Lectures on Nonlinear Plasma Kinetics is an introduction to modern non-linear plasma physics showing how many of the techniques of modern non-linear physics find applications in plasma physics and how, in turn, the results of this research find applications in astrophysics. Emphasis is given to explaining the physics of nonlinear processes and the radical change of cross-sections by collective effects. The author discusses new nonlinear phenomena involving the excitation of coherent nonlinear structures and the dynamics of their random motions in relation to new self-organization processes. He also gives a detailed description of applications of the general theory to various research fields, including the interaction of powerful radiation with matter, collective laser particle accelerators, controlled thermonuclear research, space physics, solar physics, and astrophysics.

Inhalt

1. Non-linear Plasma Kinetics in Modern Physics.- 1.1 Introduction.- 1.2 Controlled Fusion Research and Non-linear Plasma Physics.- 1.3 Laser Plasmas; Laser-Matter Interactions and Collective Plasma Processes.- 1.4 Powerful Relativistic Electron Beams.- 1.5 Powerful Accelerators and Collective Acceleration Methods.- 1.6 Dynamic Chaos, Self-organisation, and Turbulence.- 1.7 Vortex Turbulence and Self-organisation.- 1.8 Self-organisation in a Gas Discharge Plasma.- 1.9 Non-linear Processes in Dusty Plasmas.- 1.10 Non-linearities of the Ionospheric Plasma.- 1.11 Space Physics Research.- 1.12 Plasma Astrophysics.- 1.13 Cosmic-Ray Physics. Gravitational Fields.- 1.14 Outline of the Remainder of this Book.- 1.15 Recommended Literature.- 2. Collective Plasma Oscillations.- 2.1 Elementary Description of Collective Plasma Oscillations.- 2.2 Some Definitions. Debye Screening.- 2.3 Number of Particles in the Debye Sphere as a Fundamental Plasma Parameter.- 2.4 Kinetic Theory of Linear Collective Plasma Oscillations...- 2.5 Kinetic Theory of Langmuir and Ion-Sound Plasma Oscillations.- 2.6 Landau Damping 47.- 2.7 Beam-Plasma Instability 51.- Problems.- 3. Kinetics of Random Collective Excitations. Quasi-linear Interactions.- 3.1 Introduction. Distribution Function for Plasma Oscillations.- 3.2 Correlation Functions for Random Fields.- 3.3 Energy Density of Random Oscillations.- 3.4 Stimulated Vavilov-Cherenkov Emission and Landau Damping.- 3.5 Quasi-linear Equation for the Particle Distribution.- 3.6 Quasi-linear Relaxation of Beams in a Plasma.- 3.7 Quasi-linear Description and Fluctuating Fields.- Problems.- 4. Fluctuations and Particle Collisions.- 4.1 Introduction. Averaged Distributions and Fluctuations....- 4.2 Fluctuations of Independent Particles.- 4.3 Fluctuations of Charged Particles.- 4.4 Landau-Balescu Collision Integral.- 4.5 Structure of the Collision Integral. Examples.- 4.6 Conservation Laws. Kinetic and Hydrodynamic Descriptions.- 4.7 Probabilities for Particle Collisions in a Plasma.- Appendix: Belyaev-Budker Collision Integral.- Problems.- 5. General Theory of Non-linear Interactions.- 5.1 Classification of Interactions.- 5.2 General Theory of Weak Non-linear Interactions.- 5.3 Non-linear Plasma Responses.- 5.4 Approximate Expressions for the Non-linear Responses for Langmuir Waves.- 5.5 Approximate Expressions for the Non-linear Responses for Ion-Sound Waves.- 5.6 Non-linear Changes in the Particle Distributions.- 5.7 Non-linear Changes in the Particle Distributions for the Case of Random Fields.- Problems.- 6. Stimulated Scattering of Waves by Particles.- 6.1 A Simple Physical Picture of the Scattering Process.- 6.2 Description of the Stimulated Scattering Processes of Waves in a Plasma. Non-linear Landau Damping.- 6.3 Conservation Laws in an Elementary Scattering Process...- 6.4 Scattering Probabilities for Langmuir Waves.- 6.5 Scattering Probabilities for Ion-Sound Waves.- 6.6 Transition Scattering.- 6.7 Change in the Particle Distribution.- Due to Stimulated Wave Scattering.- Appendix: Scattering Processes Involving Transverse Waves.....- Problems.- 7. Plasma Turbulence.- 7.1 The General Concept of Turbulence.- 7.2 Langmuir Turbulence.- 7.3 Non-linear Stabilisation of a Beam-Plasma Instability.....- 7.4 Solar Radio Bursts.- 7.5 Ion-Sound Turbulence.- 7.6 Anomalous Plasma Resistivity.- 7.7 Turbulent Shock Waves and Turbulent Magnetic Reconnection.- Problems.- 8. Non-linear Decay Interactions.- 8.1 General Concepts.- 8.2 The Balance Equation; the Conservation Laws.- 8.3 Probabilities of the Decay Interactions.- 8.4 Decay Processes and the Turbulent Spectrum.- 8.5 Decay Processes and Plasma Diagnostics.- 8.6 Scattering in a Strongly Turbulent Plasma.- 8.7 Decay Processes and Emission in a Turbulent Plasma. Interaction of Strong Radiation with a Plasma.- Problems.- 9. Non-linear Modulational Interactions.- 9.1 Non-linear Frequency Shift and Modulational Interactions.- 9.2 Kinetic and Hydrodynamic Linear Instabilities.- 9.3 General Theory of Modulational Interactions.- 9.4 Averaging over the Plasma Frequency.- 9.5 Modulational Instability.- 9.6 Conservation Laws.- 9.7 Solitons. Self-contracting Cavitons.- Appendix: Non-linear Frequency Shifts Produced by Ion-Sound Waves.- Problems.- 10. Dissipative Structures and Strong Langmuir Turbulence.- 10.1 Introduction. Self-organisation and Strong Turbulence.....- 10.2 Resonant Interactions of Strong Regular Fields with Uniformly Distributed Particles.- 10.3 Self-consistent Description of the Interaction Between Structures and Resonant Particles.- 10.4 Excitation and Damping of Structures in Beam-Plasma Interactions.- 10.5 Non-linear Landau Damping of Structures.- 10.6 Coherent Landau Damping. Arrest of the Self-contraction..- 10.7 Coherent Transition Damping of Cavitons.- 10.8 Interaction Between Structures and Random Fields.- 10.9 General Theory of the Interaction Between Regular and Random Fields.- 10.10 Interactions Between Regular Structures and Inhomogeneous Turbulence.- 10.11 Inhomogeneity of the Turbulence Excited by Interactions with Regular Structures..- 10.12 Development of Self-organisation.- 10.13 Some General Statements About Strong Langmuir Turbulence.- 10.14 Collective Laser-Plasma Interaction Processes.- Problems.- 11. Plasma Maser Effect and Adiabatic Invariants in Non-linear Interactions.- 11.1 Introduction.- 11.2 Damping Due to Inhomogeneities Created by External Sources.- 11.3 Non-linear Permittivity in the Presence of Random Resonant Waves.- 11.4 Non-linear Interactions of Resonant and Non-resonant Random Waves.- 11.5 Adiabatic Invariants in the Interaction of Resonant and Non-resonant Waves.- 11.6 The Plasma Maser Effect for Weak Turbulence.- 11.7 The Plasma Maser Effect for Strong Turbulence.- Problems.- 12. Non-linear Interactions of Collective Oscillationsb and Waves with Particle Fluctuations.- 12.1 Introduction.- 12.2 General Relations.- 12.3 Interactions Unconnected with Fluctuations in the Particle Distribution.- 12.4 Virtual Field Fluctuations.- 12.5 Interactions Produced by Particle Fluctuations. Contribution from Virtual Fields.- 12.6 Direct Interactions with Particle Fluctuations.- 12.7 Spontaneous Scattering Processes.- Problems.- 13. Collective Effects in Bremsstrahlung of Plasma Particles.- 13.1 Introduction. Elementary Concepts of Bremsstrahlung of Colliding Particles.- 13.2 Qualitative Description of Collective Effects in Bremsstrahlung of Particles in a Plasma.- 13.3 Bremsstrahlung of Longitudinal Waves by Bare Particles..- 13.4 Bremsstrahlung Probabilities and Balance Equations.- 13.5 Bremsstrahlung Probabilities for Particles in a Plasma Including Collective Effects.- 13.6 Analysis of the Bremsstrahlung Cross-Sections for Particles in a Plasma.- 13.7 Collective Effects in Bremsstrahlung in Electron-Electron, Ion-Ion, and Electron-Ion Collisions.- Problems.- 14. Some Remarks on Plasma Non-linear Kinetics in External Magnetic Fields. Conclusion.- 14.1 Summary of Problems Considered.- 14.2 External Magnetic Fields.- 14.3 Plasma Inhomogeneities.- 14.4 Electromagnetic Effe…