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Exact damped sinusoidal electric field of nonlinear one-dimensional Vlasov-Maxwell equations

Published online by Cambridge University Press:  13 March 2009

B. Abraham-Shrauner
B. Abraham-Shrauner
Affiliation:
Department of Electrical Engineering, Washington University, St Louis, Missouri 63130
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Abstract

An exact solution for a temporally damped sinusoidal electric field which obeys the nonlinear, one-dimensional Vlasov-Maxwell equations is given. The electric field is a generalization of the O'Neil model electric field for Landau damping of plasma oscillations. The electric field is a special case of the form found from the invariance of the one-dimensional Vlasov equation under infinitesimal Lie group transformations. The time dependences of the damping decrement, of the wave-number and of the angular frequency are derived. Use of a time-dependent BGK one-particle distribution function is justified for weak damping where, in general, it is necessary to carry out a numerical calculation of the invariant of which the distribution function is a functional.

Type
Research Article
Information
Journal of Plasma Physics , Volume 32 , Issue 2 , October 1984 , pp. 197 - 205
Copyright
Copyright © Cambridge University Press 1984

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References

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