Fluctuations and Non-Linear Wave Interactions in Plasmas

Fluctuations and Non-linear Wave Interactions in Plasmas talks about a theory of fluctuations in a homogenous plasma. The title takes into consideration non-linear wave interactions.
The text first presents the statistical description of plasma, and then proceeds to covering non-linear electrodynamic equations. Next, the selection deals with the electrodynamic properties of magento-active plasma and waves in plasma. The text also tackles non-linear wave interactions, along with fluctuations in plasmas. The next chapter talks about the effect of non-linear wave interaction on fluctuations in a plasma. Chapter 8 details fluctuation-dissipation theorem, while Chapter 9 discusses kinetic equations. The tenth chapter covers the scattering and radiation of waves and the last chapter tackles wave interaction in semi-bounded plasma.
The book will be of great use to scientists and professionals who deals with plasmas.

Contenu

List of Notations

1. 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 Irreversibility
2. 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 Resonances
3. 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 Plasma
4. 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. Waves in a Magneto-active Plasma
   The Dispersion Equation for Waves in a Magneto-Plasma
   Plasma Resonances
   Refractive Indexes and Eigenwave Frequencies in a Cold Magneto-Plasma
   Thermal Waves in a Magneto-Plasma
5. Non-Linear Wave Interactions
   5.1. Non-resonant Wave Interaction and Plasma Echoes
   Resonant and Non-resonant Wave Interactions
   Plasma Echoes
   Longitudinal Echo Oscillations
   Echo Oscillations in the Case of Anti-Parallel Wave Vectors of the Perturbations
   Three-pulse Echo Oscillations
   5.2. Three-wave Resonant Coupling
   Dynamic Equations for Interacting Waves
   Conservation of Energy and Momentum of Interacting Waves
   Resonant Three-wave Coupling
   Decay Instability
   Explosive Instability
   5.3. Four-Wave Resonant Coupling
   The Resonance Condition and Dynamic Wave Equations
   Resonant Coupling of Four Waves with Fixed Phases
   Non-linear Frequency Shift of Eigenmodes in a Cold Plasma
   Effect of Electron Thermal Motion on Non-linear Frequency Shifts
   Influence of the Ion Motion
   Non-linear Eigen Frequency Shifts of Langmuir Waves 95
   5.4. Parametric Resonance in a Plasma
   Dispersion Equation for Waves in a Pump Wave Field
   Induced Scattering
   Parametric Instability
6. Fluctuations in Plasmas
   6.1. Fluctuations in Spatially Homogeneous Stationary Systems
   Space-Time Correlation Functions
   Correlators for the Distribution Function Fluctuations
   6.2. Fluctuations in a System of Non-interacting Charged Particles
   Spectral Correlators for the Fluctuations of the Distribution Function
   Spectral Distributions for the Fluctuations of Particle, Charge and Current Densities
   Higher-order Correlation Functions
   Spectral Distributions of Fluctuations in the Presence of an External Magnetic Field
   6.3. Fluctuations in an Ensemble of Charged Particles Taking into Account Electromagnetic
   Interaction between Particles (Linear Approximation)
   Effect of Coulomb Interactions between Particles on the Fluctuations of the Distribution Function
   Averaging Procedure and the Correlator for the Fluctuations of the Distribution Function
   Spectral Distributions of Particle, Charge and Current Density Fluctuations in a Plasma
   Effect of Electromagnetic Interactions bBetween Particles on Plasma Fluctuations
   Electromagnetic Fluctuations in an Isotropic Plasma
   6.4. Collective Fluctuations and the Effective Temperature (Potential Field)
   Incoherent and Coherent (Collective) Fluctuations
   Collective Fluctuations in a Non-equilibrium Plasma and the Effective Temperature
   Critical Fluctuations near the Instability Threshold
   Critical Fluctuations in a Plasma with a Directed Particle Motion
   Critical Fluctuations in a Plasma with an Anisotropic Velocity Distribution
   6.5. Collective Electromagnetic Fluctuations
   The Spectral Distribution of Fluctuations and the Effective Temperature
   High-frequency Fluctuations in a Magneto-active Plasma
   Low-frequency Fluctuations in a Magneto-active Plasma
7. Effect of Non-linear Wave Interactions on Fluctuations in a Plasma
   7.1. Equations for the Spectral Correlation Functions (Potential Field)
   The Non-linear Equation for the Fluctuation Field
   Correlation Functions
   The Equation for the Quadratic Correlation Function
   Equations for Ternary and Quaternary Correlation Functions
   7.2. The Stationary Fluctuation Spectrum Taking into Account Non-linear Corrections
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