Methods in Nonlinear Plasma Theory

Methods in Nonlinear Plasma Theory

1st Edition - February 28, 1972

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  • Author: Ronald Davidson
  • eBook ISBN: 9780323153386

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Methods in Nonlinear Plasma Theory is from lectures given in graduate classes in both University of Maryland and University of California at Berkeley. To be able to understand fully the contents in this book, the reader is assumed to be a graduate student with background of classical physics and linear plasma waves and instabilities. This text is divided into two major parts. Part I deals with the coherent nonlinear phenomena, while Part II discusses the turbulent nonlinear phenomena. Six chapters comprise Part I, where basic equations and methods are described and discussed. Some of these methods are Vlasov-Maxwell equations and Korteweg-de Vries equation. Part II meanwhile has eight chapters that discuss frameworks and theories for weak plasma turbulence. Specifically, the weak turbulence theory is presented as it is applied to electromagnetic wave-particle interactions, nonlinear wave-wave interactions, and nonlinear wave-particle interactions. This book is a useful reference for students and researchers in the study of classical physics and plasma theory.

Table of Contents

  • Preface


    General References

    Part I Coherent Nonlinear Phenomena

    Chapter 1. Introduction

    1.1 Basic Equations and Methods

    1.2 Terminology and Classification of Interactions

    1.3 Multiple-Time-Scale Perturbation Analysis of the Van der Pol Equation


    Chapter 2. The Korteweg-de Vries Equation-A Weakly Nonlinear Theory of Ion Sound Waves

    2.1 Introduction and Basic Equation

    2.2 Derivation of the Korteweg-de Vries Equation for Nonlinear Ion Sound Waves

    2.3 Solution of the Korteweg-de Vries Equation

    2.4 Examples and General Properties of the Solution

    2.5 Nonlinear Theory of Ion Sound Waves with Collisionless Dissipation


    Supplementary References

    Chapter 3. Large-Amplitude Electron Plasma Oscillations

    3.1 One-Dimensional Cold-Plasma Model

    3.2 Exact Solution in Lagrangian Variables

    3.3 Nonlinear Example with Inversion to Eulerian Variables

    3.4 Extensions of the Model

    3.5 Modifications Due to Finite Electron Temperature


    Supplementary References

    Chapter 4. Strong Wave-Particle Interactions-Particle Trapping

    4.1 Introduction

    4.2 Collisionless Damping of Electron Plasma Oscillations

    4.3 Large-Amplitude Bernstein-Greene-Kruskal Waves

    4.4 Stability of Bernstein-Greene-Kruskal Waves


    Supplementary References

    Chapter 5. Plasma Echoes

    5.1 Introduction and Basic Echo Mechanism

    5.2 Theory of Second-Order Temporal Echoes


    Supplementary References

    Chapter 6. Coherent Nonlinear Wave-Wave Interactions

    6.1 Introduction and Basic Equation

    6.2 Wave-Wave Coupling in Macroscopic Plasma Models

    6.3 Wave-Wave Coupling in Vlasov Plasma Models

    6.4 Nonlinear Theory of Resonant Three-Wave Coupling

    6.5 Examples of Resonant Three-Wave Coupling


    Supplementary References

    Part II Turbulent Nonlinear Phenomena

    Chapter 7. Statistical Frameworks for Weak Plasma Turbulence

    7.1 Basic Definitions and Terminology

    7.2 The Random Phase Approximation

    7.3 Evolution of Collective Correlations in a Vlasov Ensemble

    7.4 Discrete Particle Interactions

    7.5 Summary


    Supplementary References

    Chapter 8. Weak Turbulence Theory of Electrostatic Wave-Particle Interactions

    8.1 Introduction and Basic Assumptions

    8.2 The Weak Turbulence Kinetic Theory

    8.3 Weak Turbulence Kinetic Equations for a Multicomponent Plasma

    8.4 General Properties of the Kinetic Equations

    8.5 Electrostatic Turbulence in a Magnetoplasma

    8.6 Phase-Mixing of Free-Streaming Correlations


    Supplementary References

    Chapter 9. Stabilization of the Weak Electron Beam (Bump-in-Tail) Instability

    9.1 Introduction and Dispersion Relation

    9.2 Stabilization in One Dimension

    9.3 Stabilization in Higher Dimensions

    9.4 Range of Validity of the Theory

    9.5 Computer Simulation of the Weak Bump-in-Tail Instability

    9.6 Resonance Broadening


    Supplementary References

    Chapter 10. Stabilization of the Ion Loss-Cone Instability

    10.1 Introduction and Basic Assumptions

    10.2 Dispersion Relation

    10.3 Stabilization Process


    Chapter 11. Electron Heating by Electron-Ion Beam Instabilities

    11.1 Introduction

    11.2 Dispersion Relation

    11.3 Time Evolution of the Electron-Ion Beam System

    11.4 Computer Simulation of the Electron-Ion Beam Instability


    Supplementary References

    Chapter 12. Weak Turbulence Theory of Electromagnetic Wave-Particle Interactions

    12.1 The Vlasov-Maxwell Description

    12.2 Weak Turbulence Kinetic Theory for Parallel Propagation

    12.3 Stabilization of the Electron Whistler Instability

    12.4 Stabilization of the Garden-Hose Instability


    Supplementary References

    Chapter 13. Weak Turbulence Theory of Nonlinear Wave-Wave Interactions

    13.1 Introduction

    13.2 The Hierarchy for Wave Correlations

    13.3 The Weak Turbulence Kinetic Theory

    13.4 General Properties of the Wave Kinetic Equation

    13.5 Exact Solution of the Wave Kinetic Equation in One Dimension

    13.6 Kinetics of Resonant Three-Wave Interactions in Three Dimensions

    13.7 Kinetic Equation for Resonant Four-Wave Processes


    Supplementary References

    Chapter 14. General Weak Turbulence Theory of Nonlinear Electrostatic Interactions

    14.1 Introduction and Basic Assumptions

    14.2 Derivation of the Kinetic Equations

    14.3 Extension of the Kinetic Equations to the Multicomponent Many-Mode Case

    14.4 Properties of the Kinetic Equations

    14.5 Nonlinear Landau Damping of Electron Plasma Oscillations

    14.6 Extensions of the Weak Turbulence Theory


    Supplementary References

    Appendix A. The Korteweg-de Vries Equation and the Inverse Scattering Problem

    Appendix B. Matrix Symmetries

    Appendix C. Phase-Mixing of Free-Streaming Correlations

    Appendix D. Second-Order Two-Body Correlations in a Weakly Turbulent Plasma

    D.1 Evaluation of the Two-Body Correlation Function

    D.2 Kinetic Equation for the Waves

    D.3 Kinetic Equation for the Particles


    Appendix E. Nonlinear Wave-Particle Coupling Coefficients

    E.1 Coupling Coefficient for the Wave Kinetic Equation

    E.2 Coupling Coefficient for the Particle Kinetic Equation


    Author Index

    Subject Index

Product details

  • No. of pages: 376
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: February 28, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9780323153386

About the Author

Ronald Davidson

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