Fluctuations and Non-Linear Wave Interactions in Plasmas

List of Notations1. Statistical Description of a Plasma 1.1. Microscopic Equations The Microscopic Density The Equation of Continuity and Maxwell's Equations 1.2. The Liouville Distribution The Liouville Equation Statistical Averaging 1.3. The One-particle Distribution Function and Correlation Functions Sequence of Distribution Functions Connection between One-particle and Many-particle Distribution Functions 1.4. The Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy 1.5. Self-consistent Field Approximation The Vlasov Kinetic Equation Effects of Electromagnetic Interactions between Particles 1.6. Influence of Binary Correlations and The Collision Term The Kinetic Equation with Collisions Coulomb Collisions Correlation Weakening Principle and Irreversibility2. Non-linear Electrodynamic Equations 2.1. The Non-linear Equation for the Potential Field in a Plasma Solution of the Kinetic Equation Relation between the Polarization and the Electric Field Strength 2.2. Longitudinal Dielectric Permittivity and Non-linear Electric Susceptibilities of a Plasma General Relations Symmetry Properties The Long-Wave Limiting Case Non-Linear Susceptibilities of a Cold Plasma 2.3. Multiple-time-scale Perturbation Analysis of the Non-linear Equation for the Longitudinal Field Hierarchy of Times and Expansion in the Non-linearity Parameter Series Linear Approximation Quadratic Interaction and Three-wave Resonances Cubic Interaction and Four-wave Resonances 2.4. The General Non-linear Equation for the Field in a Plasma Maxwell'S Equations and the Non-linear Material Relation The Non-linear Equation for the Electric Field in a Plasma 2.5. The Dielectric Permittivity Tensor and Non-linear Tensor Susceptibilities of a Plasma General Formulas Symmetries of the Dielectric Permittivity Tensor Symmetries of the Non-Linear Susceptibilities Non-Linear Tensor Susceptibilities of a Cold Plasma 2.6. Hierarchy of Multiple-Time-Scale Approximate Equations for the Electromagnetic Field in a Plasma Basic Set of Equations Linear Approximation Three-wave Resonances Four-wave Resonances3. Electrodynamic Properties of a Magneto-active Plasma 3.1. Longitudinal Dielectric Permittivity and Non-linear Susceptibilities of a Plasma in the Presence of a Magnetic Field Solution of the Kinetic Equation The Dielectric Permittivity of an Equilibrium Plasma The Dielectric Permittivity of a Plasma with an Anisotropic Velocity Distribution Non-Linear Susceptibilities of a Cold Plasma 3.2. The Dielectric Permittivity Tensor of a Magneto-active Plasma Solution of the Linearized General Kinetic Equation The General Form of the Dielectric Permittivity Tensor an Equilibrium Plasma A Plasma with an Anisotropic Velocity Distribution A Cold Magneto-active Plasma 3.3. Non-linear Tensor Susceptibilities of a Magneto-active Plasma The General Case A Cold Plasma4. Waves in Plasmas 4.1. Eigenoscillations and Eigenwaves in Space-time Dispersive Media (Linear Approximation) The Dispersion Equation Wave Polarization Density and Flux of Energy Fluctuations and Averaging over Initial Phases 4.2. Waves in an Isotropic Plasma Dispersion Relations for Longitudinal and Transverse Waves Longitudinal Langmuir and Ion-sound Waves Transverse Electromagnetic Waves 4.3.