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Non-Linear Theory and Fluctuations
Plasma Electrodynamics
- 1st Edition - January 1, 1975
- Authors: A. I. Akhiezer, I. A. Akhiezer, R. V. Polovin
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 4 8 0 7 - 6
Plasma Electrodynamics, Volume 2: Non-Linear Theory and Fluctuations deals with the theory of nonlinear waves in a collisionless plasma, including the quasilinear theory, the… Read more
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Request a sales quotePlasma Electrodynamics, Volume 2: Non-Linear Theory and Fluctuations deals with the theory of nonlinear waves in a collisionless plasma, including the quasilinear theory, the theory of plasma turbulence, and the theory of electromagnetic fluctuations in a plasma. Topics covered range from nonlinear high-frequency waves in a cold plasma to the theory of plasma oscillations in the quasilinear approximation. Nonlinear wave-particle interactions are also discussed, along with scattering and transformation of waves in a plasma. Comprised of six chapters, this volume begins with a study of nonlinear waves in a collisionless plasma, focusing on nonlinear high-frequency waves in a cold plasma; Langmuir waves in a non-relativistic plasma; and longitudinal, transverse, and coupled longitudinal-transverse waves in a relativistic plasma. After expounding on the quasilinear theory, which describes the effects of the first approximation in terms of the plasma wave energy, the nonlinear interaction of waves and particles is considered. The last three chapters explore the theory of electromagnetic fluctuations in a plasma; the theory of scattering processes and the transformation of waves in a plasma; and the scattering of charged particles in a plasma. The polarization energy losses when charged particles move in a plasma are calculated. This book will be of interest to physicists.
Preface
Preface to English Edition
Chapter 8. Non-Linear Waves in a Collisionless Plasma
8.1. Non-Linear High-Frequency Waves in a Cold Plasma
8.1.1. Non-Linear Non-Relativistic Langmuir Oscillations
8.1.2. Equations Describing Non-Linear Waves in a Relativistic Plasma when there are no Thermal Effects
8.1.3. Longitudinal Waves in a Relativistic Plasma
8.1.4. Transverse Waves in a Relativistic Plasma
8.1.5. Coupled Longitudinal-Transverse Waves in a Relativistic Plasma
8.2. Non-linear Waves in an Unmagnetized Two-Temperature Plasma
8.2.1. Equations Describing a Non-Linear Wave in a Quasi-Equilibrium Plasma
8.2.2. Simple (Riemann) Waves
8.2.3. Periodic and Solitary Waves
8.2.4. Quasi-Shock Waves
8.3. Non-Linear Waves in an Unmagnetized Non-Equilibrium Plasma
8.3.1. Equations Describing a Non-Linear Wave in a Non-Equilibrium Plasma
8.3.2. Simple Waves
8.3.3. Stationary Waves
8.3.4. Multiple-Current Flow in a Non-Equilibrium Plasma
8.4. Non-Linear Waves in a Magneto-Active Plasma with Hot Electrons
8.4.1. Equations Describing a Non-Linear Wave in a Plasma in a Magnetic Field
8.4.2. Simple Magneto-Sound Waves
8.4.3. Stationary Magneto-Sound Waves
8.5. Non-Linear Low-Frequency Waves in a Cold Plasma in a Magnetic Field
8.5.1. Equations Describing a Non-Linear Wave in a Cold Magneto-Active Plasma
8.5.2. Non-Linear Waves for the Case of a Strong Magnetic Field
8.5.3. Non-Linear Waves in the Case of a Weak Magnetic Field
Chapter 9. Theory of Plasma Oscillations in the Quasi-Linear Approximation
9.1. Quasi-Linear Theory of the Oscillations of an Unmagnetized Plasma
9.1.1. The Quasi-Linear Approximation
9.1.2. Quasi-Linear Relaxation
9.1.3. Relaxation of One-Dimensional Wavepackets
9.1.4. Effect of the Coulomb Collisions on the Quasi-Linear Relaxation and Landau Damping of the Langmuir Oscillations
9.2. Quasi-Linear Theory of the Oscillations of a Magneto-Active Plasma
9.2.1. Basic Equations
9.2.2. Quasi-Linear Relaxation in a Magneto-Active Plasma
9.2.3. Relaxation of One-Dimensional Wavepackets in a Magneto-Active Plasma
9.2.4. Effect of Collisions on Quasi-Linear Relaxation and Cherenkov and Cyclotron Damping of Oscillations
Chapter 10. Non-Linear Wave-Particle Interactions
10.1. Kinetic Equations for the Waves
10.1.1. Non-Linear Equations for the Wave Amplitude
10.1.2. Equation for the Correlation Function
10.1.3. Three-Wave Processes and Non-Linear Landau Damping
10.2. Turbulent Processes in which Langmuir Waves Take Part
10.2.1. Interaction Between Langmuir Waves and Ion-Sound Waves
10.2.2. Decay Instability of Langmuir Waves
10.2.3. Non-Linear Damping of Langmuir Waves
10.3. Ion-Sound Turbulence
10.3.1. Non-Linear Damping of Ion Sound
10.3.2. Stationary Distributions of Turbulent Waves
10.4. Interaction Between Magneto-Sound and Alfvén Waves
10.4.1. The Collision Integral and the H-Theorem for the Gas of Plasmons
10.4.2. The Hamiltonian of a System of Plasmons
10.4.3. Probabilities for Three-Plasmon Processes
10.4.4. Plasmon Lifetimes
Chapter 11. Fluctuations in a Plasma
11.1. Fluctuation—Dissipation Relation
11.1.1. Space—Time Correlation Functions
11.1.2. The Spectral Density of Fluctuations and the Energy Dissipation in a Medium
11.1.3. Symmetry of the Response Tensor
11.2. Electromagnetic Fluctuations in an Equilibrium Plasma
11.2.1. Electromagnetic Fluctuations in Media with Space—Time Dispersion
11.2.2. Electromagnetic Fluctuations in an Isotropic Plasma
11.2.3. Charge Density Fluctuations
11.2.4. Current density Fluctuations
11.2.5. Electromagnetic Field Fluctuations
11.2.6. Electron and ion Density Fluctuations
11.2.7. Fluctuations in a Plasma in a Magnetic Field
11.3. Inversion of the Fluctuation—Dissipation Relation
11.3.1. Connection Between the Dielectric Permittivity of the Plasma and the Correlation Function of the Fluctuations for a System of Non-Interacting Particles
11.3.2. Dielectric Permittivity of an Isotropic Plasma
11.3.3. Dielectric Permittivity Tensor of a Plasma in a Magnetic Field
11.4. Electromagnetic Fluctuations in a Non-Isothermal Plasma
11.4.1. Fluctuations in an Isotropic Non-Isothermal Plasma
11.4.2. Fluctuations in an Anisotropic Non-Isothermal Plasma
11.4.3. Fluctuations in a Non-Isothermal Plasma in a Magnetic Field
11.5. Electromagnetic Fluctuations in a Non-Equilibrium Plasma
11.5.1. Spectral Densities of Fluctuations in a Plasma with Non-Equilibrium, but Stable Distribution Functions
11.5.2. Collective Fluctuations and Effective Temperature
11.5.3. Critical Fluctuations Near the Boundaries of Plasma Instability
11.5.4. Fluctuations in a Non-Equilibrium Plasma in a Magnetic Field
11.6. Kinetic Theory of Fluctuations
11.6.1. Fluctuations in the Distribution Function
11.6.2. Fluctuations in the Distribution Functions in a Non-Isothermal Plasma
11.6.3. Evolution in Time of the Fluctuations
11.6.4. Fluctuations in a Plasma-Beam System
11.6.5. Effect of Particle Collisions on Fluctuations in a Plasma
11.6.6. Transition to the Hydrodynamical Theory of Fluctuations
11.7. Fluctuations in a Partially Ionized Plasma in an External Electrical Field
11.7.1. Fluctuations when there is no Magnetic Field
11.7.2. Critical Fluctuations in Electrical and Magnetic Fields
Chapter 12. Scattering and Transformation of Waves in a Plasma
12.1. Scattering of Electromagnetic Waves in an Unmagnetized Plasma
12.1.1. Scattering Current
12.1.2. Scattering Cross-Section
12.1.3. Spectral Distribution of the Scattered Radiation
12.1.4. Critical Opalescence
12.2. Transformation of Transverse and Longitudinal Waves in a Plasma
12.2.1. Transformation of a Transverse Wave into a Longitudinal One
12.2.2. Transformation and Scattering of Longitudinal Waves
12.2.3. Spontaneous Emission by a Non-Equilibrium Plasma
12.3. Incoherent Reflection of Electromagnetic Waves from a Plasma
12.3.1. Reflection Coefficient
12.3.2. Spectral Distribution of the Reflected Emission
12.4. Scattering and Transformation of Waves in a Plasma in a Magnetic Field
12.4.1. Field of the Scattered Waves; Scattering and Transformation Cross-Sections
12.4.2. Scattering and Transformation of Electromagnetic Waves by Incoherent Fluctuations
12.4.3. Scattering and Transformation of Electromagnetic Waves by Resonance Fluctuations
12.4.4. Scattering and Transformation of Langmuir Waves
12.4.5. Transformation of Low-Frequency Waves by Langmuir Fluctuations
12.5. Scattering and Transformation of Waves in a Partially Ionized Plasma in an External Electrical Field
12.5.1. Scattering of Transverse Waves when there is no External Magnetic Field
12.5.2. Scattering of Transverse Waves when there is an External Magnetic Field Present
12.5.3. Critical Opalescence when Longitudinal Waves are Scattered or Transformed
12.6. Scattering and Transformation of Waves in a Turbulent Plasma
12.6.1. Transformation of Longitudinal into Transverse Waves
12.6.2. The Scattering of Electromagnetic Waves by Turbulent Ion-Sound Oscillations
12.6.3. Scattering of Electromagnetic Waves by Turbulent High-Frequency Oscillations
12.7. Echoes in a Plasma
12.7.1. Undamped Oscillations of the Distribution Function and Echo Effects in a Plasma
12.7.2. Longitudinal Field Echo Oscillations
12.7.3. Echo when the Wavevectors of the Perturbations are Antiparallel
Chapter 13. Scattering of Charged Particles in a Plasma
13.1. The Passage of Charged Particles through an Unmagnetized Plasma
13.1.1. The Field of a Charge in a Plasma
13.1.2. Polarization Energy Losses when a Charged Particle Moves through the Plasma
13.1.3. Change in the Energy of a Moving Charge, Caused by the Fluctuations of the Field in the Plasma
13.1.4. Scattering Probability and Energy Losses of a Particle
13.2. Dynamic Friction and Diffusion Coefficients in a Plasma
13.2.1. The Fokker-Planck Equation for Test Particles
13.2.2. Dynamic Friction and Diffusion Coefficients in an Electron Plasma
13.2.3. Friction and Diffusion Coefficients in a Two-Temperature Plasma
13.3. Passage of Charged Particles through an Equilibrium Plasma in a Magnetic Field
13.3.1. Scattering Probability in a Magneto-Active Plasma
13.3.2. Polarization Energy Losses of a Particle, Caused by the Interaction with the Longitudinal Field
13.3.3. Taking the Curvature into Account
13.3.4. Cherenkov Emission of a Charge Moving in a Plasma in a Magnetic Field
13.4. The Interaction of Charged Particles with a Non-Equilibrium Plasma
13.4.1. Scattering of Charged Particles by Critical Fluctuations
13.4.2. Interaction of Charged Particles with a Turbulent Plasma
13.4.3. Interaction of Charged Particles with a Turbulent Plasma in a Magnetic Field
References
Glossary
Index
- No. of pages: 320
- Language: English
- Edition: 1
- Published: January 1, 1975
- Imprint: Pergamon
- eBook ISBN: 9781483148076
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