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Nonlinear waves in a cold plasma by Lorentz transformation

Published online by Cambridge University Press:  13 March 2009

P. C. Clemmow
P. C. Clemmow
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Wave propagation in a cold, collisionless, two-component plasma is analyzed by considering, first, the frame of reference in which the field has no space dependence, and then applying a Lorentz transformation to obtain a wave whose space-time dependence is a function of t — nz / c only, where n is a constant. Exact (nonlinear, relativistic) results for known special cases, and some others, are given; and it is shown that, when there is no ambient magnetic field, the general problem in essence reduces to the solution of one second-order, nonlinear differential equation. The desirabifity of introducing a free parameter representing a stream velocity in the direction of wave propagation is emphasized; and the significance of the choice of this parameter is discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 12 , Issue 2 , October 1974 , pp. 297 - 317
Copyright
Copyright © Cambridge University Press 1974

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References

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