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
5 - Kinetic Theory and the Moment Equations
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
To analyze plasmas that have a finite temperature it is necessary to use a statistical approach called “kinetic theory” which describes the distribution of particle velocities in a plasma. In this chapter a famous equation, called the “Vlasov equation,” is derived. This equation describes the evolution of the number of particles in a six-dimensional (velocity-position) coordinate system called “phase space.” The Vlasov equation assumes that there are no collisions. The only forces considered are due to long-range electromagnetic and electrostatic forces. By taking velocity moments of the Vlasov equation, a series of equations called the moment equations are developed that allows one to take into account the evolution of the average density, velocity, and pressure of plasma. Unfortunately, the moment equations do not consist of a closed set of equations and always require additional assumptions, specifically an equation of state. By assuming an adiabatic equation of state, two new electrostatic wave modes, the Langmuir mode and the ion acoustic mode, are revealed that do not exist in a cold plasma.
- Type
- Chapter
- Information
- Introduction to Plasma PhysicsWith Space, Laboratory and Astrophysical Applications, pp. 148 - 185Publisher: Cambridge University PressPrint publication year: 2017
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