Mutually Interacting Instabilities in the Magnetosphere
It may happen that a magnetospheric plasma can admit two or more instabilities of different types, for example, a high frequency instability (electrostatic or cyclotron) and a low frequency instability (hydromagnetic or drift wave). In many such cases, the plasma wave dynamics cannot even approximately be described by a simple linear superposition of the various instabilities which are possible, because slight changes in the plasma produced by one instability may cause major changes in the growth rate of another. It is always possible to describe this interaction mathematically by saving enough terms in the Vlasov-Maxwell equations (e.g., mode-mode coupling). To some extent a physically concise and useful description is supplied by following the analysis of Dupree (1966, 1967, 1968), certain aspects of which were rediscovered independently by the author in the course of the present work. In this analysis, one takes into account the influence of the instability wave fields on particle orbits which are used to calculate the dispersion relation. In this fashion, growth rates taken from the dispersion relation depend explicitly on wave intensities, in contrast to the usual linear stability calculations. In certain cases, this explicit dependence on wave intensities is essential for description of equilibrium, since the equilibrium conditions of quasi-linear theory (Kennel and Engelmann, 1966) cannot be applied.
KeywordsDispersion Relation Pitch Angle Radial Diffusion Wave Intensity Drift Wave
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