Theory of Plasmas, 1975 The Lebedev Physics Institute Series, Vol. 61

This volume contains two papers that review certain theoretical problems that have been studied in the Laboratory of Plasma Accelerators and Plasma Physics of the P. N. Lebedev Physics Institute of the Academy of Sciences of the USSR. The review of R. R. Kikvidze and A. A. Rukhadze, "Theory of oscillations and stability of a semiconductor plasma with low carrier density in a strong electric field," is devoted to a solid-state plasma. The main attention is devoted to the fact that in such a plasma electro­ magnetic waves are effectively generated if there is a negative current-voltage characteristic in the carrier current; this effect can compete in importance with the well-known Gunn effect. In their fundamental review paper "Nonlinear theory of the interaction of waves in a plasma," V. V. Pustovalov and V. P. SHin set forth the fundamentals of the theory of nonlinear interaction of waves in a hot rarefied plasma. Besides a systematic exposition of the pro­ cedure for deriving the equations that describe the nonlinear interaction of waves in an iso­ tropic or an anisotropic (magnetized) plasma, they study many concrete examples relating to the interaction of definite types of waves under different conditions.

Theory of Oscillations and Stability of a Semiconductor Plasma with Low Carrier Density in a Strong Electric Field.- I. Homogeneous Semiconductor Plasma in a Strong Electric Field.- 1.1. Physical Meaning of the Instability Associated with a Negative Current-Voltage Characteristic.- 1.2. Basic Equations Describing a Seminconductor Plasma with Low Carrier Density.- 1.3. Oscillation Spectra of a Homogeneous Semiconductor Plasma in a Strong Electric Field.- 1.4. Effect of Diffusion on the Instability of a Semiconductor Plasma with Negative Current-Voltage Characteristic.- II Spatially Inhomogeneous Solid-State Plasma in External Fields.- 2.1. Equation of Small Oscillations of an Inhomogeneous Plasma with Low Carrier Density.- 2.2. Spectrum of Short-Wave Oscillations of an Inhomogeneous Solid-State Plasma.- 2.3. Surface Waves in a Solid-State Plasma in the Absence of a Magnetic Field.- 2.4. Surface Waves in a Bounded Magnetized Plasma with Current.- Literature Cited.- Nonlinear Theory of the Interaction of Waves in a Plasma.- Preface.- Notation.- I. Fundamentals of the Nonlinear Electrodynamics of a Medium with Time and Spatial Dispersion.- 1. The Electromagnetic Field Equations and the Material Equation..- 2. Multi-Index Permittivity Tensors and Truncated Equations of the Electromagnetic Field.- 3. Averaging of the Truncated Equations of the Electromagnetic Field with Respect to the Statistical Ensemble.- 4. Discussion of Results. Equation for the Frequencies of Interacting Electromagnetic Waves.- II Multi-Index Permittivity Tensors of a Homogeneous Isotropic Plasma.- 5. Solution of the Kinetic Equation for an Isotropic Plasma as a Power Series in the Self-Consistent Field.- 6. Permittivity Tensor of an Isotropic Plasma as the Simplest Example of the Multi-Index Tensor ?ij1...jn for n = 1. Spectra and Polarization of the Characteristic Oscillations of an Isotropic Plasma.- 7. Three-Index Tensor Sijs (?, k; ?’, k’) in an Isotropic Plasma.- 8. The Four-Index Tensor Viajb (?, k; ?’, k’) in an Isotropic Plasma.- III. Examples of Nonlinear Processes in an Isotropic Plasma.- 9. Nonlinear Interaction of Longitudinal Oscillations of an Isotropic Plasma.- 10. Nonlinear Interaction of Longitudinal and Transverse Oscillations in an Isotropic Plasma.- 11. Nonlinear Interaction of Transverse Characteristic Oscillations of an Isotropic Plasma.- 12. Effective Cross Sections of Various Scattering Processes in an Isotropic Plasma.- 13. Corrections to the Spectra of the Characteristic Oscillations of an Isotropic Plasma due to Nonlinear Interaction.- 14. Nonlinear Interaction of Characteristic Oscillations of a Plasma and the Theory of the Scattering of Electromagnetic Waves on Fluctuations of the Plasma.- IV. Multi-Index Tensors of the Complex Permittivity of a Homogeneous Magnetoactive Plasma.- 15. Solution of the Transport Equation for a Magnetoactive Plasma in the Form of a Power Series in the Self-Consistent Electric Field.- 16. Permittivity Tensor of a Magnetoactive Plasma as the Simplest Example of the Multi-Index Tensor for n = 1.- 17. The Inverse Tensor (3.17) and the Spectral Function of the Electric Fields of the Characteristic Oscillations of a Magnetoactive Plasma.- 18. Quasilongitudinal Oscillations of a Magnetoactive Plasma. Spectra and Spectral Functions.- 19. Three-Index Tensor Sijs (?, k; ?’, k’) in a Magnetoactive Plasma.- 20. Four-Index Tensor Viajb (?, k; ?’, k’) in a Magnetoactive Plasma.- 21. Conservation Laws in the Nonlinear Interaction of Plasma Oscillations as a Consequence of the Symmetry of the Multi-Index Tensors.- V. Specific Nonlinear Processes in a Magnetoactive Plasma.- 22. Decay of Quasilongitudinal Characteristic Oscillations of an Isothermal Magnetoactive Plasma.- 23. Decay of Quasilongitudinal Characteristic Oscillations of a Nonisothermal Magnetoactive Plasma.- 24. Induced Combination Scattering of High-Frequency Transverse Waves in a Cold Magnetoactive Plasma.- 25. Induced Scattering of Low-Frequency Quasilongitudinal Characteristic Oscillations of Magnetoactive Plasma on the Plasma Particles.- 26. Induced Scattering of Quasilongitudinal Characteristic Cyclotron Oscillations of a Magnetoactive Plasma on the Plasma Particles.- Conclusions.- Appendix. Multi-Index Complex Permittivity Tensors of a Cold Plasma in the Framework of the Hydrodynamic Description.- Literature Cited.