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Fluctuations and Non-Linear Wave Interactions in Plasmas
International Series in Natural Philosophy
- 1st Edition - October 30, 2013
- Author: A. G. Sitenko
- Editor: D. ter Haar
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 7 3 5 8 - 0
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 8 9 3 9 - 0
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… Read more
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Request a sales quoteFluctuations 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.
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
Iteration Process
Induced Enhancement of Fluctuations
7.3. Non-linear Frequency Shifts and Saturation of Fluctuations in a Non-equilibrium Plasma
Non-linear Eigenfrequency Shift
Saturation of the Non-equilibrium Fluctuation Level
Turbulent Fluctuations in a Beam-Plasma System
Non-linear Stabilization of the Hydrodynamic Beam-Plasma Instability
Turbulent Fluctuations in a Plasma with an Anisotropic Velocity Distribution
7.4. Spectral Correlation Functions for Electromagnetic Fluctuations
The Non-linear Equation for the Fluctuations of the Electromagnetic Field
Set of Equations for the Sequence of Correlation Functions
The Stationary Spectrum of Electromagnetic Fluctuations
Non-linear Frequency Shifts of Electromagnetic Eigenoscillations
Saturation of the Level of Non-equilibrium Electromagnetic Fluctuations
8. Fluctuation-Dissipation Theorem
8.1. Inversion of the Fluctuation-Dissipation Theorem
Relation between the Dielectric Permittivity of an Equilibrium Plasma and the Correlation
Function for Fluctuations in a System of Non-interacting Particles
Fluctuation-dissipation Theorem for a Non-equilibrium Plasma
8.2. Non-linear Fluctuation-Dissipation Relations
Relation between Non-linear Susceptibilities and Higher Order Correlation Functions for Plasma Fluctuations (Potential Case)
Spectral Correlation Functions
Sum Rules
The Non-linear Fluctuation-dissipation Theorem for Electromagnetic Fluctuations
9. Kinetic Equations
9.1. The Kinetic Equation for Particles
Spectral Distribution of Field Fluctuations and the Equation for the One-particle Function
The Balescu-Lenard Collision Term
Dynamic Friction and Diffusion Coefficients
Quasi-linear Approximation
9.2. The Kinetic Equation for Waves (Potential Field)
Time Evolution of the Spectral Distribution of the Fluctuation Field
Linear Approximation
The Kinetic Equation for Longitudinal Plasma Waves
Non-linear Landau Damping
9.3. The Kinetic Equation for Waves (General Case)
Time Evolution of the Spectral Correlation Function for the Electromagnetic Field
The Kinetic Equation for Electromagnetic Waves in a Plasma
Parametric Instability and Turbulence
10. Scattering and Radiation of Waves
10.1. Scattering and Transformation of Waves in a Plasma
Derivation of Scattering and Transformation Cross-Sections from the Kinetic Equation for Waves
Scattering and Transformation Cross-sections in an Isotropic Plasma
10.2. Scattering and Transformation of Transverse Waves
Scattering of Transverse Electromagnetic Waves in a Plasma
Spectral Distribution of Scattered Radiation
Transformation of Transverse Electromagnetic Waves into Longitudinal Langmuir and Ion-sound Waves
10.3. Scattering and Transformation of Longitudinal Waves
Scattering of Longitudinal Langmuir Waves
Transformation of Longitudinal Langmuir Waves into Longitudinal Ion-sound
Transformation of Longitudinal Langmuir Waves into Transverse Electromagnetic Waves
10.4. Radiation from a Plasma I
Plasma Bremsstrahlung
Spontaneous Emission by a Non-equilibrium Plasma
11. Wave Interaction in a Semi-bounded Plasma
11.1. Waves in a Semi-bounded Plasma
The Non-linear Equation for the Potential Field in a Semi-bounded Plasma
Dispersion Equations for Bulk and Surface Waves (Linear Approximation)
Surface Waves
The Non-linear Equation for the Field (General Case)
11.2. Non-linear Interaction of Surface Waves
Resonant Wave Interaction
Three-wave Surface Wave Decays
Non-linear Interactions of Bulk and Surface Waves
11.3. Fluctuations and Kinetic Equations for Surface Waves
Fluctuations
Kinetic Equation for Surface Waves
References
Index
Other Titles in the Series
- No. of pages: 278
- Language: English
- Edition: 1
- Published: October 30, 2013
- Imprint: Pergamon
- Paperback ISBN: 9781483173580
- eBook ISBN: 9781483189390
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