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Analytical solutions for oblique wave growth from a ring-beam distribution

Published online by Cambridge University Press:  13 March 2009

Richard M. Thorne  and
Danny Summers
Richard M. Thorne
Affiliation:
Department of Atmospheric Sciences, University of California, Los Angeles, California 90024, U.S.A.
Danny Summers
Affiliation:
Department of Atmospheric Sciences, University of California, Los Angeles, California 90024, U.S.A.
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Extract

Analytical solutions are presented for the linear growth rate of oblique plasma waves in a magnetized plasma due to resonant interactions with a model ringbeam distribution. Explicit closed-form solutions for the angular dependence are obtained in terms of modified Bessel functions of the first kind. In the limits of either quasi-longitudinal or quasi-transverse propagation the analytical solutions take the form of simple algebraic expansions, which allow an immediate comparison of the relative contributions from different harmonic resonances, and which also determine the conditions for marginal stability for any specific resonance. The results can be applied, for instance, to the growth of waves following ionization of neutrals originating from cometary, planetary, or interstellar material in the solar wind. In a weakly unstable plasma the analytical results also provide an important check on the complex numerical codes that hitherto constituted the only method available for evaluating the growth of oblique plasma waves.

Type
Research Article
Information
Journal of Plasma Physics , Volume 39 , Issue 3 , June 1988 , pp. 485 - 502
Copyright
Copyright © Cambridge University Press 1988

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References

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