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Large-amplitude electron plasma oscillations

Published online by Cambridge University Press:  01 August 2008

BARBARA ABRAHAM-SHRAUNER
BARBARA ABRAHAM-SHRAUNER*
Affiliation:
Department of Electrical and Systems Engineering, Washington University, St. Louis, MO 63130, USA ([email protected])
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Abstract

Large-amplitude electron plasma oscillations in a one-dimensional, cold electron plasma are investigated for a spatially varying, immobile ion density. The Eulerian variables are transformed to Lagrangian variables. The problem is then treated as an effective one-dimensional particle in a potential. Two examples of spatially varying ion densities that lead to analytic functions for the electron position, velocity and electric field are found by Gauss' law to have zero electron density, an unphysical result. A generic solution that includes the two examples is shown to have a spatially homogeneous ion density. A nonlinear ordinary differential equation is the condition for the appropriate form of the electron density and is solved by Lie group symmetries. A more general form of a solution is presented that possesses a spatially varying ion density, but when the necessary conditions are specified it has either zero electron density or secular terms in the electron density.

Type
Papers
Information
Journal of Plasma Physics , Volume 74 , Issue 4 , August 2008 , pp. 437 - 444
Copyright
Copyright © Cambridge University Press 2007

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