Lectures on Non-linear Plasma Kinetics

380 Pages·1995·10.326 MB·English

by  Professor Vadim N. Tsytovich (auth.)

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V. N. Tsytovich
Lectures on Non-linear
Plasma Kinetics
Translation edited by D. ter Haar
With 36 Figures
, Springer
Professor Vadim N. Tsytovich
General Physics Institute, Vavilova str. 38, 117942 Moscow, Russia
Translator: Professor D. ter Haar
P. O. Box to, Petworth, West Sussex, GU28 DRY, United Kingdom
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Professor Dr. Gunter Ecker
Ruhr-Universitiit Bochum, Fakultat flir Physik und Astronomie,
Lehrstuhl Theoretische Physik I, Universitatsstrasse 150,
0-44801 Bochum, Germany
Professor Peter Lambropoulos, Ph. D.
Max-Planck-Institut flir Quantenoptik,
0-85748 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, 117333 Moscow, Russia
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Sektion Physik der Universitat Miinchen, Am Coulombwalll,
0-85748 GarchinglMiinchen, Germany
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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. 1995
(Springer series on atoms + plasmas; 17)
ISBN-13: 978-3-642-78904-5
NE:GT CIP data applied for
ISBN -13: 978-3-642-78904-5 e-ISBN -13: 978-3-642-78902-1
DOl: 10.1007/978-3-642-78902-1
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Preface
Non-linear plasma physics is a very fast developing field which has many ap
plications, the number of which is increasing daily. Other branches of physics
are interested in this field, not only because many of the developments of non
linear physics first were met with in plasma physics, but also because the de
velopment 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 ki
netics 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 col
lective 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-
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 motion
which 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 post
graduate 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
Table of Contents
1. Non-linear Plasma Kinetics in Modern Physics ......... 1
1.1 Introduction ........................................ 1
1.2 Controlled Fusion Research
and Non-linear Plasma Physics .......................' . 4
1.3 Laser Plasmas; Laser-Matter Interactions
and Collective Plasma Processes ...................... . 5
1.4 Powerful Relativistic Electron Beams 7
1.5 Powerful Accelerators
and Collective Acceleration Methods 8
1.6 Dynamic Chaos, Self-organisation, and 'IUrbulence ....... 9
1. 7 Vortex 'IUrbulence and Self-organisation ................ 12
1.8 Self-organisation in a Gas Discharge Plasma ............. 13
1.9 Non-linear Processes in Dusty Plasmas ................. 14
1.10 Non-linearities of the Ionospheric Plasma ............... 15
1.11 Space Physics Research ............................... 15
1.12 Plasma Astrophysics ................................. 17
1.13 Cosmic-Ray Physics. Gravitational Fields ............... 18
1.14 Outline of the Remainder of this Book ................. 19
1.15 Recommended Literature ............................. 21
2. Collective Plasma Oscillations ........................... 23
2.1 Elementary Description of Collective Plasma Oscillations . 23
2.2 Some Definitions. Debye Screening ..................... 27
2.3 Number of Particles in the Debye Sphere
as a Fundamental Plasma Parameter ................... 31
2.4 Kinetic Theory of Linear Collective Plasma Oscillations .. 36
2.5 Kinetic Theory of Langmuir
and Ion-Sound Plasma Oscillations .................... 40
2.6 Landau Damping .................................... 47
2.7 Beam-Plasma Instability .............................. 51
Problems ................................................. 53
VIII Contents
3. Kinetics of Random Collective Excitations.
Quasi-linear Interactions ................................ 55
3.1 Introduction. Distribution Function
for Plasma Oscillations ............................... 55
3.2 Correlation Functions for Random Fields ............... 57
3.3 Energy Density of Random Oscillations ................. 61
3.4 Stimulated Vavilov-Cherenkov Emission
and Landau Damping ................................ 63
3.5 Quasi-linear Equation for the Particle Distribution ....... 65
3.6 Quasi-linear Relaxation of Beams in a Plasma ........... 68
3.7 Quasi-linear Description and Fluctuating Fields ......... 72
Problems ................................................. 74
4. Fluctuations and Particle Collisions ..................... 75
4.1 Introduction. Averaged Distributions and Fluctuations ... 75
4.2 Fluctuations of Independent Particles .................. 79
4.3 Fluctuations of Charged Particles ...................... 81
4.4 Landau-Balescu Collision Integral ...................... 83
4.5 Structure of the Collision Integral. Examples ............ 86
4.6 Conservation Laws.
Kinetic and Hydrodynamic Descriptions ................ 92
4.7 Probabilities for Particle Collisions in a Plasma .......... 96
Appendix: Belyaev-Budker Collision Integral .................. 104
Problems ................................................. 106
5. General Theory of Non-linear Interactions .............. 107
5.1 Classification ofInteractions .......................... 107
5.2 General Theory of Weak Non-linear Interactions ......... 113
5.3 Non-linear Plasma Responses ........................' . 119
5.4 Approximate Expressions for the Non-linear Responses
for Langmuir Waves .................................. 122
5.5 Approximate Expressions for the Non-linear Responses
for Ion-Sound Waves ................................. 125
5.6 Non-linear Changes in the Particle Distributions ......... 129
5.7 Non-linear Changes in the Particle Distributions
for the Case of Random Fields ........................ 134
Problems ................................................. 135
6. Stimulated Scattering of Waves by Particles ............ 137
6.1 A Simple Physical Picture of the Scattering Process 137
6.2 Description of the Stimulated Scattering Processes
of Waves in a Plasma. Non-linear Landau Damping 142
6.3 Conservation Laws in an Elementary Scattering Process .. 146
6.4 Scattering Probabilities for Langmuir Waves ............ 150
Contents IX
6.5 Scattering Probabilities for Ion-Sound Waves ........... 156
6.6 Transition Scattering ................................. 162
6.7 Change in the Particle Distribution
Due to Stimulated Wave Scattering .................... 165
Appendix: Scattering Processes Involving Transverse Waves 169
Problems ................................................. 171
7. Plasma Turbulence ...................................... 173
7.1 The General Concept of Thrbulence .................... 173
7.2 Langmuir Thrbulence ................................ 178
7.3 Non-linear Stabilisation of a Beam-Plasma Instability .... 184
7.4 Solar Radio Bursts ................................... 186
7.5 Ion-Sound Thrbulence ................................ 187
7.6 Anomalous Plasma Resistivity ......................... 192
7.7 Thrbulent Shock Waves
and Thrbulent Magnetic Reconnection .................. 195
Problems ................................................. 198
8. Non-linear Decay Interactions .......................... 201
8.1 General Concepts .................................... 201
8.2 The Balance Equation; the Conservation Laws .......... 204
8.3 Probabilities of the Decay Interactions ................. 206
8.4 Decay Processes and the Thrbulent Spectrum ........... 209
8.5 Decay Processes and Plasma Diagnostics ............... 211
8.6 Scattering in a Strongly Thrbulent Plasma .............. 213
8.7 Decay Processes and Emission in a Thrbulent Plasma.
Interaction of Strong Radiation with a Plasma .......... 215
Problems ................................................. 218
9. Non-linear Modulational Interactions ................... 219
9.1 Non-linear Frequency Shift and Modulational Interactions 219
9.2 Kinetic and Hydrodynamic Linear Instabilities .......... 222
9.3 General Theory of Modulational Interactions ............ 225
9.4 Averaging over the Plasma Frequency .................. 229
9.5 Modulational Instability .............................. 231
9.6 Conservation Laws ................................... 235
9.7 Solitons. Self-contracting Cavitons ..................... 239
Appendix: Non-linear Frequency Shifts
Produced by Ion-Sound Waves ........................ 243
Problems ................................................. 244
10. Dissipative Structures and Strong Langmuir Turbulence 247
10.1 Introduction. Self-organisation and Strong Thrbulence .... 247
X Contents
10.2 Resonant Interactions of Strong Regular Fields
with Uniformly Distributed Particles ................... 250
10.3 Self-consistent Description of the Interaction
Between Structures and Resonant Particles ............. 253
10.4 Excitation and Damping of Structures
in Beam-Plasma Interactions .......................... 257
10.5 Non-linear Landau Damping of Structures .............. 263
10.6 Coherent Landau Damping. Arrest of the Self-contraction . 266
10.7 Coherent Transition Damping of Cavitons .............. 269
10.8 Interaction Between Structures and Random Fields ...... 272
10.9 General Theory of the Interaction Between Regular
and Random Fields .................................. 274
10.10 Interactions Between Regular Structures
and Inhomogeneous Turbulence ........................ 276
10.11 Inhomogeneity of the Turbulence .
Excited by Interactions with Regular Structures ......... 277
10.12 Development of Self-organisation ...................... 278
10.13 Some General Statements
About Strong Langmuir Turbulence .................... 281
10.14 Collective Laser-Plasma Interaction Processes .. :........ 282
Problems ................................................. 282
11. Plasma Maser Effect and Adiabatic Invariants
in Non-linear Interactions ............................... 285
11.1 Introduction ........................................ 285
11.2 Damping Due to Inhomogeneities
Created by External Sources .......................... 289
11.3 Non-linear Permittivity in the Presence
of Random Resonant Waves ........................... 292
11.4 Non-linear Interactions of Resonant
and Non-resonant Random Waves .... . . . . . . . . . . . . . . . .. 293
11.5 Adiabatic Invariants in the Interaction of Resonant
and Non-resonant Waves .......... . . . . . . . . . . . . . . . . . .. 294
11.6 The Plasma Maser Effect for Weak Turbulence .......... 299
11.7 The Plasma Maser Effect for Strong Turbulence ......... 301
Problems ................................................. 305
12. Non-linear Interactions of Collective Oscillations
and Waves with Particle Fluctuations ................... 307
12.1 Introduction ........................................ 307
12.2 General Relations .................................... 309
12.3 Interactions Unconnected with Fluctuations
in the Particle Distribution ........................... 311
12.4 Virtual Field Fluctuations ............................ 313