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A Fourier-space description of oscillations in an inhomogeneous plasma. Part 2. Discrete approach

Published online by Cambridge University Press:  13 March 2009

P. S. Cally  and
Z. Sedláček
P. S. Cally
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
Z. Sedláček
Affiliation:
Institute of Plasma Physics, Academy of Sciences of the Czech Republic, P.O. Box 17, Za Slovankou 3, 18200 Prague 8, Czech Republic
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Abstract

The process of phase mixing in inhomogeneous MHD or cold plasmas is interpreted as one of energy propagation in discrete Fourier space. Three instructive scenarios are examined: (i) an isolated inhomogeneity with zero boundary conditions; (ii) a periodic inhomogeneity; and (iii) a monotonic inhomogeneity sandwiched between two semi-infinite uniform regions. In each case the coefficients of the associated wave equation in Fourier space for an appropriately chosen dependent variable are very nearly constant almost everywhere, so the propagation is like that of a free unreflected wave. An exception may arise in the coupling of the lowest modes, which can be highly reflective. It is argued that Fourier space is the simplest and most natural context in which to discuss the development of fine-scale oscillations.

Type
Research Article
Information
Journal of Plasma Physics , Volume 52 , Issue 2 , October 1994 , pp. 265 - 296
Copyright
Copyright © Cambridge University Press 1994

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