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Non-linear transverse waves in a Vlasov plasma

Published online by Cambridge University Press:  13 March 2009

S. Peter Gary
S. Peter Gary
Affiliation:
Applied Mathematics Department, University of St Andrews, St Andrews, Scotland
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Abstract

Non-linear transverse waves in a classical non-relativistic collisionless, Maxwellian electron gas with external magnetic field B0 are considered. There is assumed a small, sinusoidal variation in the initial electric and magnetic fields, corresponding to excitation of a discrete wave-number mode. The non-linear Vlasov equation is solved to second order in the long time limit via the Montgomery—Gorman perturbation expansion, and the time-independent, spatially homogeneous part of the second-order distribution function is used to modify the linear dispersion relation. For frequencies near the electron cyclotron frequency a non-linear damping decrement results such that, for many values of the parameters, the damping is less than the linear rate. Thus at sufficiently long times, the rate of damping of transverse electron cyclotron waves should decrease, a result similar to that for non-linear damping of longitudinal electron plasma waves.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 3 , Issue 4 , December 1969, pp. 577 - 592
Copyright
Copyright © Cambridge University Press 1969

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