# Non-Linear Theory and Fluctuations

## 1st Edition

### Plasma Electrodynamics

**Authors:**A. I. Akhiezer I. A. Akhiezer R. V. Polovin

**eBook ISBN:**9781483148076

**Imprint:**Pergamon

**Published Date:**1st January 1975

**Page Count:**320

## Description

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 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.

## Table of Contents

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

## Details

- No. of pages:
- 320

- Language:
- English

- Copyright:
- © Pergamon 1975

- Published:
- 1st January 1975

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483148076