Nonlinear Effects in Plasma

I Nonlinear Effects and Plasma Physics.- 1. Role of Nonlinear Effects in Plasma Physics.- 2. Classification of the Nonlinearities of a Plasma.- Literature Cited.- II Weak Nonlinearities in Cold Plasma.- 1. Nonlinear Equation for the Field in a Plasma.- 2. The Linear Approximation..- 3. Nonlinear Oscillations of Cold Plasma Charges.- 4. Nonlinear Oscillations of Plasma Density.- 5. Nonlinear Plasma Current...- 6. Nonlinear Equations for Transverse and Longitudinal Electromagnetic Fields.- 7. Equations for the Wave Amplitudes.- 8. Nonlinear Interaction of Weakly Damped and Weakly Growing Waves.- 9. Some Consequences of the Derived Equations.- Literature Cited.- III Nonlinear Interaction of Three Wave Packets.- 1. Wave Packets.- 2. Phase Relations for Wave Packets.- 3. Interaction of Fixed-Phase Wave Packets.- 4. Interaction of Undamped Wave Packets in an Unstable Plasma.- 5. Instability of Intense Waves in a Plasma.- 6. Random-Phase Wave Packets.- 7. Quasistationary Equilibrium States and Stability of Random-Phase Waves.- 8. Excitation of Longitudinal Waves by Strong Random Transverse Waves.- 9. Some Qualitative Implications.- Literature Cited.- IV Induced Processes in Plasma.- 1. Spontaneous and Induced Emission Processes in a Two-Level System.- 2. Interaction of Electromagnetic Waves With a Two-Level System.- 3. Packets of Interacting Waves as Negative-Temperature Systems.- 4. Density of Quanta in a Plasma.- 5. Nonlinear Wave Interaction Resulting from the Balance of Induced Emission and Absorption..- 6. Spontaneous Emission of Waves by Waves.- 7. Analogy with the Vavilov-Cerenkov Effect.- 8. The Kinetic Equation for Plasmons.- 9. Induced Combination Scattering.- Literature Cited.- V General Characteristics and Applications of Decay Processes in Plasma.- 1. Decay Processes.- 2. The Diffusion Approximation.- 3. Conservation Laws for Decay Processes.- 4. Probabilities of Decay Processes.- 5. Decay Processes in Isotropic Plasma.- 6. Three-Plasmon Decay Processes and Nonlinear Wave Absorption.- 7. Decay Interactions of Langmuif and Ion-Acoustic Waves.- 8. Four-Plasmon Decay Processes and Nonlinear Wave Absorption.- 9. Decay Interactions and Nonlinear Stabilization of a Plasma Instability.- 10 Propagation of a Strong Electromagnetic Wave in a Plasma.- 11. Stabilization of Longitudinal Waves Generated by a Beam of Transverse Waves.- 12. Decay Processes and Plasma Diagnostics.- 13. Decay Processes and Nonthermal Plasma Radiation.- 14. Decay Processes for Negative-Energy Waves: Mechanism of Nonlinear Wave Generation.- 15. Nonlinear Decay Instabilities of Transverse and Longitudinal Waves in Partially Ionized Plasma.- 16. Astrophysical Applications of Decay Interactions.- Literature Cited.- VI Induced Emission of Waves by Plasma Particles.- 1. Resonant Particles.- 2. The Quasilinear Approximation.- 3. Conservation Laws.- 4. Probabilities for the Emission of Waves by Plasma Particles.- 5. Landau Wave Damping.- 6. The One-Dimensional Quasilinear Equations.- 7. One-Dimensional Theory of Saturation Effects for Landau Wave Absorption.- 8. Stability of an Isotropic Particle Distribution.- 9. Acceleration of Particles Interacting with Plasma Waves.- 10. Isotropization of Plasma Particles.- 11. Astrophysical Applications of Acceleration and Isotropization of Particles by Plasma Waves.- 12. On the Acceleration of Electrons and Ions under Laboratory Conditions.- 13. Effective Collision Frequency of Particles and Waves.- 14. Quasilinear Theory of Beam Instability in a Plasma.- 15. Effects of Oscillation Pileup in the Development of Beam Instability.- 16. Limits of Applicability of the Quasilinear Approximation: Hydrodynamic Beam Instabilities of Longitudinal Waves.- 17. Hydrodynamic Instabilities of Beams Caused by Anisotropy of the Distribution Function.- Literature Cited.- VII Induced Scattering of Waves by Plasma Particles.- 1. Resonances of Plasma Particles with Several Waves.- 2. The Wave Kinetic Equation.- 3. The Conservation Laws..- 4. Some General Consequences of the Kinetic Equations for Induced Scattering.- 5. Induced Scattering of Waves with Beams of Particles Present in the Plasma.- 6. Scattering Mechanisms.- 7. Compton Scattering of Longitudinal Waves.- 8. Nonlinear Scattering of Longitudinal Waves.- 9. Nonlinear Interaction of Langmuir Waves in Scattering by Plasma Electrons.- 10. Scattering Probabilities.- Literature Cited.- VIII Induced Scattering of Electromagnetic Waves in an Isotropic Plasma.- 1. Nonlinear Interactions of Langmuir Waves in Scattering by Electrons.- 2. Nonlinear Scattering by Electrons Through Virtual Transverse Waves.- 3. Induced Scattering of Langmuir Waves by Ions.- 4. Comparison of the Energy Transfer by Induced Scattering and by Decay of Langmuir Waves into Ion-Acoustic Waves.- 5. Induced Scattering of Ion-Acoustic Waves.- 6. Induced Scattering of Langmuir Waves with Conversion into Ion-Acoustic Waves..- 7. Induced Scattering of Transverse Waves into Transverse Waves.- 8. Induced Scattering of Langmuir Waves into Transverse Waves.- Literature Cited.- IX Some Applications of Induced Wave Scattering in Plasma.- 1. Conversion of Longitudinal into Transverse Waves.- 2. Stabilization of Beam Instabilities by Induced Scattering of Langmuir Waves into Langmuir Waves.- 3. Acceleration of Electrons During the Development of Beam Instability.- 4. On the Stabilization of Beam Instabilities by Induced Scattering of Langmuir into Ion-Acoustic Waves.- 5. Stability of Relativistie Beams with Respect to Langmuir Wave Generation..- 6. Interaction Efficiency of Nonrelativistic Beams with Plasma.- 7. Quasistationary Spectra of Acoustic Oscillations Excited by an Electron Current.- 8. Induced Scattering Effects and Plasma Heating.- 9. Effective Collision Frequency for Particles with Waves in Induced Scattering.- 10. Ion Acceleration by Induced Wave Scattering.- 11. Transfer of Langmuir Waves in Induced Scattering and the Acceleration of High-Energy Particles.- Literature Cited.- X Current Trends in Research on Nonlinear Effects in Plasma.- 1. Development of Theory Based on the Kinetic Equations for Plasmons.- 2. Development of Research on the Nonlinear Dispersion Properties of Plasma.- 3. Development of the Theory of the Low-Frequency Nonlinear Characteristics of Plasma.- 4. Nonlinear Dispersion Characteristics of Plasma in the Field of a Fixed-Phase Wave.- 5. Large-Amplitude Nonlinear Waves.- Conclusions.- Literature Cited.- Appendix 1 Derivation of the Nonlinear Equations for Slowly Varying Amplitudes of the Interacting Fields.- Appendix 2 Averaging of the Nonlinear Equations over the Phases of the Interacting Waves.- Appendix 3 General Method for Calculating the Probabilities of the Decay, Emission, and Scattering of Waves.- Appendix 4 Methods of Calculating the Nonlinear Dispersion Characteristics of a Plasma.- Literature Cited in the Appendices.