Springer Series on AtolUS+PlasDlas. Editor: G. Ecker. Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Tokyo

Transcription

1 Springer Series on AtolUS+PlasDlas 7 Editor: G. Ecker Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Tokyo

2 Springer Series on AtoDls+Plas... as Editors: G. Ecker P. Lambropoulos 1.1. Sobel'man H. Walther Managing Editor: H. K. V. Lotsch Polarized Electrons 2nd Edition By J. Kessler II Resonance Phenomena in Electron-Atom Collisions By V. I. Lengyel, V. T. Navrotsky and E. P. Sabad 2 Multiphoton Processes Editors: P. Lambropoulos and S. J. Smith 12 Atomic Spectra and Radiative Transitions 2nd Edition 3 Atomic Many-Body Theory By I. I. Sobel'man 2nd Edition By I. Lindgren and J. Morrison 13 Multiphoton Processes in Atoms By N. B. Delone and V. P. Krainov 4 Elementary Processes in Hydrogen-Helium Plasmas 14 Atoms in Plasmas Cross Sections and Reaction By V. S. Lisitsa Rate Coefficients 15 Excitation of Atoms and By R. K. Janev, W. D. Langer, Broadening of Spectral Lines K. Evans, Jr. and D. E. Post, Jr. By I. I. Sobel'man, L. Vainshtein 5 Pulsed Electrical Discharge in and E. Yukov Vacuum 16 Reference Data on Multicharged By G. A. Mesyats and D. I. Proskurovsky Ions 6 Atomic and Molecular By V. G. Pal'chikov and V. Shevelko Spectroscopy 2nd Edition 17 Lectures on Non-linear Plasma Basic Aspects and Practical Applications Kinetics By S. Svanberg By V. N. Tsytovich 7 Interference of Atomic States By E. B. Alexandrov, M. P. Chaika and. G. I. Khvostenko 8 Plasma Physics 2nd Edition Basic Theory with Fusion Applications By K. Nishikawa and M. Wakatani 9 Plasma Spectroscopy The Influence of Microwave and Laser Fields By E. Oks IO Film Deposition by Plasma Techniques By M. Konuma

3 V. N. Tsytovich Lectures on Non-linear Plasma Kinetics Translation edited by D. ter Haar With 36 Figures, Springer

4 Professor Vadim N. Tsytovich General Physics Institute, Vavilova str. 38, Moscow, Russia Translator: Professor D. ter Haar P. O. Box to, Petworth, West Sussex, GU28 DRY, United Kingdom Series Editors: Professor Dr. Gunter Ecker Ruhr-Universitiit Bochum, Fakultat flir Physik und Astronomie, Lehrstuhl Theoretische Physik I, Universitatsstrasse 150, Bochum, Germany Professor Peter Lambropoulos, Ph. D. Max-Planck-Institut flir Quantenoptik, Garching, Germany, and Foundation for Research and Technology - Hellas (FO.R.T.H.), Institute of Electronic Structure & Laser (IESL), University of Crete, PO Box 1527, Heraklion, Crete 71110, Greece Professor Igor I. Sobel'man Lebedev Physical Institute, Russian Academy of Sciences, Leninsky Prospekt 53, Moscow, Russia Professor Dr. Herbert Walther Sektion Physik der Universitat Miinchen, Am Coulombwalll, GarchinglMiinchen, Germany Managing Editor: Dr.-Ing. Helmut K.V. Lotsch Springer-Verlag, Tiergartenstrasse 17, D Heidelberg, Germany Die Deutsche Bibliothek - CIP-Einheitsaufnahme Cytovic, Vadim N.: Lectures on nonlinear plasma kinetics I V. N. Tsytovich. Trans!. ep. by D. ter Haar. - Berlin; Heidelberg; New York: Springer (Springer series on atoms + plasmas; 17) ISBN-13: NE:GT CIP data applied for ISBN -13: e-isbn -13: DOl: / This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1995 Softcoverreprint of the hardcover 1st edition 1995 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready copy from the translator using a Springer T EX macro package SPIN / I 0 - Printed on acid-free paper

5 Preface Non-linear plasma physics is a very fast developing field which has many applications, the number of which is increasing daily. Other branches of physics are interested in this field, not only because many of the developments of nonlinear physics first were met with in plasma physics, but also because the development of methods for dealing with non-linear problems is extremely fast and it is also often possible to use plasma problems to illustrate fundamental non-linear phenomena. During the last ten years I have given lectures on non-linear plasma kinetics to students of the Moscow Institute for Physics and Technology and I have found it necessary to change my presentation each year. As I want to present new developments as well as old established results, when new discoveries appear, it has been necessary for me not only to fit those in at the appropriate places, but also to rearrange the old material to take into account the effect of the new results; sometimes I have had to change the main presentation completely. It looks to me that this procedure was finally convergent, and I hope that the material as given here is presented in the simplest possible way, without loss of generality. I feel that I have also been able to present the material in such a way that throughout the book there are just two leading ideas. The first one is that I am showing the very close relations between the different types of non-linear interactions and that they are all based on a simple picture of the physical nature of the interactions. Many aspects of this line of reasoning are never properly emphasised and some of them are still not widely used by researchers in this field. The second leading idea is even more general: I show that collective effects produce drastic changes in all known wave-particle interaction processes, such as particle collisions, wave scattering, and the emission of waves. I try to emphasise that in a plasma the corresponding cross-sections depend strongly on the distributions of other particles and waves and that this is a collective effect which can change the cross-sections, sometimes by several orders of magnitude. Even research workers in the field of non-linear plasma physics are not well acquainted with these two ideas. It is clear from research papers that these two points are not well understood. Moreover, students starting to learn the techniques of non-linear plasma physics from the original literature are buried by details about particular kinds of interac-

6 VI Preface tions and lose sight of the general ideas. I have tried to avoid this difficulty by concentrating on the fundamental ideas for a single type of collective motionwhich is also probably ~he simplest one: electrostatic collective motions. When I tried to write out my lectures I had to follow a logical presentation and this led me automatically in some cases to problems which had not yet been solved, or even stated properly. In this way my own research profited from the writing of this book. I have had to interrupt my work on the book, pursue my research, and publish various research papers showing, I think, the importance of these new processes for many problems in non-linear plasma dynamics. After that I incorporated the new results in my lectures to postgraduate students. Since this material fitted very nicely in my presentation, I could not exclude it from the book, when I tried to present the new material in the simplest possible way. Moreover, I felt that these problems arose from my desire to follow a logical presentation when preparing the book. The fact that the book contains a discussion of these new problems does not mean that it is a mixture of a monograph and a textbook. On the other hand, the material presented here should also be of interest to active reserach workers in the field. This book was edited and improved by Professor Dik ter Haar, to whom I am extremely grateful for his efforts which made the publication of this book possible. I am also grateful to him for many helpful suggestions and discussions of the problems to which this book is devoted. v. N. Tsytovich

7 Table of Contents 1. Non-linear Plasma Kinetics in Modern Physics Introduction Controlled Fusion Research and Non-linear Plasma Physics...'. Laser Plasmas; Laser-Matter Interactions and Collective Plasma Processes.... Powerful Relativistic Electron Beams Powerful Accelerators and Collective Acceleration Methods Dynamic Chaos, Self-organisation, and 'IUrbulence Vortex 'IUrbulence and Self-organisation Self-organisation in a Gas Discharge Plasma Non-linear Processes in Dusty Plasmas Non-linearities of the Ionospheric Plasma Space Physics Research Plasma Astrophysics Cosmic-Ray Physics. Gravitational Fields Outline of the Remainder of this Book Recommended Literature Collective Plasma Oscillations Elementary Description of Collective Plasma Oscillations Some Definitions. Debye Screening Number of Particles in the Debye Sphere as a Fundamental Plasma Parameter Kinetic Theory of Linear Collective Plasma Oscillations Kinetic Theory of Langmuir and Ion-Sound Plasma Oscillations Landau Damping Beam-Plasma Instability Problems... 53

8 VIII Contents 3. Kinetics of Random Collective Excitations. Quasi-linear Interactions Introduction. Distribution Function for Plasma Oscillations Correlation Functions for Random Fields Energy Density of Random Oscillations Stimulated Vavilov-Cherenkov Emission and Landau Damping Quasi-linear Equation for the Particle Distribution Quasi-linear Relaxation of Beams in a Plasma Quasi-linear Description and Fluctuating Fields Problems Fluctuations and Particle Collisions Introduction. Averaged Distributions and Fluctuations Fluctuations of Independent Particles Fluctuations of Charged Particles Landau-Balescu Collision Integral Structure of the Collision Integral. Examples Conservation Laws. Kinetic and Hydrodynamic Descriptions Probabilities for Particle Collisions in a Plasma Appendix: Belyaev-Budker Collision Integral Problems General Theory of Non-linear Interactions Classification ofinteractions General Theory of Weak Non-linear Interactions Non-linear Plasma Responses...' Approximate Expressions for the Non-linear Responses for Langmuir Waves Approximate Expressions for the Non-linear Responses for Ion-Sound Waves Non-linear Changes in the Particle Distributions Non-linear Changes in the Particle Distributions for the Case of Random Fields Problems Stimulated Scattering of Waves by Particles A Simple Physical Picture of the Scattering Process Description of the Stimulated Scattering Processes of Waves in a Plasma. Non-linear Landau Damping Conservation Laws in an Elementary Scattering Process Scattering Probabilities for Langmuir Waves

9 Contents IX 6.5 Scattering Probabilities for Ion-Sound Waves Transition Scattering Change in the Particle Distribution Due to Stimulated Wave Scattering Appendix: Scattering Processes Involving Transverse Waves 169 Problems Plasma Turbulence The General Concept of Thrbulence Langmuir Thrbulence Non-linear Stabilisation of a Beam-Plasma Instability Solar Radio Bursts Ion-Sound Thrbulence Anomalous Plasma Resistivity Thrbulent Shock Waves and Thrbulent Magnetic Reconnection Problems Non-linear Decay Interactions General Concepts The Balance Equation; the Conservation Laws Probabilities of the Decay Interactions Decay Processes and the Thrbulent Spectrum Decay Processes and Plasma Diagnostics Scattering in a Strongly Thrbulent Plasma Decay Processes and Emission in a Thrbulent Plasma. Interaction of Strong Radiation with a Plasma Problems Non-linear Modulational Interactions Non-linear Frequency Shift and Modulational Interactions Kinetic and Hydrodynamic Linear Instabilities General Theory of Modulational Interactions Averaging over the Plasma Frequency Modulational Instability Conservation Laws Solitons. Self-contracting Cavitons Appendix: Non-linear Frequency Shifts Produced by Ion-Sound Waves Problems Dissipative Structures and Strong Langmuir Turbulence Introduction. Self-organisation and Strong Thrbulence

10 X Contents 10.2 Resonant Interactions of Strong Regular Fields with Uniformly Distributed Particles Self-consistent Description of the Interaction Between Structures and Resonant Particles Excitation and Damping of Structures in Beam-Plasma Interactions Non-linear Landau Damping of Structures Coherent Landau Damping. Arrest of the Self-contraction Coherent Transition Damping of Cavitons Interaction Between Structures and Random Fields General Theory of the Interaction Between Regular and Random Fields Interactions Between Regular Structures and Inhomogeneous Turbulence Inhomogeneity of the Turbulence. Excited by Interactions with Regular Structures Development of Self-organisation Some General Statements About Strong Langmuir Turbulence Collective Laser-Plasma Interaction Processes.. : Problems Plasma Maser Effect and Adiabatic Invariants in Non-linear Interactions Introduction Damping Due to Inhomogeneities Created by External Sources Non-linear Permittivity in the Presence of Random Resonant Waves Non-linear Interactions of Resonant and Non-resonant Random Waves Adiabatic Invariants in the Interaction of Resonant and Non-resonant Waves The Plasma Maser Effect for Weak Turbulence The Plasma Maser Effect for Strong Turbulence Problems Non-linear Interactions of Collective Oscillations and Waves with Particle Fluctuations Introduction General Relations Interactions Unconnected with Fluctuations in the Particle Distribution Virtual Field Fluctuations

11 Contents XI 12.5 Interactions Produced by Particle Fluctuations. Contribution from Virtual Fields Direct Interactions with Particle Fluctuations Spontaneous Scattering Processes Problems Collective Effects in Bremsstrahlung of Plasma Particles Introduction. Elementary Concepts of Bremsstrahlung of Colliding Particles... ; Qualitative Description of Collective Effects in Bremsstrahlung of Particles in a Plasma Bremsstrahlung of Longitudinal Waves by Bare Particles Bremsstrahlung Probabilities and Balance Equations Bremsstrahlung Probabilities for Particles in a Plasma Including Collective Effects Analysis of the Bremsstrahlung Cross-Sections for Particles in a Plasma Collective Effects in Bremsstrahlung in Electron-Electron, Ion-Ion, and Electron-Ion Collisions Problems... ',' Some Remarks on Plasma Non-linear Kinetics in External Magnetic Fields. Conclusion Summary of Problems Considered External Magnetic Fields Plasma Inhomogeneities Electromagnetic Effects Relativistic Effects Quantum Effects Conclusion. Acknowledgements Glossary Index