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
6 - Magnetohydrodynamics
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
The field known as magnetohydrodynamics (MHD) dates to the earliest days of plasma physics and assumes that a plasma is a charged conducting fluid that responds to electromagnetic fields governed by Maxwell’s equations. Since this fluid approach ignores cyclotron motions, the MHD model is valid only at low frequencies, well below the lowest ion cyclotron frequency, and at large spatial scales, much larger than the largest ion cyclotron radius. In this chapter we show that, except for an Ohm’s law conductivity that relates the current to the electric field, all of the basic MHD equations can be derived from the moment equations given in Chapter 5. An approximate conductivity equation, called the “generalized Ohm’s law,” is derived that relates charges and current in the plasma to the large scale electric and magnetic fields. Equations are also derived showing that the magnetic field produces an anisotropic pressure that adds to the plasma pressure, and that the magnetic field lines cab be “frozen” into the plasma if the conductivity is sufficiently large.
- Type
- Chapter
- Information
- Introduction to Plasma PhysicsWith Space, Laboratory and Astrophysical Applications, pp. 186 - 220Publisher: Cambridge University PressPrint publication year: 2017
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