THEORY OF PLASMAS TEORIYA PLAZMY TEOPMH lljla3mbi
The Lebedev Physics Institute Series Editors: Academicians D. V. Skobel'tsyn and N. G. Basov P. N. Lebedev Physics Institute, Academy of Sciences of the USSR Volume 30 Volume 31 Volume 32 Volume 33 Volume 34 Volume 35 Volume 36 Volume 37 Volume 38 Volume 39 Volume 40 Volume 41 Volume 42 Volume 43 Volume 44 Volume 45 Volume 46 Volume 47 Volume 48 Volume 49 Volume 50 Volume 51 Volume 52 Volume 53 Volume 54 Volume 55 Volume 56 Volume 57 Volume 58 Volume 59 Volume 60 Volume 61 Volume 62 Volume 63 Volume 65 Volume 67 Volume 70 In preparation Volume 64 Volume 66 Volume 68 Volume 69 Volume 71 Volume 72 Volume 73 Volume 74 Volume 75 Physical Optics Quantum Electronics in Lasers and Masers, Part 1 Plasma Physics Studies of Nuclear Reactions Photomesic and Photonuclear Processes Electronic and Vibrational Spectra of Molecules Photo disintegration of Nuclei in the Giant Resonance Region Electrical and Optical Properties of Semiconductors Wide band Cruciform Radio Telescope Research Optical Studies in Liquids and Solids Experimental Physics: Methods and Apparatus The Nucleon Compton Effect at Low and Medium Energies Electronics in Experimental Physics Nonlinear Optics Nuclear Physics and Interaction of Particles with Matter Programming and Computer Techniques in Experimental Physics Cosmic Rays and Nuclear Interactions at High Energies Radio Astronomy: Instruments and Observations Surface Properties of Semiconductors and Dynamics of Ionic Crystals Quantum Electronics and Paramagnetic Resonance Electroluminescence Physics of Atomic Collisions Quantum Electronics in Lasers and Masers, Part 2 Studies in Nuclear Physics Photomesic and Photonuclear Reactions and Investigation Methods with Synchrotrons Optical Properties of Metals and Intermolecular Interactions Physical Processes in Lasers Theory of Interaction of Elementary Par~icles at High Energies Investigations in Nonlinear Optics and Hyperacoustics Luminescence and Nonlinear Optics Spectroscopy of Laser Crystals with Ionic Structure Theory of Plasmas Methods in Stellar Atmosphere and Interplanetary Plasma Research Nuclear Reactions and Interaction of Neutrons and Matter Stellarators Physical Investigations in Strong Magnetic Fields Group-Theoretical Methods in Physics Primary Cosmic Radiation Theory of Collective Particle Acceleration and Relativistic Electron Beam Emission Radiative Recombination in Semiconducting Crystals Nuclear Reactions and Accelerators of Charged Particles Photonuclear and Photomesic Processes Physical Acoustics and Optics: Molecular Scattering of Light; Propagation of Hypersound; Metal Optics Microwave-Plasma Interactions Neutral Current Layers in a Plasma Optical Properties of Semiconductors
Proceedings (Trudy) of the P. N. Lebedev Physics Institute Volume 61 THEORY OF PLASMAS Edited by Academician D. V. Skobel'tsyn Director, P. N. Lebedev Physics Institute Academy oj Sciences oj the USSR, Moscow Translated from Russian by Julian B. Barbour CONSULTANTS BUREAU NEW YORK AND LONDON
Main entry under title: Theory of plasmas. Library of Congress Cataloging in Publication Data (Proceedings (Trudy) of the P. N. Lebedev Physics Institute; v. 61) Translation of Teorila plazmy. Includes bibliographical references. CONTENTS: Kikvidze, R. R. and Rukhadze, A. A. Theory of oscillations and stability of a semiconductor plasma with low carrier density in a strong electric field. - Pustovalov, V. V. and SHin, V. P. Non linear theory of the interaction of waves in a plasma. 1. Plasma (Ionized gases) 2. Plasma waves. 3. Semiconductors, Effect of radiation on. I. Skobel'fsyn, Dmitrii VIadimirovich, 1892 ed. II. Series: Akademila nauk SSSR. Fizicheskil institut. Proceedings; v. 6l. QCI.A4114 vol. 61 [QC718] 530.08s [530.4'4] ISBN 978-1-4757-0132-6 ISBN 978-1-4757-0130-2 (ebook) 74 34269 DOI 10.1007/978-1-4757-0130-2 The original Russian text was published by Nauka Press in Moscow in 1972 for the Academy of Sciences of the USSR as Volume 61 of the Proceedings of the P. N. Lebedev Physics Institute. This translation is published under an agreement with the Copyright Agency of the USSR (VAAP). 1975 Consultants Bureau, New York A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 United Kingdom edition published by Consultants Bureau, London A Division of Plenum Publishing Company, Ltd. Davis House (4th Floor), 8 Scrubs Lane, Harlesden, London, NWlO 6SE, England All rights reserved No part of this book 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
PREFACE This volume contains two papers that review certain theoretical problems that have been studied in the Laboratory of Plasma Accelerators and Plasma Physics of the P. N. Lebedev Physics Institute of the Academy of Sciences of the USSR. The review of R. R. Kikvidze and A. A. Rukhadze, "Theory of oscillations and stability of a semiconductor plasma with low carrier density in a strong electric field," is devoted to a solid-state plasma. The main attention is devoted to the fact that in such a plasma electromagnetic waves are effectively generated if there is a negative current-voltage characteristic in the carrier current; this effect can compete in importance with the well-known Gunn effect. In their fundamental review paper "Nonlinear theory of the interaction of waves in a plasma," V. V. Pustovalov and V. P. SHin set forth the fundamentals of the theory of nonlinear interaction of waves in a hot rarefied plasma. Besides a systematic exposition of the procedure for deriving the equations that describe the nonlinear interaction of waves in an isotropic or an anisotropic (magnetized) plasma, they study many concrete examples relating to the interaction of definite types of waves under different conditions. v
CONTENTS THEORY OF OSCILLATIONS AND STABILITY OF A SEMICONDUCTOR PLASMA WITH LOW CARRIER DENSITY IN A STRONG ELECTRIC FIELD R. R. Kikvidze and A. A. Rukhadze Introduction......................................... 1 Chapter I. Homogeneous Semiconductor Plasma in a Strong Electric Field.... 5 1.1. Physical Meaning of the Instability Associated with a Negative Current-Voltage Characteristic.............. 5 1.2. Basic Equations Describing a Seminconductor Plasma with Low Carrier Density.................................. 8 1.3. Oscillation Spectra of a Homogeneous Semiconductor Plasma in a Strong Electric Field.......................... 11 1.4. Effect of Diffusion on the Instability of a Semiconductor Plasma with Negative Current-Voltage Characteristic...... 20 Chapter II. Spatially Inhomogeneous Solid-State Plasma in External Fields.. 25 2.1. Equation of Small Oscillations of an Inhomogeneous Plasma with Low Carrier Density........................... 25 2.2. Spectrum of Short-Wave Oscillations of an Inhomogeneous Solid-State Plasma............................ 28 2.3. Surface Waves in a Solid-State Plasma in the Absence of a Magnetic Field................................. 30 2.4. Surface Waves in a Bounded Magnetized Plasma with Current...... 33 Literature Cited............................................... 35 NONLINEAR THEORY OF THE INTERACTION OF WAVES IN A PLASMA V. V. Pustovalov and V. P. Silin Preface Notation Introduction...'.... ". CI " " " " 0 " " " " " " " " " " Chapter I. Fundamentals of the Nonlinear Electrodynamics of a Medium with Time and Spatial Dispersion........................ 42 1. The Electromagnetic Field Equations and the Material Equation....... 42 2. Multi-Index Permittivity Tensors and Truncated Equations of the Electromagnetic Field......... 45 3. Averaging of the Truncated Equations of the Electromagnetic Field with Respect to the Statistical Ensemble.......... 49 4. Discussion of Results. Equation for the Frequencies of Interacting Electromagnetic Waves.................... 55 vii 37 38 41
viii CONTENTS Chapter II. Multi-Index Permittivity Tensors of a Homogeneous Isotropic Plasma.. 57 5. Solution of the Kinetic Equation for an Isotropic Plasma as a Power Series in the Self-Consistent Field........... 59 6. Permittivity Tensor of an Isotropic Plasma as the Simplest Example of the Multi-Index Tensor iji... jn for n = 1. Spectra and Polarization of the Characteristic Oscillations of an Isotropic Plasma.... 64 7. Three-Index Tensor Sijs (w, k; w', k') in an Isotropic Plasma.. 74 8. The Four-Index Tensor Viajb (w, k; w', k') in an Isotropic Plasma...... 84 Chapter III. Examples of Nonlinear Processes in an Isotropic Plasma....... 89 9. Nonlinear Interaction of Longitudinal Oscillations of an Isotropic Plasma 91 10. Nonlinear Interaction of Longitudinal and Transv.erse Oscillations in an Isotropic Plasma... It 0 108 11. Nonlinear Interaction of Transverse Characteristic Oscillations of an Isotropic Plas rna............................. II 0 116 12. Effective Cross Sections of Various Scattering Processes in an Isotropic Plasma... 0 0 0 121 13. Corrections to the Spectra of the Characteristic Oscillations of an Isotropic Plasma due to Nonlinear Interaction......... 127 14. Nonlinear Interaction of Characteristic Oscillations of a Plasma and the Theory of the Scattering of Electromagnetic Waves on Fluctuations of the Plasma................ 133 Chapter IV. Multi-Index Tensors of the Complex Permittivity of a Homogeneous Magnetoactive Plasma............ 140 15. Solution of the Transport Equation for a Magnetoactive Plasma in the Form of a Power Series in the Self-Consistent Electric Field... 142 16. Permittivity Tensor of a Magnetoactive Plasma as the Simplest Example of the Multi-Index Tensor for n = 1........ 149 17. The Inverse Tensor (3.17) and the Spectral Function of the Electric Fields of the Characteristic Oscillations of a Magnetoactive Plasma...... 158 18. Quasilongitudinal Oscillations of a Magnetoactive Plasma. Spectra and Spectral Functions............ 166 19. Three-Index Tensor Sijs (w, k; w', k') in a Magnetoactive Plasma......... 176 20. Four-Index Tensor Viajb (w, k; w', k') in a Magnetoactive Plasma..... 197 21. Conservation Laws in the Nonlinear Interaction of Plasma Oscillations as a Consequence of the Symmetry of the Multi-Index Tensors....... 203 Chapter V. Specific Nonlinear Processes in a Magnetoactive Plasma.... 209 22. Decay of Quasilongitudinal Characteristic Oscillations of an Isothermal Magnetoactive Plasma......... 210 23. Decay of Quasilongitudinal Characteristic Oscillations of a Nonisothermal Magnetoactive Plasma.......... 215 24. Induced Combination Scattering of High-Frequency Transverse Waves in a Cold Magnetoactive Plasma.... 220 25. Induced Scattering of Low-Frequency Quasilongitudinal Characteristic Oscillations of Magnetoactive Plasma on the Plasma Particles 222 26. Induced Scattering of Quasilongitudinal Characteristic Cyclotron Oscillations of a Magnetoactive Plasma on the Plasma Particles.... 233 Conclusions... 240 Appendix. Multi-Index Complex Permittivity Tensors of a Cold Plasma in the Framework of the Hydrodynamic Description...... 241 Literature Cited... II 252