Lectures on Non-linear Plasma Kinetics

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 Effects.- 14.5 Relativistic Effects.- 14.6 Quantum Effects.- 14.7 Conclusion. Acknowledgements.