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Stability of relativistic transverse cold plasma waves Part 1. Circularly polarized waves

Published online by Cambridge University Press:  13 March 2009

F. J. Romeiras
F. J. Romeiras
Affiliation:
Centro de Eloctrodinâmica, Instituto Superior Técnico, Lisboa-1, Portugal
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Abstract

This paper is concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized electron–ion plasma. These nonlinear waves are of fixed profile, superluminous, period.ic and transverse. The small perturbations are assumed to propagate in the same direction as the nonlinear wave. A Lagrangian method is used to derive the perturbation equations. The analysis is carried out in the frame where the nonlinear waves are space independent and then the results Lorentz transformed to the laboratory frame. Part 1 refers to circularly polarized waves. In this case it is possible to integrate the equations and obtain an algebraic dispersion relation in the form of an eighth order polynomial equation in the frequency. The analytical and numerical solution of this equation, for a wide range of variation of the parameters involved, reveals the existence of a very unstable mode. Particular attention is given to very large wave amplitudes for which the plasma behaves like an electron–positron plasma; in this case the growth rate of the unstable mode can be as high as the frequency of the nonlinear wave.

Type
Research Article
Information
Journal of Plasma Physics , Volume 20 , Issue 3 , December 1978 , pp. 479 - 501
Copyright
Copyright © Cambridge University Press 1978

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