Nonlinear Effects in Plasma, Softcover reprint of the original 1st ed. 1970

For some time now there has been an interest in the nop. ­ linear interaction of electromagnetic waves in plasma [1,2]. But only in the last few years has the theory of nonlinear wave inter­ action effects undergone such vigorous development as to result in the formulation of clear phYSical concepts regarding the mech­ anisms of interaction. This development has been engendered by attempts to solve many of the plasma-physical problems accom­ panying the tremendous growth of experimental research [3]. The importance of nonlinear effects in modern plasma physics is dis­ cussed in detail in Chap. I. At this point we merely stress the fact that today the analysis of nonlinear effects is a practical ne­ cessity in any experiment involving plasma instabilities. We should also point out that plasma instabilities can assert them­ selves extensively in solids (solid state plasma) and play an im­ portant part in the study of cosmic plasma. Consequently, the problems of nonlinear wave interaction in plasma are of concern to those working in widely different areas of physics. Yet it is difficult to assimilate the results of investigations on nonlinear effects, owing to the complicated way in which the results of orig­ inal research are presented. In the present book the author hopes in some measure to fill the need for a text on the physics of non­ linear effects that is accessible to a fairly general audience.

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.