Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Particle orbit theory
- 3 Macroscopic equations
- 4 Ideal magnetohydrodynamics
- 5 Resistive magnetohydrodynamics
- 6 Waves in unbounded homogeneous plasmas
- 7 Collisionless kinetic theory
- 8 Collisional kinetic theory
- 9 Plasma radiation
- 10 Non-linear plasma physics
- 11 Aspects of inhomogeneous plasmas
- 12 The classical theory of plasmas
- Appendix 1 Numerical values of physical constants and plasma parameters
- Appendix 2 List of symbols
- References
- Index
3 - Macroscopic equations
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Particle orbit theory
- 3 Macroscopic equations
- 4 Ideal magnetohydrodynamics
- 5 Resistive magnetohydrodynamics
- 6 Waves in unbounded homogeneous plasmas
- 7 Collisionless kinetic theory
- 8 Collisional kinetic theory
- 9 Plasma radiation
- 10 Non-linear plasma physics
- 11 Aspects of inhomogeneous plasmas
- 12 The classical theory of plasmas
- Appendix 1 Numerical values of physical constants and plasma parameters
- Appendix 2 List of symbols
- References
- Index
Summary
Introduction
When the fields induced by the motion of the plasma particles are significant in determining that motion, particle orbit theory is no longer an apt description of plasma behaviour. The problem of solving the Lorentz equation self-consistently, where the fields are the result of the motion of many particles, is no longer practicable and a different approach is required. In this chapter, by treating the plasma as a fluid, we derive various sets of equations which describe both the dynamics of the plasma in electromagnetic fields and the generation of those fields by the plasma.
The fluid equations of neutral gases and liquids are usually derived by treating the fluid as a continuous medium and considering the dynamics of a small volume of the fluid. The aim is to develop a macroscopic model that, as far as possible, is independent of the detail of what happens at the molecular level. In this sense the approach is the opposite of that adopted in particle orbit theory where we seek information about a plasma by examining the motion of individual ions and electrons. In experiments one seldom makes measurements or observations at the microscopic level so we require a macroscopic description of a plasma similar to the fluid description of neutral gases and liquids. This is obtained here by an extension of the methods of fluid dynamics, an approach that conveniently skims over some fundamental difficulties inherent in plasmas. The chief of these is that a plasma is not really one fluid but at least two, one consisting of ions and the other electrons.
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- The Physics of Plasmas , pp. 48 - 76Publisher: Cambridge University PressPrint publication year: 2003