Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Characteristic Parameters of a Plasma
- 3 Single-Particle Motions
- 4 Waves in a Cold Plasma
- 5 Kinetic Theory and the Moment Equations
- 6 Magnetohydrodynamics
- 7 MHD Equilibria and Stability
- 8 Discontinuities and Shock Waves
- 9 Electrostatic Waves in a Hot Unmagnetized Plasma
- 10 Waves in a Hot Magnetized Plasma
- 11 Nonlinear Effects
- 12 Collisional Processes
- Appendix A Symbols
- Appendix B Useful Trigonometric Identities
- Appendix C Vector Differential Operators
- Appendix D Vector Calculus Identities
- Index
- References
11 - Nonlinear Effects
Published online by Cambridge University Press: 16 March 2017
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Characteristic Parameters of a Plasma
- 3 Single-Particle Motions
- 4 Waves in a Cold Plasma
- 5 Kinetic Theory and the Moment Equations
- 6 Magnetohydrodynamics
- 7 MHD Equilibria and Stability
- 8 Discontinuities and Shock Waves
- 9 Electrostatic Waves in a Hot Unmagnetized Plasma
- 10 Waves in a Hot Magnetized Plasma
- 11 Nonlinear Effects
- 12 Collisional Processes
- Appendix A Symbols
- Appendix B Useful Trigonometric Identities
- Appendix C Vector Differential Operators
- Appendix D Vector Calculus Identities
- Index
- References
Summary
An analysis is given of various types of nonlinear effects that can occur in plasmas. The topics covered are quasi-linear theory, wave-wave interactions, Langmuir wave solitons, and stationary nonlinear electrostatic potentials. Quasi-linear theory describes how an electrostatic wave driven by an unstable velocity distribution function causes the velocity distribution function to evolve in such a way that it eliminates the instability. The discussion of wave-wave interactions describes how a wave can nonlinearly interact with another wave to produce a third wave at either the sum or difference of the frequencies of the two interacting waves. The section on Langmuir wave solitons describes how a very intense single wave can alter the initial local plasma density in such a way as to form intense isolated wave structure known as a solitons. The section on stationary electrostatic potentials shows how highly nonlinear self-consistent electrostatic structures can form in otherwise time-stationary plasmas. Although there are many other nonlinear processes that can occur, these examples provide a good overview of the methods used to analyze these effects.
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- Information
- Introduction to Plasma PhysicsWith Space, Laboratory and Astrophysical Applications, pp. 428 - 478Publisher: Cambridge University PressPrint publication year: 2017
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