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The general Lie group and similarity solutions for the one-dimensional Vlasov–Maxwell equations

Published online by Cambridge University Press:  13 March 2009

Dana Roberts
Dana Roberts
Affiliation:
Department of Electrical Engineering, Washington University, St Louis, Missouri 63130
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Abstract

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 33 , Issue 2 , April 1985 , pp. 219 - 236
Copyright
Copyright © Cambridge University Press 1985

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References

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