This monograph presents a comprehensive description of the theoretical foundations and experimental applications of spec...

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Hans R. Griem

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This monograph presents a comprehensive description of the theoretical foundations and experimental applications of spectroscopic methods in plasma physics research. The first three chapters introduce the classical and quantum theories of radiation, with detailed descriptions of line strengths and high density effects. The next chapter describes theoretical and experimental aspects of spectral line broadening. The following five chapters are concerned with continuous spectra, level kinetics and cross sections, thermodynamic equilibrium relations, radiative energy transfer, and radiative energy losses. The book concludes with three chapters covering the basics of various applications of plasma spectroscopy to density and temperature measurements and to the determination of some other plasma properties. Over one thousand references guide the reader not only to original research covered in the chapters, but also to experimental details and instrumentation. This will be an important text and reference for all those working on plasmas in physics, optics, nuclear engineering, and chemistry, as well as astronomy, astrophysics and space physics.

CAMBRIDGE MONOGRAPHS ON PLASMA PHYSICS General Editors: M.G. Haines, K.I. Hopcraft, I.H. Hutchinson, C M . Surko and K. Schindler

PRINCIPLES OF PLASMA SPECTROSCOPY

CAMBRIDGE MONOGRAPHS ON PLASMA PHYSICS 1. D. Biskamp Nonlinear Magnetohydrodynamics 2. H. R. Griem Principles of Plasma Spectroscopy

Principles of Plasma Spectroscopy Hans R. Griem University of Maryland at College Park

CAMBRIDGE UNIVERSITY PRESS

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcon 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Cambridge University Press 1997 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1997 First paperback edition 2005 Typeset in 10/13pt Times A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication data Griem, Hans R. Principles of plasma spectroscopy / Hans R. Griem. p. cm. - (Cambridge monographs on plasma physics ; 2) Includes bibliographical references and index. ISBN 0 521 45504 9 (hardback) 1. Plasma spectroscopy. I. Title. II. Series. QC718.8.S6G75 1997 530.4'46-dc21 96-37158 CIP ISBN 0 521 45504 9 hardback ISBN 0 521 61941 6 paperback

Contents

Preface

x

Symbols

xii

1 1.1 1.2 1.3 1.4 1.5 1.6

Classical theory of radiation Electromagnetic equations and fields from moving charges Emission of radiation Absorption by harmonic oscillators Radiation damping Scattering of radiation Optical refractivity

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

Quantum theory of radiation Quantum theory of particles and fields Radiative transition probabilities Density of final states of the radiation field and normalization of the vector potential Spontaneous emission Absorption Induced emission Natural line broadening Scattering of radiation Resonance fluorescence Optical refractivity

17 18 20 22 23 27 30 33

3 3.1 3.2 3.3 3.4 3.5 3.6

Oscillator and line strengths Relative line strengths Absolute line strengths for one-electron atoms Line strengths for two- and more-electron atoms Sum rules Plasma effects on oscillator and line strengths Measurements of radiative transition probabilities

35 37 39 43 45 49 52

vii

1 2 3 4 6 7 9 11 11 14

viii 4 4.1 4.2 4.3 4.4 4.5 4.6

Contents

4.7 4.8 4.9 4.10 4.11

Spectral line broadening General theory of pressure broadening Electron scattering theory of line broadening Ion microfields Plasma screening of electron collisions Kinetic theory models of dynamical ion effects Collisional narrowing and correlations between Doppler and Stark broadening Stark broadening calculations Effects of neutral perturbers Line profile and width measurements Line shift and asymmetry measurements Effects of plasma wave fields

54 57 66 68 78 83 88 90 100 105 116 122

5 5.1 5.2 5.3 5.4 5.5 5.6

Continuous spectra Photoionization cross sections Approximate calculations of photoionization cross sections Continuum absorption coefficients Continuum emission coefficients High density effects Experiments

132 134 136 140 144 147 151

6 6.1 6.2 6.3 6.4 6.5

Cross sections and level kinetics Kinetic models Collisional ionization and three-body recombination Collisional excitation and deexcitation Autoionization and dielectronic recombination Heavy particle collisions

156 158 167 172 177 183

7 7.1 7.2 7.3 7.4 7.5 7.6

Thermodynamic equilibrium relations Thermodynamic equilibrium and statistical mechanics Ionization equilibrium equations High density corrections Partition functions Equations of state for dense plasmas Validity conditions for local thermodynamic equilibrium

187 188 192 193 203 210 212

8 8.1 8.2 8.3 8.4 8.5

Radiative energy transfer Effective absorption coefficients Effective emission coefficients and redistribution functions Radiative transfer equation and source function Transient problems and escape factors Reconstruction of source distributions from intensities

221 222 225 230 235 239

Contents

ix

9 9.1 9.2 9.3 9.4

Radiation losses Bremsstrahlung losses Recombination radiation losses Line radiation losses Numerical calculations of radiation losses

244 245 248 250 252

10 10.1 10.2 10.3 10.4

Spectroscopic density measurements Densities from spectral line widths and profiles Densities from absolute continuum intensities Densities from absolute line intensities Electron densities from relative line intensities

258 259 268 271 273

11 11.1 11.2

279 281

11.3 11.4 11.5 11.6 11.7 11.8

Spectroscopic temperature measurements Relative intensities of lines of the same atom or ion Relative line intensities of subsequent ionization stages of the same element Lines from isoelectronic transitions of different elements Relative continuum intensities Ratios of line and continuum intensities Intensities from optically thick layers Line intensities in rapidly ionizing plasmas Doppler profiles

12 12.1 12.2 12.3 12.4 12.5 12.6

Other diagnostic applications of plasma spectroscopy Charge exchange recombination spectroscopy Beam emission spectroscopy (BES) Polarization spectroscopy Magnetic field measurements Electric field measurements Effective charge measurements

300 301 306 312 314 318 320

References

324

Index

362

283 287 290 291 292 296 297

Preface

This book was written for the benefit of young researchers in diverse disciplines ranging from experimental plasma physics to astrophysics, and graduate students wanting to enter the interdisciplinary area of research now generally called plasma spectroscopy. The author has attempted to develop the theoretical foundations of the numerous applications of plasma spectroscopy from first principles. However, some familiarity with atomic structure and collision calculations, with quantum-mechanical perturbation theory and with statistical mechanics of plasmas is assumed. The emphasis is on the quantitative emission spectroscopy of atoms and ions immersed in high-temperature plasmas and in weak radiation fields, where multi-photon processes are not important. As in the author's previous books on plasma spectroscopy and spectral line broadening written, respectively, over three and two decades ago, various applications are discussed in considerable detail, as are the underlying critical experiments. Hopefully, the reader will find the numerous references useful and current up to the latter part of 1995. They provide advice concerning access to basic data, which are needed for the implementation of many of the experimental methods, and to descriptions of instrumentation. The author has once more benefited from his experience in teaching special lecture courses at the University of Maryland and recently also at the Ruhr University in Bochum and some of its neighboring institutions. His thanks are not only due to the advanced graduate students and fellow scientists in these courses but also to many colleagues at these and other institutions, who so generously provided advice, criticism and new research results. Of all these colleagues, I owe particular thanks to Ray Elton and to John Hey for their sustained and critical help with the manuscript. Any remaining errors or deficiencies are entirely my responsibility, and I would be grateful if they were communicated to me.

Preface

xi

I am most grateful to Dorothea F. Brosius, who so patiently and professionally prepared numerous drafts and the final computerized manuscript. Very special thanks go to her and to my wife Irmgard for all the help and encouragement.

1996, College Park, Maryland

Symbols

Symbol

Definition

a a0 a

ratio of ion-ion separation and Debye radius Bohr radius (unit) polarization vector transition probability (per unit time) for spontaneous emission (m —> n) transition probability for autoionization Fourier transform of fieldstrength distribution ampere (unit of current) vector potential vector potential Fourier components bound-bound beam emission spectroscopy magnetic fieldstrength velocity of light coefficient for three-body recombination charge exchange Fourier transform of line shape (dipole autocorrelation function) coulomb (unit of charge) charge exchange recombination spectroscopy collisional-radiative capture radiative cascade spherical Racah tensor (rank 1) line shift dielectronic capture coefficient

Anm A

mj

A(k) A A bb BES B c Cm CX

C(s) C

CHERS CR

CRC

CU) d djm

Introduced on Page

Xll

70 40 17 19 177 68

2 2

12 250 306

2 2

161 255 59 2 218 161

215, 301 39

55 178

Symbols

xiii

differential scattering cross section 28 differential oscillator strength 148 dielectronic recombination 249 dipole moment 64 diffusion coefficient 89 dipole transition operator 60 factors for dipole transition matrix elements 45 displacement vector 9 conditional average of time-dependent dipole 85 operator e charge of electron 2 Em excitation energy 160 En energy of state n 15 Er energy of radiation field 11 £oo ionization energy 104 EOJ field energy per mode 13 Ep Fermi energy 75 EH ionization energy of hydrogen 46 EL(CO) binding energy of lowest bound state for 145 radiative recombination Eza~l (groundstate) ionization energy of atom a 160 with ionic charge z — 1 ESB excitation saturation balance 217 E electric fieldstrength 2 Ew Fourier component of E 4 / final state quantum number 57 fj frequency of collisions of type j 65 fmn absorption oscillator strength (n -> m) 21 fnm emission oscillator strength (m —• n) 22 /(ri,r2, * * •) correlation function 75 /(£) Maxwell energy distribution 167 f(0, (j)) scattering amplitude 66 fb free-bound 248 // free-free 247 F free energy 203 Fo Holtsmark's normal fieldstrength 68 FQ fieldstrength corresponding to a perturbing 77 ion at the mean ion-ion separation F(r, s) relaxation (unified) theory function 60 FWHM full width between half of maximum intensity points 54 Fm flux of particles in state m 166 F' gradient of micro-fieldstrength 78 df/dE dr d D D Du D2, ... D D(F, t)

xiv F(r, s) g geff gn g(rjjc) g(co) g G Gw G(r; s, sf) G(Aco) G(0) h{*u r2, —) H H Hi Ho(P) H[ H(P) Jf i iron IT(CO)

J(co,Q) j J J J(co) k k k K K ^max f L L(co) LTE

Symbols electric fieldstrength 64 Lande factor 316 effective Gaunt factor for line widths 94 statistical weight 17, 191 two particle correlation function 69 Gaunt factor 137 effective Gaunt factor for inelastic cross 173 sections factor in semiempirical line width formula 94 (radial) continuum wave function 135 Green's function 61 kinetic theory line profile function 86 natural logarithm of A(k) 75 Ursell cluster functions 75 Hamilton operator 11 radiation flux 231 interaction Hamiltonian 14 Holtsmark distribution function 69 effective interaction Hamiltonian 16 distribution of reduced fieldstrength 70 Baranger's collision operator 65 initial state quantum number 57 spectrally integrated line intensity of m to n 281 transition intensity of blackbody radiation (Planck's law) 23 spectral and directional intensity 21 (one-electron) total angular momentum 39 quantum number total angular momentum quantum number 36 beam particle current 306 mean intensity 222 wavenumber 17 Boltzmann constant 23, 191 transform variable associated with the 68 microfield-strength plasma wavenumber 79 second moment of the directional intensity 231 maximum plasma wavenumber 80 single electron orbital angular momentum 39 quantum number total orbital angular momentum quantum number 44 line shape function 54 local thermodynamic equilibrium 156

Symbols J£{CD)

m m(me) M M, Mf n n rib nc ncj ncr flmax rica no n} n(co) N Ne(N) Nm Np(Nt) N p p(ri>r2> * * ) p P P Pa Pe Pe Pnm P(F) P(co) PLTE P P P^) qo qco, n) 15 probability distribution for field vectors 68 spectral power 57 partial local thermodynamic equilibrium 156 volume polarization 9 canonical momentum 11 dipole transition operator 38 maximum momentum transfer 174 destruction, creation operators 12 heat 190 average ion charge 199

xvi

Symbols

distribution function quasisteady state mean electron-electron separation classical electron radius population coefficient for level m (from the ground state) population coefficient for level m ri(m) (by recombination) component q of tensor operator r'1^ position vector r 1? ratio of doubly and singly ionized perturbers reactance matrix i? R radiation cooling rate constant R line intensity ratio ratio of ionization and photon emission rates R internuclear distance for level crossing R» (one-electron) radial wave function RnAr) minimum impact parameter Ro ion-sphere radius Ro R(a>,Q;co',Q') redistribution function total electron spin quantum number S spectral density of charge density fluctuations S relative intensity of plasma satellites S ionization rate coefficient S entropy S S -matrix for collision j S: line strength Snm probability for photon to remain in a plasma S" after n scatterings source function S(co) Poynting vector t(s,O) time development operator temperature T electron, ion and atom temperatures Te, Tz, Ta ion temperature if various ion species are Tt thermalized Laplace transform of time development T{co) operator Tr trace ratio of kinetic electron energy and excitation u energy spectral energy density of radiation field

6(r)

QSS re ro ro(m)

/f>

s

60 217 73 4 162 162 37 2 71 93 247 281 307 185 39 174 198 227 45 79 124 158 190 65 36 239 230 4 59 54 279 280 63 59 173 222

Symbols u(s, 0) U Un UQ v w W W Wmn W(F) W{¥ f —> F) W x Xmg z z z z zeff zn zp zf Z Za Zn a a a a a ccd P /? Pi y y ynm y(u) Tu df(p) AEZ

xvii

interaction representation time evolution operator 59 interaction Hamiltonian 60 time-independent wave function 15 spectral energy density of wave field 123 velocity 2 half (HWHM) line width 55 Racah coefficient 38 number of microscopic distributions 189 transition probability for absorption 22 microfield distribution function 58 transition rate between microfield states 85 weber (unit of magnetic flux) 2 displacement vector 3 excitation rate coefficient (ground state to state m) 160 effective nuclear charge 3 nuclear charge 40 charge state label 158 ionic charge 159 effective ionic charge 271, 320 number of bound electrons in n-th shell 159 charge of perturbing ions 69 effective charge 246 number of bound electrons (per atom or ion) 48 internal partition function 190, 193 effective nuclear charge for n-th shell 253 Planck-Larkin partition function 207

fine-structure constant ion broadening parameter phase angle recombination rate coefficient a-particle effective dielectronic recombination coefficient reduced micro-fieldstrength ratio of ionization and thermal energies escape factor decay (damping) rate set of quantum numbers (radiative) damping constant effective Gaunt factor ion-ion coupling parameter phase shift of free electron wave function reduction of ionization energy

3 92 123 158 301 180 68 168 237 6 37 27 173 73 208 140, 195

xviii AZi

Aco *d

era e' e" e(K,Aoi) e(

CAMBRIDGE MONOGRAPHS ON PLASMA PHYSICS General Editors: M.G. Haines, K.I. Hopcraft, I.H. Hutchinson, C M . Surko and K. Schindler

PRINCIPLES OF PLASMA SPECTROSCOPY

CAMBRIDGE MONOGRAPHS ON PLASMA PHYSICS 1. D. Biskamp Nonlinear Magnetohydrodynamics 2. H. R. Griem Principles of Plasma Spectroscopy

Principles of Plasma Spectroscopy Hans R. Griem University of Maryland at College Park

CAMBRIDGE UNIVERSITY PRESS

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcon 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Cambridge University Press 1997 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1997 First paperback edition 2005 Typeset in 10/13pt Times A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication data Griem, Hans R. Principles of plasma spectroscopy / Hans R. Griem. p. cm. - (Cambridge monographs on plasma physics ; 2) Includes bibliographical references and index. ISBN 0 521 45504 9 (hardback) 1. Plasma spectroscopy. I. Title. II. Series. QC718.8.S6G75 1997 530.4'46-dc21 96-37158 CIP ISBN 0 521 45504 9 hardback ISBN 0 521 61941 6 paperback

Contents

Preface

x

Symbols

xii

1 1.1 1.2 1.3 1.4 1.5 1.6

Classical theory of radiation Electromagnetic equations and fields from moving charges Emission of radiation Absorption by harmonic oscillators Radiation damping Scattering of radiation Optical refractivity

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

Quantum theory of radiation Quantum theory of particles and fields Radiative transition probabilities Density of final states of the radiation field and normalization of the vector potential Spontaneous emission Absorption Induced emission Natural line broadening Scattering of radiation Resonance fluorescence Optical refractivity

17 18 20 22 23 27 30 33

3 3.1 3.2 3.3 3.4 3.5 3.6

Oscillator and line strengths Relative line strengths Absolute line strengths for one-electron atoms Line strengths for two- and more-electron atoms Sum rules Plasma effects on oscillator and line strengths Measurements of radiative transition probabilities

35 37 39 43 45 49 52

vii

1 2 3 4 6 7 9 11 11 14

viii 4 4.1 4.2 4.3 4.4 4.5 4.6

Contents

4.7 4.8 4.9 4.10 4.11

Spectral line broadening General theory of pressure broadening Electron scattering theory of line broadening Ion microfields Plasma screening of electron collisions Kinetic theory models of dynamical ion effects Collisional narrowing and correlations between Doppler and Stark broadening Stark broadening calculations Effects of neutral perturbers Line profile and width measurements Line shift and asymmetry measurements Effects of plasma wave fields

54 57 66 68 78 83 88 90 100 105 116 122

5 5.1 5.2 5.3 5.4 5.5 5.6

Continuous spectra Photoionization cross sections Approximate calculations of photoionization cross sections Continuum absorption coefficients Continuum emission coefficients High density effects Experiments

132 134 136 140 144 147 151

6 6.1 6.2 6.3 6.4 6.5

Cross sections and level kinetics Kinetic models Collisional ionization and three-body recombination Collisional excitation and deexcitation Autoionization and dielectronic recombination Heavy particle collisions

156 158 167 172 177 183

7 7.1 7.2 7.3 7.4 7.5 7.6

Thermodynamic equilibrium relations Thermodynamic equilibrium and statistical mechanics Ionization equilibrium equations High density corrections Partition functions Equations of state for dense plasmas Validity conditions for local thermodynamic equilibrium

187 188 192 193 203 210 212

8 8.1 8.2 8.3 8.4 8.5

Radiative energy transfer Effective absorption coefficients Effective emission coefficients and redistribution functions Radiative transfer equation and source function Transient problems and escape factors Reconstruction of source distributions from intensities

221 222 225 230 235 239

Contents

ix

9 9.1 9.2 9.3 9.4

Radiation losses Bremsstrahlung losses Recombination radiation losses Line radiation losses Numerical calculations of radiation losses

244 245 248 250 252

10 10.1 10.2 10.3 10.4

Spectroscopic density measurements Densities from spectral line widths and profiles Densities from absolute continuum intensities Densities from absolute line intensities Electron densities from relative line intensities

258 259 268 271 273

11 11.1 11.2

279 281

11.3 11.4 11.5 11.6 11.7 11.8

Spectroscopic temperature measurements Relative intensities of lines of the same atom or ion Relative line intensities of subsequent ionization stages of the same element Lines from isoelectronic transitions of different elements Relative continuum intensities Ratios of line and continuum intensities Intensities from optically thick layers Line intensities in rapidly ionizing plasmas Doppler profiles

12 12.1 12.2 12.3 12.4 12.5 12.6

Other diagnostic applications of plasma spectroscopy Charge exchange recombination spectroscopy Beam emission spectroscopy (BES) Polarization spectroscopy Magnetic field measurements Electric field measurements Effective charge measurements

300 301 306 312 314 318 320

References

324

Index

362

283 287 290 291 292 296 297

Preface

This book was written for the benefit of young researchers in diverse disciplines ranging from experimental plasma physics to astrophysics, and graduate students wanting to enter the interdisciplinary area of research now generally called plasma spectroscopy. The author has attempted to develop the theoretical foundations of the numerous applications of plasma spectroscopy from first principles. However, some familiarity with atomic structure and collision calculations, with quantum-mechanical perturbation theory and with statistical mechanics of plasmas is assumed. The emphasis is on the quantitative emission spectroscopy of atoms and ions immersed in high-temperature plasmas and in weak radiation fields, where multi-photon processes are not important. As in the author's previous books on plasma spectroscopy and spectral line broadening written, respectively, over three and two decades ago, various applications are discussed in considerable detail, as are the underlying critical experiments. Hopefully, the reader will find the numerous references useful and current up to the latter part of 1995. They provide advice concerning access to basic data, which are needed for the implementation of many of the experimental methods, and to descriptions of instrumentation. The author has once more benefited from his experience in teaching special lecture courses at the University of Maryland and recently also at the Ruhr University in Bochum and some of its neighboring institutions. His thanks are not only due to the advanced graduate students and fellow scientists in these courses but also to many colleagues at these and other institutions, who so generously provided advice, criticism and new research results. Of all these colleagues, I owe particular thanks to Ray Elton and to John Hey for their sustained and critical help with the manuscript. Any remaining errors or deficiencies are entirely my responsibility, and I would be grateful if they were communicated to me.

Preface

xi

I am most grateful to Dorothea F. Brosius, who so patiently and professionally prepared numerous drafts and the final computerized manuscript. Very special thanks go to her and to my wife Irmgard for all the help and encouragement.

1996, College Park, Maryland

Symbols

Symbol

Definition

a a0 a

ratio of ion-ion separation and Debye radius Bohr radius (unit) polarization vector transition probability (per unit time) for spontaneous emission (m —> n) transition probability for autoionization Fourier transform of fieldstrength distribution ampere (unit of current) vector potential vector potential Fourier components bound-bound beam emission spectroscopy magnetic fieldstrength velocity of light coefficient for three-body recombination charge exchange Fourier transform of line shape (dipole autocorrelation function) coulomb (unit of charge) charge exchange recombination spectroscopy collisional-radiative capture radiative cascade spherical Racah tensor (rank 1) line shift dielectronic capture coefficient

Anm A

mj

A(k) A A bb BES B c Cm CX

C(s) C

CHERS CR

CRC

CU) d djm

Introduced on Page

Xll

70 40 17 19 177 68

2 2

12 250 306

2 2

161 255 59 2 218 161

215, 301 39

55 178

Symbols

xiii

differential scattering cross section 28 differential oscillator strength 148 dielectronic recombination 249 dipole moment 64 diffusion coefficient 89 dipole transition operator 60 factors for dipole transition matrix elements 45 displacement vector 9 conditional average of time-dependent dipole 85 operator e charge of electron 2 Em excitation energy 160 En energy of state n 15 Er energy of radiation field 11 £oo ionization energy 104 EOJ field energy per mode 13 Ep Fermi energy 75 EH ionization energy of hydrogen 46 EL(CO) binding energy of lowest bound state for 145 radiative recombination Eza~l (groundstate) ionization energy of atom a 160 with ionic charge z — 1 ESB excitation saturation balance 217 E electric fieldstrength 2 Ew Fourier component of E 4 / final state quantum number 57 fj frequency of collisions of type j 65 fmn absorption oscillator strength (n -> m) 21 fnm emission oscillator strength (m —• n) 22 /(ri,r2, * * •) correlation function 75 /(£) Maxwell energy distribution 167 f(0, (j)) scattering amplitude 66 fb free-bound 248 // free-free 247 F free energy 203 Fo Holtsmark's normal fieldstrength 68 FQ fieldstrength corresponding to a perturbing 77 ion at the mean ion-ion separation F(r, s) relaxation (unified) theory function 60 FWHM full width between half of maximum intensity points 54 Fm flux of particles in state m 166 F' gradient of micro-fieldstrength 78 df/dE dr d D D Du D2, ... D D(F, t)

xiv F(r, s) g geff gn g(rjjc) g(co) g G Gw G(r; s, sf) G(Aco) G(0) h{*u r2, —) H H Hi Ho(P) H[ H(P) Jf i iron IT(CO)

J(co,Q) j J J J(co) k k k K K ^max f L L(co) LTE

Symbols electric fieldstrength 64 Lande factor 316 effective Gaunt factor for line widths 94 statistical weight 17, 191 two particle correlation function 69 Gaunt factor 137 effective Gaunt factor for inelastic cross 173 sections factor in semiempirical line width formula 94 (radial) continuum wave function 135 Green's function 61 kinetic theory line profile function 86 natural logarithm of A(k) 75 Ursell cluster functions 75 Hamilton operator 11 radiation flux 231 interaction Hamiltonian 14 Holtsmark distribution function 69 effective interaction Hamiltonian 16 distribution of reduced fieldstrength 70 Baranger's collision operator 65 initial state quantum number 57 spectrally integrated line intensity of m to n 281 transition intensity of blackbody radiation (Planck's law) 23 spectral and directional intensity 21 (one-electron) total angular momentum 39 quantum number total angular momentum quantum number 36 beam particle current 306 mean intensity 222 wavenumber 17 Boltzmann constant 23, 191 transform variable associated with the 68 microfield-strength plasma wavenumber 79 second moment of the directional intensity 231 maximum plasma wavenumber 80 single electron orbital angular momentum 39 quantum number total orbital angular momentum quantum number 44 line shape function 54 local thermodynamic equilibrium 156

Symbols J£{CD)

m m(me) M M, Mf n n rib nc ncj ncr flmax rica no n} n(co) N Ne(N) Nm Np(Nt) N p p(ri>r2> * * ) p P P Pa Pe Pe Pnm P(F) P(co) PLTE P P P^) qo qco, n) 15 probability distribution for field vectors 68 spectral power 57 partial local thermodynamic equilibrium 156 volume polarization 9 canonical momentum 11 dipole transition operator 38 maximum momentum transfer 174 destruction, creation operators 12 heat 190 average ion charge 199

xvi

Symbols

distribution function quasisteady state mean electron-electron separation classical electron radius population coefficient for level m (from the ground state) population coefficient for level m ri(m) (by recombination) component q of tensor operator r'1^ position vector r 1? ratio of doubly and singly ionized perturbers reactance matrix i? R radiation cooling rate constant R line intensity ratio ratio of ionization and photon emission rates R internuclear distance for level crossing R» (one-electron) radial wave function RnAr) minimum impact parameter Ro ion-sphere radius Ro R(a>,Q;co',Q') redistribution function total electron spin quantum number S spectral density of charge density fluctuations S relative intensity of plasma satellites S ionization rate coefficient S entropy S S -matrix for collision j S: line strength Snm probability for photon to remain in a plasma S" after n scatterings source function S(co) Poynting vector t(s,O) time development operator temperature T electron, ion and atom temperatures Te, Tz, Ta ion temperature if various ion species are Tt thermalized Laplace transform of time development T{co) operator Tr trace ratio of kinetic electron energy and excitation u energy spectral energy density of radiation field

6(r)

QSS re ro ro(m)

/f>

s

60 217 73 4 162 162 37 2 71 93 247 281 307 185 39 174 198 227 45 79 124 158 190 65 36 239 230 4 59 54 279 280 63 59 173 222

Symbols u(s, 0) U Un UQ v w W W Wmn W(F) W{¥ f —> F) W x Xmg z z z z zeff zn zp zf Z Za Zn a a a a a ccd P /? Pi y y ynm y(u) Tu df(p) AEZ

xvii

interaction representation time evolution operator 59 interaction Hamiltonian 60 time-independent wave function 15 spectral energy density of wave field 123 velocity 2 half (HWHM) line width 55 Racah coefficient 38 number of microscopic distributions 189 transition probability for absorption 22 microfield distribution function 58 transition rate between microfield states 85 weber (unit of magnetic flux) 2 displacement vector 3 excitation rate coefficient (ground state to state m) 160 effective nuclear charge 3 nuclear charge 40 charge state label 158 ionic charge 159 effective ionic charge 271, 320 number of bound electrons in n-th shell 159 charge of perturbing ions 69 effective charge 246 number of bound electrons (per atom or ion) 48 internal partition function 190, 193 effective nuclear charge for n-th shell 253 Planck-Larkin partition function 207

fine-structure constant ion broadening parameter phase angle recombination rate coefficient a-particle effective dielectronic recombination coefficient reduced micro-fieldstrength ratio of ionization and thermal energies escape factor decay (damping) rate set of quantum numbers (radiative) damping constant effective Gaunt factor ion-ion coupling parameter phase shift of free electron wave function reduction of ionization energy

3 92 123 158 301 180 68 168 237 6 37 27 173 73 208 140, 195

xviii AZi

Aco *d

era e' e" e(K,Aoi) e(

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