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Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

Published online by Cambridge University Press:  13 March 2009

Dana Aaron Roberts  and
Barbara Abraham-Shrauner
Dana Aaron Roberts
Affiliation:
Electrical Engineering Department, Washington University, St. Louis, MO 63130
Barbara Abraham-Shrauner
Affiliation:
Electrical Engineering Department, Washington University, St. Louis, MO 63130
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Abstract

Lie group point transformations applied to the one-dimensional Vlasov– Maxwell equations yield general similarity forms for the dependent and independent variables. One class of such solutions is seemingly like Bern-stein-Greene-Kruskal solutions in allowing a relatively free choice of electric field, but with a more complex time dependence. The phase trajectories of the particles are found here for both temporally damped and (possibly unphysical) growing electric fields in this class by numerical integration in the original and in transformed co-ordinates. The analysis, which includes an analytic consideration of phase-plane fixed (critical) points, shows the advantages of the new co-ordinates, and reveals qualitative features of the distribution function.

Type
Research Article
Information
Journal of Plasma Physics , Volume 38 , Issue 3 , December 1987 , pp. 335 - 350
Copyright
Copyright © Cambridge University Press 1987

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