Book contents
- Frontmatter
- Contents
- Acknowledgements
- Introduction
- 1 Basic equations
- 2 Propagation in a cold plasma
- 3 Parallel propagation (weakly relativistic approximation)
- 4 Parallel propagation (non-relativistic approximation)
- 5 Quasi-longitudinal approximation
- 6 Quasi-electrostatic approximation
- 7 Growth and damping of the waves
- 8 Non-linear effects
- 9 Applications to the Earth's magnetosphere
- References
- Solutions to the problems
- Index
5 - Quasi-longitudinal approximation
Published online by Cambridge University Press: 30 October 2009
- Frontmatter
- Contents
- Acknowledgements
- Introduction
- 1 Basic equations
- 2 Propagation in a cold plasma
- 3 Parallel propagation (weakly relativistic approximation)
- 4 Parallel propagation (non-relativistic approximation)
- 5 Quasi-longitudinal approximation
- 6 Quasi-electrostatic approximation
- 7 Growth and damping of the waves
- 8 Non-linear effects
- 9 Applications to the Earth's magnetosphere
- References
- Solutions to the problems
- Index
Summary
In this chapter we generalize the results of Chapters 3 and 4 to the case of quasi-longitudinal whistler-mode propagation. As in Section 2.1 we consider whistler-mode propagation as quasi-longitudinal if either ⃒θ⃒ ≪ 1 (see inequalities (2.14) and (2.17)) in the plasma with arbitrary electron density (inequalities (2.10) and (2.12) are not necessarily valid), or inequalities (2.9) and (2.10) (or (2.12)) are valid simultaneously provided the whistlermode wave normal angle θ is not close to the resonance cone angle θR0 in & cold plasma (see equation (2.13)). First we consider the case ⃒θ⃒ ≪ 1 when whistler-mode waves propagate almost parallel to the magnetic field.
As was shown in Chapter 1, when we impose no restrictions on the electron density we should use the general relativistic expressions for the elements of the plasma dielectric tensor in the form (1.73). Assuming that the waves propagate through plasma with the electron distribution function (1.76) and imposing conditions (1.77) we write these expressions in a much simpler form (1.78). Also, we assume that the electron temperature is so low that it can only slightly perturb the corresponding whistler-mode dispersion equation in a cold plasma, i.e.
where N is the whistler-mode refractive index in a hot plasma, and N0 the whistler-mode refractive index in a cold plasma defined by (2.15).
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- Whistler-mode Waves in a Hot Plasma , pp. 94 - 120Publisher: Cambridge University PressPrint publication year: 1993