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Methods in Nonlinear Plasma Theory
1st Edition - February 28, 1972
Author: Ronald Davidson
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 5 3 3 8 - 6
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… Read more
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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.
Preface
Acknowledgments
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
References
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
References
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
References
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
References
Supplementary References
Chapter 5. Plasma Echoes
5.1 Introduction and Basic Echo Mechanism
5.2 Theory of Second-Order Temporal Echoes
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
References
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
Reference
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
Reference
Author Index
Subject Index
- No. of pages: 376
- Language: English
- Edition: 1
- Published: February 28, 1972
- Imprint: Academic Press
- eBook ISBN: 9780323153386