for (a) rotating asymmetric modes and (b) for circular symmetric modes are shown in Figure 2. TE- and TM-modes in a circular waveguide can be decomposed into a series of plane waves, each propagating at the Brillouin angle TB relative to the waveguide axis:

TB = arcsin (Xmn/koa) Xmn: ko: a:

root of Bessel function (or derivative) free-space wavenumber radius of the launcher waveguide

(1)

328

M. Thumm, et. al.

Rc

m a Xmn

Figure 2. Principal schemes of quasi-optical mode converters and amplitude distribution at the launcher. The electric field orientation shown in b) applies only for TEon modes.

The requirement of a zero azimuthal electric field at the waveguide wall defines their relative phases. In the q.o. limit, a plane wave front is represented by one ray. Its transverse location is defined by the requirement that at a particular point of interest the ray direction must coincide with the direction of the Poynting vector of the original TE- or TM-mode field distribution. If the point of interest is located at the waveguide wall the ray has the distance: Rc =

m a X mn

(2)

from the waveguide axis. Hence, if all plane waves are represented by q.o. rays they form a caustic at the radius Rc (Figure 2). In an unperturbed circular waveguide, the density of the rays along the caustic is uniform [2].

Q-O Mode Converters ….

329

The distance that a ray has propagated in the axial direction between two subsequent reflections from the waveguide wall is LB

ª § m ·2 º 2a «1 ¨ ¸ » «¬ © X mn ¹ »¼

1/ 2

cot T B .

(3)

In the transverse direction a section of angle: 'M

2T

§ m · 2 arccos ¨ ¸ © X mn ¹

(4)

reflects all rays exactly once. Accordingly, for modes with mz0 the reflection points of each of the rays are placed on the waveguide surface in a helical line with the angle of inclination [3] \ = arctan (T tanTB/sinT)

(5)

and the distance (pitch) that a ray has propagated in the axial direction when it has completed a full turn is [3] H = 2S a cot \ 2

§ m · 1¨ ¸ ß © X mn ¹ 2S a 2 X mn § m · arccos ¨ ¸ © X mn ¹

= Lc = launcher cut length

(6)

which is the launcher cut length. Hence waveguide sections (wound parallelograms: "G region") with the length Lc and the transverse width defined by a'M reflect each ray once. Back scattering effects due to diffraction of the incident high-order mode by the helical and straight edges of the launcher have been estimated by using the method of equivalent currents [8]. For TB >

LNA

M

M

>>

Divider

LNA HPA >>

M

M

HPA

>>

>>

M

LNA

>>

HPA

>>

LNA

>>

HPA

M

Phase shifter

Combiner

¦

RX

TX

a) Block- diagram of active PAA Radiator M

M

M

M

¦

Phase shifter Combiner/ divider Diplexer

HPA

TX

LNA

RX

b) Block- diagram of passive PAA Figure 1. Active and passive PAA’s.

where: R -radar range, m, Pa - average radiated power, W, S - effective antenna area at reception, sq.m, Veff - radar cross-section (RCS) of the target, sq.m, q2 - signal-to-noise ratio, k - Boltsman's constant Teff - effective noise temperature of the receiving system. It is proportional to the average radiating power multiplied by the receiving antenna area, and does not depend on wavelength. Since the cost of producing the power and the cost of creating the antenna grows as wavelength decreases, it is expedient to develop exclusive

356

Tolkachev, Yegorov, Shishlov

surveillance radars operating at a relatively long-meter or decimeter-wave band. Interference immunity and target data accuracy of these radars are lower than aforementioned parameters of radars operating in short-wave bands. The required energy for single-target tracking depends on the singlepulse radiated energy E, in J [1]:

R4

E SV eff 1 u 2 2 4S q O kTeff

(2)

In that case, the range of coverage depends on the wavelength as O-1/2, i.e., it grows with the decrease of wavelength because of the higher concentrations of energy in space. Thus, radar coverage range, frequency selectivity, and interference immunity, increase. Consequently, it is desirable to develop target-track radars operating at the short centimeter waveband or at the long-wave part of the millimeter-wave band. Thus, the ratio of energy consumption per detection and per tracking grows with decreasing of wavelength. In real radar systems, energy consumption per tracking as a rule, is much less than the consumption per detection in S-band (O a 10 cm) systems, and is incomparably less in X-band (O a 3 cm) systems and, in particular, in Ka-band (O a 0.8 cm) systems. That is the reason for the 1972 Anti Ballistic Missile (ABM)-Defense Systems Treaty defining that excess of 3106 Wsq.m value of radar average, radiated power multiplied by aperture area as an indication of the fact that the radar belongs to the strategic (anti-intercontinental ballistic missile) radar category:

Pa S d 3 u 10 6

W sq.m

(3)

Let us attempt now to estimate limitations on multifunction radars in high frequency bands, using as an example, ABM-defense radars and keeping in mind that these estimations are qualitatively valid for other high-power multifunction radars. The considerable troposphere attenuation of millimeter and sub-millimeter waves limits their application in radar and communication. The most favorable area of their application is the near-Earth space, where molecular absorption is absent and the influence of ionized clouds is insignificant.

Radar and Communications Systems

357

Millimeter waves can be effectively used both in cellular communication systems as well as in radar systems if a few tens of kilometers coverage range is acceptable (for example, anti-aircraft defense radar systems) or, in systems operating at high elevation angles (more than 20 deg, for example, anti-missile defense radars). The data rate of a communication system depends on the signal-to-noise ratio q of the front-end amplifier, which is expressed by the communication link equation [2]:

q

· 1 1 ¸ 2 2 ¸ © Teff ¹ O R kB §

Pa S t ¨¨ S r

(4)

where: Pa - average transmitting power, St - transmitting antenna aperture area, Sr - receiving antenna aperture area, Teff - effective noise temperature of the receiving system, R - distance of communication link, k - Boltsman's constant, B - bandwidth. From Equation (4), one can see that system capacity increases at higher frequencies due to the concentration of energy radiated by the transmitting antenna to space. On the other hand, the value of q is proportional to energetic efficiency Pa St of transmitting antenna and Sr /Teff -of receiving antenna.

3.

COMPARISON OF PASSIVE PAA AND ACTIVE PAA

Along with conditions of radio-wave propagation, the main limitation of using higher frequency ranges is the radar cost. Currently, the cost of a PAA and of a power amplifier, connected to the PAA or included in its structure, makes up 70-90% of total radar cost. Basing on our averaged, expert estimations, we make a qualitative assessment of PAA elements cost realizing radiation of 2 kW average power per one sq.m of passive or active PAA aperture, as a function of operational frequency.

358


As applied to passive PAA, the cost consists predominantly of two components: cost of aperture phase-control elements (aperture phase shifters) and cost of a transmitter. Currently, semiconductor and ferrite elements are widely used for phase control in passive PAAs. Cost estimations for passive PAA elements implemented by leading R&D engineer Dr. Yu. B. Korchemkin, are presented in Tables 1, 2.

Table 1. The cost of a PAA element using ferrite phase shifters. Optimistic (pessimistic) estimate

1 2 3 4 5

The cost, USD PAA element O=10 cm 6 cm 3 cm 1 cm Phase-shifting section (ferrite, waveguide, coil) 100 40 20 15 Radiator (two dielectric rods) 60 30 15 5 Armature (cradle, body, radome) 40 20 10 5 Control circuit, supply, special-purpose 40 20 15 10 processor Mechanical construction 100 60 30 15 TOTAL 340(600) 170(300) 85(150) 50(90)

Table 2. The cost of a PAA element using semiconductor phase shifters. Optimistic (pessimistic) estimate The cost, USD PAA element O=10 cm 6 cm 3 cm 1 cm 1 Phase-shifting section (p-i-n diodes, plate, 200 180 170 160 tuner) 2 Radiator (two planes with stripline radiators) 60 30 15 5 3 Armature (cradle, body, radome) 40 20 10 5 4 Control circuit, supply, special-purpose 30 20 20 20 processor 5 Mechanical construction 80 70 60 50 TOTAL 340(600) 320(500) 275(400) 240(350)

Let us suppose that spacing of radiating element is 0.7O, which corresponds approximately to a 90-degree sector of electronic beam steering. From (1), the number of array elements N a O2. The cost of one square meter of the aperture for that case is shown in Fig. 2. The cost of high power amplifiers for radars with passive PAA using different microwave vacuum tubes can be found from expert evaluation as presented in the Figure 3.


1 000

thou USD Ferriteelement antenna aperture

100

359

Semiconductorelement antenna aperture

O , cm 10 0,1

1

10

100

1

Figure 2. Cost of one sq.m of passive PAA aperture as a function of wavelength.

1000

thou USD

Pa= Generaluse devices

100

10

2 kW

Gyro devices

1 0,1

1

10

O, cm

100

Figure 3. Cost of power amplification by means of various types of microwave vacuum devices.

In an active PAA, cost is determined by the basic element of the semiconductor APAA module including the power amplifier. If the power flux density at the unit aperture surface is fixed, the cost of the module slowly depends on the frequency band and, according to expert estimations, is about USD 1000 - 2000 [3,4]. The cost of mechanical construction can be estimated equal roughly to one fourth of the module cost.

360

Tolkachev, Yegorov, Shishlov Figure 4 comprises cost estimates for both passive and active PAA’s .

10000

thou USD

Passive PAA using generaluse amplifiers

Thaad (USA)

1000

Semiconductorelement active PAA

Passive PAA using gyro devices Wavelength for expedient applying the semiconductorelement active PAAs

100

10 0,1

1

Wavelengths for possible applying the semiconductorelement active PAAs

Wavelengths for applying the passive PAAs microwave vacuum using devices

O, ɫm 10

100

ȿL/M-2080 (Israel)

1

Figure 4. Cost of one sq.m of PAA aperture radiating 2 kW average power as a function of wavelength.

It is necessary to mention that cost of any radio system consists of two components: initial cost of development, and cost of maintenance. From our experience, expenses for maintenance of radio-systems with passive PAA exceed expenses for fabrication of the systems. At the same time, our experience of handling with radio systems containing APAA shows that expenses for maintenance are about 10–25% of the initial expenses for fabrication. It is appropriate to mention that reliability of radar systems with passive PAA in many respects is defined by the reliability of a vacuum HPA with high-voltage power supply. As a rule, a lifetime of the HPA is much less than a specified life of the whole radar. For this reason, the HPA is substituted many times during the specified life of the radar. As for the transmitting APAA, it represents a system of many highreliability solid-state power-radiating sources working in parallel. In case of


361

M channels failure of initial number N, energetic efficiency of the antenna changes as follows:

( Pa S ) N M 2M | 1 N ( Pa S ) N

(5)

This means that 10% failure of modules leads to about 1 dB degradation of energetic efficiency. Similar relations are valid for receiving APAA. Maintenance statistics of radio systems with APAA is evidence of high reliability of receiving and transmitting solid-state modules. Mean time between failures is about 200 000 hours for receiving modules and about 100 000 hours for transmitting modules [3]. Similar data are obtained in our developments. This reliability of modules provides degradation of energetic efficiency of APAA of about 1 dB during 10 000 hours. Of course, such performance is achieved in case of optimal construction of antenna with appropriate cooling system, protection from mechanical and environment exposures. Trustworthy results of research and development the APG-77 radar for F22 fighter gave evidence of the fact that radars with active and passive PAA have similar cost of development. But the system with a passive PAA exceeded for about two times the available volume and weight, and had a power consumption that exceeded the capability of airborne power supply [5]. At the same time, Figures 2 and 3 allow one to propose the expedience of applying the general-use vacuum devices, in particular the gyrodevices packaged with permanent magnets, in large and powerful millimeter-wave radars [6].

4.

EXAMPLES OF PAA OF RADAR SYSTEMS

Let us consider several examples of radars with PAA. The EL/M-2080 radar recently developed in Israel is an example of the multifunctional L-band radar using solid-state APAA. Though there is very little information on the characteristics of the radar in publications, some indirect data allows supposition that the antenna area is about 25 sq.m, and the number of solid-state hybrid modules containing power bipolar transistors is about 600. It is possible to expect that the average power of each module is in the 30 to 60 W interval. Hence, PaS # 4.5105 - 106 W sq.m., that is the value of Pa S that complies with the restriction of the 1972 ABM-defense Systems Treaty. The cost of

362


manufacturing the solid-state modules of the radar is probably about 1,000,000 USD. Several specimens of the radar have been manufactured [7]. The multifunctional X-band radar of THAAD system is the other interesting example of APAA with very large quantity of modules. The antenna area of the radar is 9.2 sq.m, the number of solid-state modules is 25 344, and antenna array spacing is 0.6 O. No information about the module average power is available from publications, however it is possible to suppose that it is between 1 and 10 W. Hence, Pa S = 2.51052.5106 W sq.m. The cost of a solid-state module is about 1000 USD, that is the overall cost of modules for one APAA is about 25,000,000 USD [8], [9]. Thus, costs of these two radars differ roughly by 25:1, though the searching capabilities of the radars are approximately equal to one another. The cost difference of the radars is caused by higher measurement accuracy and interference immunity of the THAAD system. Whereas there exist no powerful radars with solid-state APAA in millimeter wave band currently, the radar “Ruza” (35 GHz) created in 1989 (Fig. 5) by JSC “Radiophyzika” (Moscow) in cooperation with other companies, is the most remarkable example of radar with PAA which is passive for transmission and active for reception [10,11]. The array antenna contains 120 large radiators with ferrite phase shifters. The total antenna aperture is about 40 sq.m. The radar uses gyroklystron power amplifiers. Average radiated power is 50 kW, hence, Pa S | 2106 W sq.m. Due to very large spacing of elements, the PAA has conical sector of electronic beam steering of about 1q. The PAA is installed on the positioner, which provides mechanical beam steering in the upper hemisphere.


363

Figure 5. Radar “Rusa”.

For similar radar with a wide angle of electronical beam steering, the other passive PAA was developed by JSC “Radiophyzika” [12]. This reflective-type PAA developed on basis of ferrite phase shifter is shown in the Fig. 6. The PAA contains about 3600 phase shifters arranged over hexagonal grid with spacing 1.1O. Protruding waveguide-dielectric rod radiators form a flat-topped pattern that suppresses grating lobes. The PAA has a sector of electronic beam steering about r25q. The array has hexagonal aperture with diameter of its inscribed circle of 0.64 ɦ. Effective illumination of the aperture is provided by a quasi-optical exciter. In combination with a commercial klystron on TWT HPA with average output power of 2 kW, the system can provide Pa Seff | 5u102 W sq.m.

364


Figure 6. Reflective PAA of Ka-band.

The described array can be used as not only a single antenna but as a subarray of a large “semi-active” PAA of hexagonal structure. For example, assembled with approximately 102 subarrays with HPA, such an antenna would have Pa Seff | 3u106 W sq.m.

5.

APAA FOR COMMUNICATION SYSTEMS

As to communications, the trends are partly similar to radar systems and partly different. On the one hand, it is necessary to note that the trend of using higher frequency bands is very attractive in communications because it ensures considerable advantage of system throughput rate, allows a reduction in power consumption, reduces the overall dimensions of hardware, and increases the system interference immunity. These advantages seem to be very valuable especially in the case of satellite antennas for communications. On the other hand, communication systems usually operate within the angular coverage, which is far less than required coverage of radar systems. Hence, requirements to the radiating power of communication systems are, in general, far easier than that of radars, and very small APAA containing a few hundreds or even a few tens of elements are widely used in this case. Applying of APAA in communication systems is extremely expedient in


365

respect of serviceability, as it allows rejection of insufficiently reliable vacuum high-voltage microwave devices. Also, it permits an increase in efficiency and flexibility of communication systems. Very high reliability, possibility to form many beams with independent electronic scanning, broad capability of pattern shaping, make APAA a very attractive and reasonable technical solution in these systems despite the costs of the antenna systems being rather high. Apparently, the APAA replaces conventional antennas not only in microwave, but in millimeter-wave systems too, first of all, in satellite communication systems. As far as we know, the first APAA for mobile satellite communications through high elliptic satellite "Molniya" was developed in the Soviet Union in 1970 [13]. The airborne APAA of L-band (800/900 MHz), containing 64 elements providing one electronically steered beam near the upper hemisphere (r80q) is shown in Fig. 7. The system’s transmitting antenna has Pa Seff | 102 W sq.m.

Figure 7. L-band airborne APAA for communication system through the satellite “Molniya".

366


Another APAA developed for geostationary communication satellite “Kupon” [14] (Ku-band) is shown in the Fig. 8. It contains 64 elements. The modules are arranged in nodes of a hexagonal grid with spacing about 3O , which provides a beam coverage area about r9q, which is enough to cover the earth from the geostationary orbit. The antenna has four independently steered and shaped beams. Maximum Pa Seff of the APAA is about 10 W sq.m.

Figure 8. Ku-band APAA of communication satellite “Kupon”.

The APAA developed by “Boeing” [15, 16] and used in mobile satellite communication system of millimeter wave band is shown in Fig. 9. The APAA consists of 91 elements. Hermetic active modules containing monolithic microwave integrated circuits (MMIC) are arranged in nodes of a hexagonal grid with spacing of approximately 0.6O , that provides r70qsector of electronical beam steering. Despite each channel containing rather


367

Figure 9. APAA (f =44 GHz) for satellite communications.

powerful HPA (Pout = 0.6 W), the parameter Pa Seff | 10 -1 W sq.m is rather small. The most impressive example of Ku-band APAA for experimental high data rate (Gigabit) satellite is under development by CRL and MELCO (Japan) [17]. Both transmitting and receiving APAAs contain about 2800 elements with a 2.4 m aperture diameter for transmitting (18 GHz), and 1.6 m for receiving (28 GHz). Output power of the transmitting APAA must be about 400 W. Noise figure of receiving APAA will be less than 3.5 dB. The array consists of horn radiators spaced at about 2.2O, which provides r10qsector of electronical beam steering. Efficiency of the transmitting APAA Pa Seff | 2 10 3 Wsq.m is very high for this frequency band. Transmitting (Fig. 10) and receiving antenna subarray units containing 64 channels each were already successfully developed and tested [17]. Use of APAA containing MMIC is supposed in many advanced Ka-band satellite communication systems [9]. To support space missions, communication systems in the frequency range from S-band to Ka-band are used, and the transmit power is from 200W to 400 kW. Future upgrades to navigation, command uplink and emergency recovery complexes will require still higher frequency and higher power

368


transmitters. These specifications can be met with combinations of both solid-state and vacuum electronic devices [18].

a) Antenna Aperture (44 Subarray Unit)

b) Subarray Unit Figure 10. Antenna configuration of the transmitting APAA for Gigabit satellite.


369

CONCLUSION Radar and communication systems with active phase arrays are superior to passive systems at relatively low frequencies, but lose their competitive edge when approaching the millimeter-wave band. Beginning with Ka-band, the highest powers can be employed in practice only with passive phased arrays.

6.

REFERENCES

1. M.I. Skolnik, Radar Handbook, McGRAW-HILL, 1970. 2. L.Kantor at al, Handbook on Satellite Communications and Broadcasting. - Radio i Svyaz, Moscow, 1988. 3. Nicolas Fourikis. Phased Array-Based Systems and Applications. John Willey & Sons, Inc.1996. 4. Eliot D. Cohen, Trends in the Development of MMICs and Packages for Active Electronically scanned Arrays. - IEEE International Symposium on Phased Array Systems and Technology, Boston, 1996, ɪ.p. 1 - 4. 5. John A. Malas. F-22 Radar Development. NAECON - 97, p.831 - 839. 6. A.V. Gaponov-Grekhov, V.L. Granatshtein. Application of High-Power Microwaves. Boston-London, Artech House, 1994. 7. S. Dryer at al. EL/M 2080 ATBM Early Warning and Fire Control Radar System. IEEE International Symposium on Phased Array Systems and Technology 1996, ɪ 11-16. 8. M. Sarcione at al. The Design, Development and Testing of the THAAD Solid State Phased Array. IEEE International Symposium on Phased Array Systems and Technology. Boston, 1996, ɪ. 260-265. 9. E. Brookner. Phased Array for the New Millennium. 2000 IEEE International Conference on Phased Array Systems and Technology, 2000, ɪ.3-13. 10. A.A. Tolkachev at al. A Megawatt Power Millimeter-Wave Phased-Array Radar. IEEE Aerospace and Electronic Systems Magazine, July 2000 ISSN 0885-8985, v 15, ʋ 7, ɪ. 25-31. 11. A.A. Tolkachev, at al. Large Apertured Radar Phased Array Antenna of Ka-band , Proceedings of the XVIII Moscow International Conference on Antenna Theory and Technology, Moscow, 1998, p.p.15-23. 12. A.A. Tolkachev, at al. High Gain Antenna Systems for Millimeter Wave Radars with Combined Electronical and Mechanical Beam Steering. IEEE International Symposium on Phased Array Systems and Technology. Boston, 1996, ɪ.p. 266-271. 13. E.N. Yegorov, A.L. Epshtein, G.Ya. Guskov, B.A. Levitan, G.V. Sbitnev, A.V. Shishlov. New Technologies in Multibeam and Scanning Antennas for Communication Systems. Proceedings of the APSCC'94 Workshop, Seoul, Korea,1994, p.p. 211 - 221. 14. E.N. Yegorov, V.V. Likhtenvald, G.V. Sbitnev. The system of Active Phased Array Antennas for satellite relay "Kupon". Proceedings of the XVIII Moscow International Conference on Antenna Theory and Technology, Moscow, 1998, p.p 55-61. 15. G.W. Fitzsimmons, B.J. Lamberty, D.T. Harvey, D.E. Riemer, E.J. Vertatschitsch, J.E. Wallace, A connectorless Module for an EHF Phased Array Antenna. Microwave Journal., 1994, vol. 37, No 1, p.114-126.

370


16. D.E. Riemer, Packaging Design of Wide-Angle Phased-Array Antenna for Frequencies Above 20 GHz, IEEE Trans., 1995, v. AP-43, No.9, p. 915-920. 17. T. Sakura, H. Aruga, S. Kitao, H. Nakaguro, A. Akaishi, N, Kadowaki, T. Araki. Development of Ka-band Multibeam Active Phased Array Antenna for Gigabit Satellite. Proceedings of the Fifth Ka-band Utilization Conference, Taormina, Italy, 1999, p.p. 515 522. 18. M. A. Kodis, D.S. Abraham D.D. Morabito Deep space C3: High Power Uplinks, AIP Conf. Proceedings 691, High Energy Density and High Power RF, Ed. S. H. Gold, G. S. Nusinovich, 2003, pp. 47-53.

ON ANTENNA SYSTEMS FOR SPACE APPLICATIONS Scientific and Remote Sensing Satellite Applications

Kees van ’t Klooster ESA Estec, Noordwijk, The Netherlands Abstract:

Examples of satellite projects accomplished by the European Space Agency (ESA) are broadly summarized with references and with attention to antenna aspects. Antennas are discussed for scientific or remote sensing applications. Limited power resources onboard the satellite, mass constraints and harsh space environmental factors dictate requirements, which often can only be satisfied after accurate efforts for design, realization and testing processes of antennas. Gain, coverage or pattern properties and polarization requirements must be satisfied for antennas. Requirements can be more demanding for microwave instrument antennas since instruments must measure accurately in absolute sense. Accurate knowledge of radiation behavior (vector behavior) is needed. High power transmission and very low power reception can dictate requirements for passive intermodulation (PIM). Multipaction aspects must be addressed to assure that no breakdown occurs because it might jeopardize antenna functionality. Quasi-optical techniques for high power applications are addressed in these proceedings. This paper describes with references, that there is some synergy in antenna development with the field of quasi-optics and high power rf-engineering; that there are developments and application scenarios for tools and techniques for antennas, which could be used for other applications discussed elsewhere in these proceedings and vice-versa.

Key words:

Satellite Antenna, Instrument Antenna, High Performance Antennas

1.

INTRODUCTION

Antenna system aspects are described after a review of a number of ESA satellite projects, in particular for (planetary) scientific missions and remote sensing applications. Antennas are needed for any satellite, telecom or microwave instrument functionality. Power resources onboard the satellites are limited and launch costs impose stringent requirements on several aspects for satellite sub-systems. Requirements for antennas are stringent for low mass, for environmental aspects related to exposure to harsh space conditions (temperature, radiation aspects, etc.) and survival of demanding launch-loads.


372

K. van’t Klooster

It makes a realisation of space antennas to an intriguing and demanding field of work. Satellite-antenna applications call for high accuracy, effective use of accurate design tools, specialised manufacturing and dedicated rf and environmental testing. When telecommunication antennas are used by satellites to transmit and receive client data geostationary or while orbiting the Earth, they must satisfy requirements for coverage. This often comes with a minimum gain requirement to be met within certain angular directions as seen from the satellite (coverage zone), while side-lobe control with maximum allowed levels is needed in directions outside the coverage. Alternatively, a number of independent beams might be required with sufficient isolation to serve different user areas. High power signals on transmission can co-exist simultaneously on the satellite with very weak signals in receive bands. This imposes a requirement for the antenna to be free of inter-modulation effects (PIM). When more transmitting carrier signals are used (serving different channels), passive intermodulation signals (weak signal) can be generated due to non-linear behaviour caused by physical hardware properties. Such a weak signal can appear as noise in one or more receiving bands at harmonic frequencies related to the different transmit signals. Such a situation is critical, when an antenna is used for both transmission and reception at the same time. In remote sensing applications, the antenna acts as microwave instrument sensor. It needs to be characterised sometimes in an absolute vector sense (amplitude, polarisation-state and phase) with requirements for stability over a long time, in different temperature situations in space. It leads to a necessity of accurate knowledge of absolute levels with minimum and maximum boundary constraints for complex radiation behaviour. Testing aspects can become very demanding and an example is given below with an antenna system for Cryosat. An example of results is presented to indicate progress in assessment of antenna performances, to indicate the accurate comparison between prediction and test results for phase measurements [8]. Other instrument sensor antennas are described in [8], are worth reading. High power concentration points may occur within antenna sub-systems. It could under certain conditions lead to voltage breakdown or multipaction, which may jeopardise functioning or even lead to damage. It requires careful design and testing if needed, to guarantee a multipaction-free antenna subsystem. Standards are developed [15] and dedicated workshops are organised by ESA in collaboration with national agencies [9]. Quasi optical techniques are employed by antenna systems operating at millimetre and sub-millimetre frequencies. Passive radiometers are an example where accuracy and coverage of certain frequency bands may call for

On Antenna Systems for Space Applications

373

channel de-multiplexing with reflecting and/or dichroic mirrors that act on Gaussian beams in, for example, a focal region of larger reflector systems. We introduced an application of polarisation considerations, using Laguerre expansions to represent vectorial field behaviour in a beam waveguide for millimetre wave radio-meters with a distinct set of modes [11]. The use of such methods is adopted in radio telescopes or ground-station antennas (beam-waveguides for instance). Alternative tools, based on general applicable and versatile physical optics analyses, have been made more and more accessible [12, 13], with clear progress shown in [14], using tools as described in [12]. The impact of reflection loss is important in radiometer antennas, in which small deviations in noise temperature must be determined. Examples are discussed of recent test results for samples related to the high performance, advanced composite reflector technology for the Planck project. The results have been obtained by the test facility at the Applied Physics Institute in Nizhny Novgorod. The latter facility was developed for testing reflection losses of mirrors and (diamond) windows for high power applications. Low reflection loss is very important in high power applications. We used the facility for measuring the reflection loss of reflector samples for extremely low power applications: the determination of reflection properties of advanced new composite and coated antenna materials for application in a radiometer antenna, for which a low reflection loss is mandatory. The application requires the receipt of extremely weak signals of cosmic background, which must be measured by the Planck project [6, 7]. The use of comparable tools and techniques for different applications is of interest, for example: analyses of beam-waveguides, multiband capabilities, and high accuracies in a determination of low reflection losses.

1.1

European Space Agency

Fifteen European countries work together in an inter-governmental organisation to provide and promote, for exclusively peaceful purposes, good boundary conditions for Space Science, Research and Technology and Space Applications. Space activities and programmes are elaborated with a long-term space policy and an industrial policy. Coordination takes place with national programmes. Certain directions are obligatory for participating members, for example, Space Science. There are also optional program elements, for telecommunications, for Earth remote sensing and for space transportation for example. It supports priorities within member-states. Successful developments can, after initial implementations, be transferred to new, specially established organisations, like Eumetsat for meteorological

374

K. van’t Klooster

satellites, Eutelsat for telecommunication applications, Arianespace (rockets, launchers), Inmarsat for maritime telecommunication applications. ESA headquarters are located in Paris, France and the main technical centre, ESTEC is located in Noordwijk, The Netherlands. Other ESA establishments are ESOC for operation of satellites in Darmstadt in Germany, ESRIN in Frascati in Italy and VILSPA in Villafranca in Spain. More extensive information about ESA, its programmes and implementation is found on the website www.esa.int with various informative links to program elements, ESA establishments, ongoing satellite projects, (whether in preparation or in orbit), and information about educational programs [ref 1, 2, 3]. Several conferences and workshops, related to different technical topic areas, are organised. See [10] for a variety of subjects.

2.

ESA’S SCIENTIFIC SATELLITES

2.1

Past and Ongoing Satellite Missions

A number of ESA scientific satellites have been launched (more than 25), and an increasing amount of applications calling for data communication over larger distances [2], because several satellites are being sent much farther out into the planetary system. The first interplanetary satellite for ESA was Giotto, which was guided close to the comet Halley with dedicated navigation procedures, based on very long baseline interferometry (VLBI). Extensive international collaboration (Russia, NASA, and ESA) within the so-called pathfinder project allowed precise navigation of Giotto close to Halley’s comet. This was based on interferometric data processing of data received from satellites, which passed by Halley before Giotto did this (for instance the Russian Vega mission). Other ESA scientific satellite missions included Hipparcos for accurate astrometry and the Infrared Space Observatory (ISO), both orbiting the Earth in dedicated elliptical orbits. Hipparcos completed its astrometry mission in an orbit, which was not planned (due to a failure of an engine). The mission’s success was made possible thanks to dedicated ESOC orbit analyses. Antennas on-board these satellites are used for telecommanding and telemetry and for data down linking. Antennas for such tasks on such scientific spacecraft – in a near-Earth orbit and for the required data volume – have been often realised with a wide angular coverage: low-gain and broad radiation patterns are of interest in order to access the satellites under a variety of satellite orientations during such elliptical orbits. A wide radiation pattern also implies, that the effects of scattering and/or reflections of the satellite


375

structure must be analysed in advance, in order to know the radiation performance of antennas, once they are placed on the satellite. It is important to understand the angular volume, in satellite coordinate frame, within which access for a link with the ground station on the Earth is possible. Such analysis task comes often back for every new satellite, because structures are different in configuration (with impact on the scattering). The interplanetary mission Ulysses was sent into a polar orbit around the Sun by means of gravity assistance from the planet Jupiter. Ulysses is now, in 2004, once again approaching Jupiter. Ulysses has a high gain S-X band antenna on-board and low gain antennas with cardioids-type of patterns. Power on-board the satellite is generated by a thermal-nuclear generator, because the distance to the Sun is too high to make efficient use of solar generators. The high gain S-X (dual) band antenna has a coaxial feed for S band with the X-band feed located in the central configuration of the coaxial S-band feed, slightly ex-centric located. The antenna permits finding information about pointing aspects, using information at S- and X-band assisted (almost like conical scanning. A picture and some other details are found in [16]. SOHO is the name of a satellite, which is navigated around the equilibrium point between the Earth and the Sun. The satellite monitors the Sun continuously and provides several first discoveries of comets plunging into the Sun. The link with the ground-station on the Earth is provided with an S-band mechanically moving reflector antenna. Cassini-Huygens is a NASA mission, jointly with ESA and the Italian Space Agency. Today, at the actual time of writing, Cassini entered into a Saturn orbit. The ESA provided element to the mission is a probe with instrumentation. This probe is expected to land on the moon Titan (on 14 Jan 2005). Some aspects are discussed below. There is collaboration with other agencies, in particular NASA. The Deep Space Network of NASA is used in a several cases for telecommunication and data-downlink of scientific data as recorded by the instruments on-board the satellites. Efforts are discussed between agencies worldwide for standard approaches for Deep Space telecommunications within committees like the CCSDS [4] to elaborate well-engineered, standardised approaches for space data handling systems (reduced cost/risk and permitting interoperability). Another ongoing satellite mission related to investigation of the space radiation environment is Cluster, a group of four satellites within Earth’s orbit with reception capability of low frequency signals. Long wire antennas are characteristic as receiving antennas on-board each satellite. The Newton mission (formerly called XMM) and the Integral mission are operating from a highly elliptical orbit around the Earth. Instrumentation on-

376

K. van’t Klooster

board provides observation capacity at ultra-short wavelengths in the X-ray regime. Newton has been the heaviest scientific satellite so far launched by ESA (Ariane V). The dedicated developed technology for the high precision X-ray lens system on XMM has found derived applications for ultra high precision millimetre and sub-millimetre wave radio telescopes. The reflecting surface of a prototype for the ALMA radio telescopes was realised with ‘XMM-derived’ panel technology [17]. New technologies for potential future applications are investigated on dedicated small satellites. For instance, electric propulsion is expected for a future mission to Mercury (Bepi-Colombo mission). Electric propulsion is currently functioning and provides an early demonstration on the SMART-I satellite. This satellite SMART-1 is currently spiralling away from the Earth with the Moon as its destination, using an electro-propulsion engine. A new topic area related to antennas is being studied: if the radio frequency signal as generated by the electro-propulsion engine can be controlled, such an engine can be used as RF- beacon in space. This subject has been initiated by ESA and is being studied under General Study program. The first dedicated planetary mission of ESA is Mars-Express, currently orbiting the planet Mars and providing regularly high-resolution images. The telecommand and telemetry, as well as data downlinking are fully controlled by ESOC with the new ESA Deep Space Antenna, which was realised in Australia (New Norcia). The realisation of the latter ESA Deep Space Antenna was needed, because of the increased number of (inter-) planetary missions and with the NASA Deep Space Network more and more loaded.

Figure 1. High Gain Antenna for the Rosetta Satellite.


377

Also the ESA mission Rosetta l, launched in early 2004, calls for the use of this Deep Space Antenna. Rosetta is expected to encounter a comet, to send a lander to the comet and to perform in-situ investigations, and this would be accomplished at a distance of several millions of kilometres away from the Earth. Fig.1 shows the high gain antenna for the Rosetta satellite. It operates in the allocated Deep Space telecommunication bands near 2 GHz (front-fed parabola) and near 8 GHz (Cassegrain configuration, with a dichroic sub reflector). The ground station antenna is an important element for such distant satellites and must perform with high reliability. The 35-meter antenna as constructed in Australia, provides accessibility for such distant satellite missions during several (about 6 to 8) hours a day. Optimum coverage for deep space missions requires antennas roughly spaced 120˚ apart over the globe, as is seen by NASA Deep Space Network with facilities in California (Goldstone USA), Spain and Australia. Currently ESA has a second ground station under construction near Madrid, Spain and a third station is under discussion.

Figure 2. ESA's first Deep Space Ground station Antenna in New Norcia in Australia.

Fig.2 shows a picture of the ESA 35 meter antenna. The schematic layout is shown in Fig.3. The dual reflector configuration is shaped for optimum efficiency and is fed by an S-X band beam-waveguide system inside the supporting tower. The beam-waveguide permits a rotation about elevation and azimuth axes with the rf radiation guided through the rotating junctions without little rf impact. Such beam-waveguide system can be optimised and analysed with dedicated tools, comparable to tools as applied elsewhere with quasi-optical

378

K. van’t Klooster

techniques. Consultants from JPL have carried out initial design-studies for the antenna erected in Australia. They have been involved in support to the antenna contractor. Detailed analyses under ESA supervision have been carried out also in Europe, results of which have been published in a number of occasions [14, 19, and 20]. The structural design of the antenna was realised by German specialists of the Vertex team, who were formerly involved in the design of the millimetre wave radio telescope at Pico Veleta in Spain. A turning head antenna with very good and stabile properties resulted, capable to operate at S and X-band deep space frequencies. It has also been prepared in part for later operation at Ka-band (also an allocated deep space frequency band). AZIMLITH AXIS SUBREFLECTOR

MAIN REFLECTOR

ELEVATION PORTION

F1

M2, Paraboka

M1 ELEVATION AXIS

AZIMUTH PORTION

ELEVATIONBEARNGS

Kaband M4a, Dichroic M3, Paraboka M1, moves with Bard Az M4b, plane M2, M3, M4 move with Az M5, M6, M7 are not moving

F3

AZIMUTHEEAFINGS F2

NOTTOSCALE

M8, Dichroic

M7, plane M5, Elipse

X-band S-band

PEDESTAL

Figure 3. Schematic Layout of the Deep Space Antenna of fig.2.

Fig.4 shows the pattern predictions for S- band frequency derived with GRASP8 antenna software, based on physical optics. Fig. 5 shows results for X-band. The influence of the complex response of the dichroic sub-reflector


379

is included in the analysis. In general, the offset geometry of the larger elliptically shaped reflector in the bottom of the beam-waveguide system, leads to some cross-polarisation level. The dichroic reflector is all-metal for low-loss and power handling reasons.

Figure 4. Deep Space Antenna Performance Prediction (S-band) [20].

It separates S- and X-bands and has a certain transfer/reflection response as a function of the angle of incidence. The overall cross-polarisation of a beam-waveguide depends on this. Final performances have been analysed and show an increase in cross-polar level, within specifications [19, 20]. Final performances are functional for the application and with the robust mechanical construction a reliable ground station antenna has been realised.

Figure 5. Deep Space Antenna Performance Prediction (X-band).

380

K. van’t Klooster

Early July 2004, the Cassini satellite will be put into orbit around Saturn. A few months later, orbit insertion around the moon Titan will follow. The ESA provided probe named Huygens, will be detached from the Cassini spacecraft and land on the moon Titan. The probe will carry out several measurements during the landing, whilst hanging under its parachute, if it survives the landing, and if there is battery power left after the landing. The measured data are transmitted to the Cassini spacecraft in orbit around Titan. Cassini receives the data with its high gain telecommunication antenna and stores it in its on-board memory. After the landing of Huygens on Titan, the Cassini spacecraft will be reoriented towards the Earth and will relay the data from its mass memory towards the Earth, using the NASA Deep Space Network. Huygens transmit power is about 10 watts and a residual carrier will have a strength of several watts. If it were possible to receive this weak signal on Earth in a narrow bandwidth of 1 Hz, this weak signal would require a very large aperture (>70 m). ESA, under its General Study program, has requested investigation of the feasibility of the signal reception using Very Long Baseline Interferometry (VLBI) techniques. The study results indicated such feasibility [5]. Following this, proposals have been submitted by JIVE for observation time at radio telescopes to the necessary supervising radio-astronomical entities (NRAO, EVN, and Australia). The receiving and recording capacity at the observing stations during the landing of Huygens on Titan needs some adaptation, (as of June 2004), but the initial plan is nearing completion. ESA is discussing with the Joint VLBI Institute (JIVE) in Europe in such a way, that JIVE oversees and elaborates the implementation of such unique experiment to receive the weak residual carrier. JIVE operates the most advanced 20-channel correlator (www.jive.nl), capable also to handle Mark 5 data recording systems based on disks. This Huygens VLBI tracking experiment is in interesting contrast (extremely low power) with the subject of the NATO Advanced Study Institute on Quasi Optical Techniques for High Power Applications. The mentioned VLBI experiment will first demonstrate a recording of very low power flux density (the low watt carrier signal of Huygens, which is controlled in the Huygens probe by an ultra stabile oscillator). Furthermore, using VLBI techniques, very low signal to noise levels are possible at the different radio telescopes. Correlation processing provides an increase in dynamic range, it permits to subdivide the reception band in very narrow frequency bins, this with the reception band sampled at the Nyquist sampling rate. The predicted scientific result is, as indicated in the feasibility study under the ESA General Study Programme, that the landing trajectory of Huygens can be determined with a resolution close to a kilometre, when


381

Huygens is hanging on its parachute and carried by the winds possibly present in the Titan atmosphere. As there is no telecommunication with the Cassini spacecraft during the landing, the reception of this carrier signal (on Earth) by means of radio telescopes, permits detection of activity by the Huygens probe, This is the only sign received by other means than by the Cassini spacecraft. A resolution of 1 kilometre at 1200.000.000 kilometres distance is two orders better than achievable with the Hubble Space Telescope. Such record resolution is possible thanks to a radio astronomical technique, called phase referencing. For the subject under investigation, usually an unknown radio-astronomical source, the weak Huygens signal is mapped against a celestial background, using so-called calibration sources within the angular field near the signal under observation. Such a technique permits observation with high (record) angular accuracy, thanks to the transfer of phase accuracy to the processing of the signal of interest. For details, one can consult the General Study Report on the ESA website www.esa.int.

2.2

Planned ESA Scientific Missions and Antenna Related Subjects

There are ESA planetary missions planned, like Venus Express and Bepi Colombo and possibly more to come. A second Deep Space Antenna, similar to the one discussed above, is under construction now in Spain. Its planned use is for data downlink in X-band for Venus Express. S-band is not implemented in this new ground-station antenna, only X-band, and in the future--Ka-band. The Venus Express mission relies on recurrent use of technologies as developed for the Mars Express mission. The high-gain antenna for Venus Express is different in size (thus in gain) and material properties. Venus is closer to the Sun, therefore, the thermal constraints imposed different resins for the reflector and dichroic sub-reflector. A dual frequency band operation with dedicated dichroic, associated optimisation processes, low loss, and technology implementations are of generic interest. Details about the Mars-Express and Venus Express high gain antenna are found in [21]. For the Bepi-Colombo satellite planned for launch towards Mercury, requirements are more demanding, being so close to the Sun, at 30% of the Earth to Sun distance, thus a factor 9 increase in radiation intensity from the Sun, compared to near-Earth orbits. The environmental temperatures can be high (or low during planet occultation) and dedicated processes, technologies and mechanisms are needed for such high gain antenna. Additional stringent

382

K. van’t Klooster

requirements include high accurate rf-performances for radio science experiments (amplitude and phase stability), which will permit accurate ranging data. The antenna is therefore investigated to develop necessary technologies. Bepi-Colombo is an international co-operation, based on the reciprocity of information and data exchange, and no exchange of funds between ESA and JAXA [22]. The Huygens experiment mentioned earlier (VLBI-tracking of the carrier signal coming from the probe), leads to novel and interesting navigation capabilities for planetary missions. This is important when it comes to accurate determination of angular windows for insertion into planetary orbits. Current recommendations (ǻ-DOR) to derive navigation data are described in [4]. Strong signals are transmitted with dedicated tones modulated on the carrier signal by the spacecraft and strong radio astronomical sources are used as celestial reference during interferometric observation with a number of Earth station antennas. The weak calibration sources employed during the Huygens experiment call for broadband observation of celestial reference sources for calibration purposes and so, a weak signal coming from the probe is compared in angular position with such reference sources. It may result, in the future, that monitoring of weak systematic signals of for instance, small satellites, probes or planetary landers permit accurate navigation, using VLBI techniques and phase referencing, and using celestial sources as a reference. Alternatively, exploiting the range of other parameter settings within the chain, potentially low-bit rate data links may be established and exploited. By using such interferometric techniques, in such a case one might use low gain antennas potentially, which is obviously convenient on-board a small satellite. In this context, an initial study deserves to be mentioned by the University of Toronto within ESA’s Aurora program. [35]. A number of radio astronomy satellites worldwide are being prepared for a mission in an orbit location close to the Sun-Earth equilibrium point L2 (Lagrange point). The L2-point is located about 1500000 kilometres away from the Earth in the direction away from the Sun. The location would permit un-obscured observation capability during the whole year of a celestial angular volume directed away from the Sun. This angular volume of observation moves with the Earth-Sun direction around the Sun during the year. Cosmic background radiation is measured today by the NASA mission MAP [23]. ESA has the mission Herschel (near-infrared sub-mm observatory) and Planck in a realisation phase for launch in 2007. Herschel will carry a Cassegrain telescope-antenna, realised with CSIC technology. It has a primary mirror (3.5 m diameter) [24] and in the secondary focus cooled detectors operating at -271 Kelvin. It is the largest telescope of its type ever


383

built and is realised in Europe within a contract activity between ESA and Atrium in Toulouse (France). The Planck satellite will measure cosmic

Figure 6. (left) Planck Satellite Configuration with radio-telescope antenna inside a baffle.

Fig. 6 shows the Planck satellite configuration with the dual reflector antenna subsystem with an effective aperture diameter of about 1.5 meters. The surface accuracy of the Planck telescope antenna is below 10 µm and the antenna system is located within a baffle to have very low impact of stray radiation. For more details, consults [25]. We have carried out highly accurate measurements of reflection loss on samples of both Planck reflector and baffle material. The conclusions of the tests were that there could be interesting phenomena: a baffle material well suited for optical applications, appeared to have two times higher reflection loss at millimetre wave frequencies than the expected losses (a type of

384

K. van’t Klooster

aluminum). For instance, the backside of the baffle material, also aluminum but not very pretty, appeared to be very good. It had very low reflection losses, almost comparable to values as expected from pure aluminum (fig.7). The Planck reflector is realised with dedicated composite materials (resins and carbon fibre), coated with dedicated materials and vacuum deposited aluminium. The finishing layer (plasil), deposits in vacuum, and protects the aluminium from corrosion. (Fig.9) The measurements have been carried out in the Applied Physics Institute (Fig.7, 8) in a band (100 – 200 GHz).

Figure 7. Schematic Description of Highly Accurate Reflection Loss Measurement Facility of Applied Physics Institute, Nizhny Novgorod, courtesy V. Parshin.

Reflectivity testing of composite materials with surface coatings is important to demonstrate actual values of the reflection losses. Extrapolation from tests carried out in a particular frequency band to expected results in another frequency band cannot be guaranteed, so testing in other frequency bands is therefore recommended [6,7]. For further details concerning ESA’s satellite missions within the scientific satellite program, the reader is (again) referred to the website www.esa.int under the science projects.


385

Figure 8. Quasi-Optical Test Facility at Applied Physics Institute in Nizhny Novgorod.

Figure 9. Results of reflection loss measurement of two samples (picture left) of Planck telescope reflector material (indicated with x and +) and baffle material (squares, backside of sample) and three curves for aluminum and silver as calculated and measured with calibration mirrors of Applied Physics Institute, courtesy V. Parshin, N. Novgorod.

386

3.

K. van’t Klooster

EXAMPLES OF ANTENNAS FOR REMOTE SENSING SATELLITES

A few sophisticated Earth Observation satellites have been into space, starting with meteorological satellites like the spinning Meteosat satellites (MOP - Meteosat Operational and its successor Meteosat Second Generation or MSG) [26]. A cylindrical electronically despun antenna keeps an antenna beam pointed towards the Earth, while the satellite is spinning at 100 revolutions per minute. (With every revolution one line is recorded, for an image of the Earth to be built up). For MSG one has expanded on imaging and spectral capability, compared to earlier MOP satellites. The electronically despun antenna mentioned, has been used in Europe for more than 25 years in Meteosat satellites. Moreover, for MSG, the UHF data collection function has also been realised with a cylindrical-switched UHF cylindrical antenna with crossed dipoles as elements. Electronically despinning doesn’t disturb the acquisition of the image; it has no mechanical movement in the antenna. The L-band antenna transmits the raw measured data towards the Earth and transmits processed images (which are up linked for re-distribution) to users. The antennas are described in [27]. Active remote sensing has seen strong developments in Europe with satellite missions like ERS-1 and ERS-2, which provided synthetic aperture radar data over a period more than 10 years. The active microwave instrument (AMI) on-board the ERS satellites can be connected to either the Wind-Scatterometer Antennas (WSA-mode) or to a Synthetic Aperture Radar antenna (SAR-mode), using a microwave-switching matrix. The latter switch-matrix routes the pulsed high-power (5.2 kilowatt peak) to the WSA or SAR antennas as necessary. During the development phase, a lot of attention has been spent to multipactor issues for components, for the switching matrix and for the antennas. With at that time novel technologies for the antenna, the critical locations for multipactor were investigated by analysis and by testing. One example is the main coupling slot in the slotted waveguide SAR antenna. The radiation characteristics of the 10 m long SAR antenna have been thoroughly tested before launch, even in full polarisation sense, although the antenna is polarised linearly (vertically). The planar near-field (ESA-Ericsson) facility has been used. ERS exploits only a single, vertical polarisation [16, 28]. Subsequent studies have allowed investigating limited multi-beam capabilities of SAR antennas, using low-loss, slotted waveguide approaches, as described in [29, 30, 31, 32, 33]. Although accurate tools were developed for passive slotted waveguide antennas [31], the passive antenna was abandoned. An active SAR antenna was developed for the next SAR missionENVISATof ESA. Slotted waveguide design tools 31]were used


387

within the SAR instrument for the Cassini mission by Alenia and slotted waveguide developments [32] and derived configurations contributed to very early developments for the dual-polarised slotted waveguide antenna configuration currently implemented in the active phased array configuration for TerraSAR-X [34]. A recent development for SAR antennas is based on an interesting hybrid type of approach. A reflector antenna is realised with a limited, dedicated set of beams to cover about 80 to 100 km wide strip in scansar mode, or 20 km in high-resolution strip map mode. Rolling of the satellite permits access to a range of incidence angles on the ground. Again, multipaction is an issue to be taken into account. Such type of approach permits to arrive at a simple satellite configuration, which can possibly be launched by a small (cheap) launcher [40]. A recent example of highly accurate prediction, manufacturing and realisation is presented with the antenna sub-system for the interferometric radar altimeter (SIRAL instrument) for Cryosat mission [8].

Figure 10. Cryosat SIRAL Antenna Configuration (Courtesy Saab-Ericsson).

The reader is referred to www.esa.int for background information about Earth observation missions. Accurate prediction results and verification by measurement have been presented, with some examples in [8] and are repeated here in part (courtesy Saab-Ericsson).

388

K. van’t Klooster

phase diff 0.6 0.5 0.4 0.3 0.2 0.1 -0.8

-0.6

-0.4

0 -0.2 -0.1 0

0.2

0.4

0.6

0.8

-0.2

Figure 11. SIRAL Antenna System Phase Distribution, predicted with GRASP (left) and Measurement (along Horizontal line) [8].

Progress in both modelling and antenna testing is reflected by such results (fig.11, 12). Note that accurate antenna measurements of phase distributions require additional verification techniques to determine effects of the test range. Also. the modelling of the antenna performances requires accurate assessment of all necessary details to be included in the antenna model (analysed with GRASP [12]). Requirements placed on phase response of the antenna sub-system have been several times more stringent than what is normally encountered for telecommunication applications. Thus, SIRAL antenna technology (fig.10) is of interest for telecommunication applications at higher frequency bands (Ka-band and above like Q and V band).

Figure 12. SIRAL Antenna System Phase Difference Distribution as Measured [8].


389

Correcting mirrors are discussed elsewhere in this paper. An approach is discussed, based on phase retrieval from a set of amplitude measurements. In antenna testing, phase retrieval is pursued for accurately setting the reflector panels of (sub) millimeter wave radio telescopes. We have explored the implementation of a technology based on a flexible membrane, for correcting the wave front of a (sub) millimeter wave radiometer antenna and demonstrated this in a laboratory test configuration. Artificial assumptions were made for a main-reflector assembly, which could suffer deformations based on in orbit thermal situations. A correctable sub reflector was introduced to correct for such deformations. It has been demonstrated that such approach can assist in correcting (compare to correcting mirrors in a gyrotron). For antenna applications, such technique can also be useful for applications as shaping of the beam and/or pointing correction or high accurate pointing of the beam. Correction of deformation errors has been demonstrated and thus it contributed to a better behavior of the dual reflector radiometer antenna. The necessary surface shape for the correcting mirror was derived with standard antenna synthesis techniques and we know that in this situation, there are more methods to derive the surface. A further optimization in the process was made, using Zernicke polynomial expansion, to arrive at convenient sample point settings for actuators for a set of deformation configurations to be corrected. The technological implementation includes considerations of membrane material and thickness aspects and adaptability for a set of different deformation cases. The result shows flexibility and a controllability of the membrane [39, 41, 42]. The nickel electroforming technique has been used for a prototype, sub-millimeter wave radio telescope in the ALMA project, as reported in [38]. Such new, advanced technologies are of generic interest. In [36] other complimentary references are found for antennas for remote sensing applications. This topic is too broad to include in this discussion. Rf instruments are as accurate as their calibration. Calibration is very important. For calibration in orbit of SAR instruments, one uses active calibrators or passive corner-reflectors. We did elaborate with investigations the use of reflector antennas (a deviating type of target) for calibration of radar cross section for SAR. In [37] these passive reflector antennas are discussed as potential calibrator and as shown recently, a relatively interesting result has been obtained. ERS SAR observations have assisted us to receive better knowledge of the properties of such calibrators.

390

4.

K. van’t Klooster

CONCLUDING REMARKS

Some antenna applications and related developments have been discussed in the context of mission applications. The subject is too extensive to be complete in a short exposition such as this. Only scientific and remote sensing satellite applications have been dealt with. References indicate a way to further information. It is shown, that several interesting antennas have been realised within ESA activities and that there is more to come. The use of comparable tools and techniques for different applications (antenna field or high-power applications) is of interest, like for instance (crosspolarisation) analyses of beam-waveguides, multiband aspects, and high accuracies in determination of low reflection losses.

5.

REFERENCES

[1]

ESA General Information: http://www.esa.int

[2]

ESA General Information on Scientific Satellites: http://www.esa.int/esaSC/index.html

[3] [4] [5]

ESA Education Programme: http://www.esa.int/esaED/index.html. http://www.ccsds.org/ In ESA Scientific Publication SP-544, obtainable from ESA, 2004. ‘VLBI Tracking of the Huygens Probe in the Atmosphere of Titan’, S.V. Pogrebenko, L.I. Gurvits, R. M. Campbell, I. M. Avruch, J.-P. Lebreton, C.G.M. van’t Klooster. Proceedings of ICATT 2003, September 2003, Conference Proceedings,, Sebastopol

[6]

‘Reflectivity of Antenna and Mirror Reflectors between 110 and 200 GHz’, Svetlana E. Myasnikova, Vladimir V. Parshin, Kees van ‘t Klooster, G.Valsecchi, [7] Proceedings of Antennas and Propagation Symposium, Columbus, USA June 2003, ‘Reflectivity of Antenna Reflectors: Measurements at Frequencies between 110 and 200 GHz’, C.G.M. van ‘t Klooster, V.V.Parshin, S.E.Myasnikova, [8] Proceedings EUSAR 2004, 25-27 May, Ulm Germany, ‘SIRAL Antenna Design and Performance of the SAR Interferometer Radar Altimeter Antenna Subsystem for CRYOSAT Mission’, M. Baunge, H. Ekstrom, M. Lindholm, M. Petersson, V. Sohtell, K. Woxlin, (Saab Ericsson), J.C.Angevain, P.deChateau-Thierry, J.David, L.Phalippou, L. Rey (Alcatel Space). [9] http://www.estec.esa.nl/conferences/03C26/index.html [10] http://www.estec.esa.nl/conferences/past_events.html [11] Proceedings Journees Internationales de Nice sur les Antennes (JINA), France, 1990. ‘Analysis of a Reflector Antenna with Quasi-Optical Front-End using Gaussian Beams’, G.A. van Dooren, C.G.M. van ‘t Klooster. [12] http://www.ticra.com and find information about software like GRASP for antennas.

[13] Proceedings of IEEE Antennas and Propagation Symposium, San Jose, 1990, ‘Physical Optics Analysis of a Beam Waveguide with Six Reflectors’, P.S.Kildal, J.Kuhnle, C.G.M. van ‘t Klooster, R. Graham.


391

[14] Proceedings of IEEE AP Symposium, Salt Lake City, July 2000, USA, ‘Analysis of Beam Waveguides for Reflector Antenna Systems’, M. Lumholt, K. Pontoppidan, K. van ‘t Klooster. [15] Proceedings of ESA Workshop on Multipactor and PIM, Sept. 2003, Estec, Noordwijk The Netherlands (http://www.estec.esa.nl/conferences/03C26/index.html), ‘An ECSS-E-20-01A Compatible Software Tool for the Evaluation/Prediction of Multipactor Breakdown for Single- and Multi-Carrier Signals’, S. Strijk (ESA/Estec). [16] Proceedings Journees Internationales de Nice sur les Antennes (JINA), France, 1990. ‘Antennas for Remote Sensing and Scientific Satellites’, C.G.M. van ‘t Klooster, N.E.Jensen, (invited paper). [17] Proceedings of the ICATT2003 Antenna Conference, Sebastopol, Ukraine, 2003, ‘A Spin-Off of Space Technology: Highly Accurate Reflector Panels for a Prototype ALMA Radio Telescope’, Kees van ‘t Klooster, Giuseppe Valsecchi, Josef Eder. [18] Proceedings of IEEE Antennas and Propagation Symposium, Columbus, 2003, USA. ‘A Reconformable Reflector for a Sub-Millimetre Wave Reflector Antenna’, C.G.M. van ‘t Klooster, F. Zocchi, P. Binda, H.H. Viskum. [19] Proceedings of ESA Workshop on TT&C, Estec 29-31 October 2001, Noordwijk. ‘Analysis of Frequency Selective Surfaces in Beam-waveguide Antenna’, M. Lumholt, K. Pontoppidan, K. van ‘t Klooster, P. Besso. [20] ESA Contract Report S-1005-03, ESA-Contract 13400/98, by Ticra. ‘Extended Analyses of the 35 m ESA Deep Space Antenna’, M. Lumholt. [21] Proceedings of 27th ESA Antenna Workshop on Innovative Periodic Antennas, Santiago de Compostela, 9-11 March 2004. ‘Mars Express and Venus Express High gain Antennas’, Caballero, R ; Palacios, C; Encinar, J. [22] http://www.esa.int/export/esaSC/120391_index_0_m.html or http://www.esa.int/science/bepicolombo and http://www.stp.isas.jaxa.jp/mercury/ [23] http://map.gsfc.nasa.gov/m_mm.html [24] http://www.esa.int/science/herschel [25] http://www.esa.int/science/planck

[26] http://www.eumetsat.de [27] Proceedings Conference Mathematical Methods in Electromagnetic Theory (MMET), ‘The Antenna Sub-System for Meteosat Second Generation Satelliktes, Modelling Tools and Needs’, C.G.M van ‘t Klooster, M. di Fausto, I. Florio, A.Rosa, B.Robert, VIIIth MMET, Kharkov, Ukraine, 2000, invited paper. [28] Proceedings Journees Internationales de Nice sur les Antennes (JINA), France, 1992. ‘ ERS-1 Antenna Performances in Orbit’, C.G.M. van ‘t Klooster, F.O. Aidt. [29] Proceedings of IEE – ICAP Conference, York, UK, 1991. ‘ A Dual-Beam Slotted Waveguide Array Antenna for SAR Applications’, M. Bonnedal, I. Karlsson, C.G.M. van ‘t Klooster. [30] Proceedings of IEEE Antennas and Propagation Symposium, London, Canada, 1991. ‘Multiple Beam Slotted Waveguide Antenna for Spaceborne Synthetic Aperture Radar’ C.G.M. van ‘t Klooster, M. Bonnedal, I.Karlsson, N.Chr. Albertsen. [31] Proceedings of PIERS Conference, 1994, Noordwijk, The Netherlands, ‘A Compound Slot Waveguide Array’, N. Chr. Albertsen, e.a. [32] Proceedings of IEEE Antennas and Propagation Conference, Chicago, USA, 1992. ‘Dual polarised Slotted Waveguide SARantenna’, L.Josefsson, C.G.M. van ‘t Klooster. [33] ESA Technology Quarterly, Preparing for the Future, Nr.1, September 1991. ‘Dual Beam Slotted Waveguide Antenna’, C.G.M. van ‘t Klooster.

392

K. van’t Klooster

[34] Proceedings EUSAR 2004, 25-27 May, Ulm Germany, ‘The TerraSAR-X Mission’, R. Werninghaus, e.a. [35] University of Toronto, General Studies, www.esa.int/GS http://www.utias-sfl.net/SpecialProjects/ARTEMISIndex.html [36] Proceedings of Conference, 12-14 April 1999, ‘Perspectives on Radio Astronomy: Technologies for Large Antenna Arrays’ edited by A.B. Smolders, M.P.van Haarlem, www.astron.nl [37] In Proc. JINA Conference, Nice 1998, ‘On the Use of Ground-Based Parabolic Reflector Antennas for External Calibration of Space-borne SAR’, van ‘t Klooster, C., Zherdev, P.A., Borisov, M, Gusevski, V, Zakharov, A.I., Buck, C.H. [38] In: Proc. of IEEE Antennas and Propagation Conf., ’High Precision Electroformed Nickel Panel Technology for Submillimetre Radio Telescope Antennas’, G. Valsecchi, J. Eder, G. Grisoni, C. van ‘t Klooster, L. Fanchi, 2003, Columbus, Ohio, USA. [39] In: Proc. of IEEE Antennas and Propagation Conf., ‘A Reconformable Reflector for a Sub-mmwave Reflector Antenna’, F.Zocchi, P.Binda, H.H.Viskum, van ‘t Klooster, K. [40] Proceedings EUSAR 2004, 25-27 May, Ulm Germany, ‘A Low Cost Mutlifeed Antenna’, Chr.Heer, B. Grafmueller, L. Kanderhag, M.Viberg, Kees van ’t Klooster. [41] Proceedings of 25th ESA Antenna Workshop Estec, 18-20 September 2002, Noordwijk. “Reconformable Sub-reflector for Sub-Millimetre Wave Radiometer”, F.Zocchi, G.Valsecchi, H. Viskum, K. van ‘t Klooster. [42] In AIAA Proceedings, Yokoma, April, 2003, Japan, “Corrective Sub Reflector for Millimetre and Sub-Millimetre Wave Appplications”, H.H. Viskum, C. van ‘t Klooster, F. Zocchi, P.Binda, R. Wagner.

INTENSE MICROWAVE PULSE TRANSMISSION THROUGH ELECTRICALLY CONTROLLED FERRITE PHASE SHIFTERS

N. Kolganov1, N. Kovalov1, V. Kashin2, E. Danilov2 1

Institute of Applied Physics, Nizhny Novgorod, Russia; Special Design Bureau “Almaz”, Moscow, Russia.

2

Abstract:

Transmission of X-band ~1 MW pulses through a Faraday phase shifter is followed by (a) distortion of the RF envelope if pulse is longer than ~ 10 ns, and (b) reduction of the phase shifter effective electric length after a series of pulses. The ferrite degradation is reversible: after a cycle of magnetization, the pulse form is reproduced. These effects should be taken into account at designing ferrite lenses for high-power microwave pattern control.

Key words:

high power microwaves, beam scanning, phase shifter, ferrites, pulse energy limitation.

Electrically controlled ferrite phase shifters usually operate with the RF magnetic field H small compared with the coercive field H c . However in high power pulsed microwave systems the latter condition may be violated. This paper describes results of an experiment [1] with a Faraday phase shifter that operated under condition H !! H c . The phase shifter is represented by a section of circular cross section waveguide filled with a ferrite 3C418. The input RF pulse (shown in Fig. 1) had a carrier frequency of 10 GHz, a peak power up to 1 MW, and a duration near 20 ns; however, because of intra-pulse modulation, the bandwidth was ~100 MHz.


394

N. Kolganov, N. Kovalov, V. Kashin, E. Danilov

Figure 1. Envelope of pulse incident onto the phase shifter.

Figure 2. Envelope of pulse transmitted through phase shifter with I = 0q.

Intense Microwave Pulse Transmission

395

Figure3. Envelope of pulse transmitted through phase shifter with I = 650q.

For these tests, the residual magnetization direction coincided with the direction of wave propagation. The H11 wave mode was circular polarized, but at the ends of the phase shifter it was converted into the H 10 mode of rectangular cross section waveguide. Before injection of the microwave pulse, the ferrite was magnetized by means of a procedure shown in Fig. 4: x at first a negative sufficiently-large external field H 0 put the ferrite from a previous state BS ' to the saturated state 1; x then a positive external field H 0 put the ferrite into state 2; x finally the external magnetic field was put to zero and the ferrite came to the operating state B S . During RF pulse transmission, the external magnetic field was absent.

396


2 BS

BS '

1

Figure 4. Ferrite magnetization procedure within the saturated magnetization loop. (Hc = 0.9 Oe, Br = 1.4 kG).

The dependence of the effective electric length of the phase shifter on the residual magnetization was measured by means of a special low power microwave scheme, before and after a sequence of RF pulses, with the switching and measurements performed during 3-4 minutes. For definiteness, the length I 0 was attributed to the residue magnetization B0 Br | 1400 Gs . Correspondingly, the residual magnetizations B0 Br | 1400 Gs and B0 Br 0 resulted in I 650q and I 360q lengths. The measurement precision was within r 2q . Compared to the input pulse, the output pulse was shortened and distorted, as shown in Figs. 2 and 3, presumably owing to excitation of ferrite spin waves. After re-magnetization of the ferrite to its primary state, the pulses were reproducible. After transmission of a sequence of microwave pulses through the phase shifter, its electric length changed, as shown in Figs. 5 and 6; but later, i.e., after a few days, it remained constant. After transmission of a train of pulses, the larger the initial magnetization of the ferrite, the larger was found

Intense Microwave Pulse Transmission

397

to be the defect in the electric length. After a magnetization cycle (see Fig. 4) the ferrite returned to its primary state.

Figure 5. Dependence of defect in electric length for I

'I

on the number of pulses in a train N

90 q ; curves 1-5 correspond to peak powers of 50; 100; 200; 400 and 800 kW respectively.

Figure 6. The same as as Figure 5, but for I

0q .

398


Thus, the ferrite degradation after high power microwave pulse transmission is seen to be reversible. To reduce the degradation, it is necessary to limit the RF pulse energy. For instance, a lens composed of the above described phase shifters might scan wave flows of ~1 MW/cm2 density, if the pulse duration were in the range 5-8 ns.

REFERENCE 1.

E.A.Danilov, V.A.Kashin, N.F.Kovalev, H.G.Kolganov, Electronika (In Russian). 2001. v.46, N8, pp. 1007-1010.

Radiotechnika

and

INDEX OF AUTHORS

Kalynova, G, 3, 15 Kapilevich, B. 25 Kashin, V. 393 Kasparek, W. 115, 241 Katsenelenbaum, B. 65 Kharchev, N. 115 Kinkead, A. 199 Kirilenko, A. 41 Koldanov, V. 199 Kolganov, N. 393 Kolik, L. 115 Korchemkin, Yu. 165 Korovin, S. 131 Kovalev N. 95, 177, 393 Kulik, D. 41 Kumric, H. 241 Kusyi, O. 65 Kuzikov, S. 147, 199 Lapierre, L. 305 LaPointe, M. 147, 199 Laqua, H. 241 Leuterer, F. 241 Likin, K. 115 Lisak, M. 305 Litvak, A. 147 Lobaev, M. 199 Lukovnikov, D. 147 Lurie, Y. 253 Malygin, V. 3, 147 Martín, R. 115 Mesiats, G. 283 Michel, G. 241, 325 Milevsky, N. 165 Neilson, J. 55 Nezhevenko, O. 147, 199 Petelin, M. 147, 185, 283 Petrov, A. 115 Phelps, A. 105, 131

Abubakirov, E. 95 Anderson, D. 305 Arnold, A. 325 Batanov, G. 115 Belousov, V. 3 Blyakhman, A. 273, 283 Bogdashov, A. 15, 147 Bratman, V. 105 Bruns, W. 73 Buyanova, M. 305 Caryotakis, G. 185 Chirkov, A. 3, 147 Clunie, D. 283 Cross, A. 105 Dammertz, G. 241 Danilov, E. 393 Denisenko, V. 165 Denisov, G. 3, 15, 105, 147 Drumm, O. 325 Erckmann, V. 241 Fedorov, V. 165 Fernández, A. 115 Fix, A. 147 Gantenbein, G. 241 Ginzburg, N. 131 Gold, S. 199 Golubiatnikov, G. 297 Gorbachev, A. 199 Grünert, M. 241 Harris, R. 283 Henke, H. 73 Hirshfield, J. 147, 199 Holzhauer, E. 241 Ilin, V, 3 Isaev, V. 199 Ivanov, O. 199 Jin, J. 325 Jordan, U. 305

399

400 Pinhasi, Y. 219, 253 Piosczyk, B. 325 Plaum, B. 241 Popov, L. 3 Postoenko, G. 185, 283 Puech, J. 305 Rodin, Yu. 147 Rostov, V. 131 Rud, L. 41 Rzesnicki, T. 325 Samsonov, S. 105 Sarksyan, K. 115 Sazontov, A. 305 Schamiloglu, E. 177 Scheitrum, G. 185 Schwörer, K. 241 Semenov, V. 305 Serdobintsev, G. 147 Shishlov, A. 353 Shmelyov, M. 147

Index of Authors Sombrin, J. 305 Thumm, M. 325 Tkachenko, V. 41 Tolkachev, A. 353 Tulpakov, V. 95 Turchin, I. 185 Udiljak, R. 305 van’t Klooster, K. 371 Vdovicheva, N. 305 Vikharev, A. 199 Voitovich, N. 65 Wacker, R. 241 Wagner, D. 241, 325 Wardrop, B. 283 Weissgerber, M. 241 Yahalom, A. 219, 253 Yakovlev, V. 147 Yalandin, M. 131 Yang, X. 325 Yegorov, E. 353

Quasi-Optical Control of Intense Microwave Transmission

Microwave Transmission Networks, Second Edition

Quasioptical Systems: Gaussian Beam Quasioptical Propogation and Applications (IEEE Press Series on RF and Microwave Technology)

Quasioptical Systems: Gaussian Beam Quasioptical Propogation and Applications (IEEE Press Series on RF and Microwave Technology)

Microwave Transmission Networks: Planning, Design, and Deployment

Modelling Parasite Transmission and Control

Transmission

Transmission

Transmission

Transmission

Transmission

Microwave Radio Transmission, Design Guide, Second Edition (Artech House Microwave Library)

Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications

Intense Electron and Ion Beams

Atoms in Intense Laser Fields

Transmission of the Flame

The Transmission of Affect

MICROWAVE PROCESSING OF MATERIALS

Digital Transmission

Aesthetic Applications of Intense Pulsed Light

Final Transmission

Terminal Transmission

Analysis of Multiconductor Transmission Lines

Fundamentals of Digital Television Transmission

The Transmission of Chinese Medicine

microwave applications

Microwave Measurements

Microwave Projects

Microwave Applications

Microwave Technology

Atoms in Intense Laser Fields

Quasi-Optical Control of Intense Microwave Transmission

Microwave Transmission Networks, Second Edition

Quasioptical Systems: Gaussian Beam Quasioptical Propogation and Applications (IEEE Press Series on RF and Microwave Technology)

Quasioptical Systems: Gaussian Beam Quasioptical Propogation and Applications (IEEE Press Series on RF and Microwave Technology)

Microwave Transmission Networks: Planning, Design, and Deployment

Modelling Parasite Transmission and Control

Transmission

Transmission

Transmission

Transmission

Transmission

Microwave Radio Transmission, Design Guide, Second Edition (Artech House Microwave Library)

Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications

Intense Electron and Ion Beams

Atoms in Intense Laser Fields

Transmission of the Flame

The Transmission of Affect

MICROWAVE PROCESSING OF MATERIALS

Digital Transmission

Aesthetic Applications of Intense Pulsed Light

Final Transmission

Terminal Transmission

Analysis of Multiconductor Transmission Lines

Fundamentals of Digital Television Transmission

The Transmission of Chinese Medicine

microwave applications

Microwave Measurements

Microwave Projects

Microwave Applications

Microwave Technology

Atoms in Intense Laser Fields

Recommend Documents