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Weakly multi-dimensional cosmic-ray-modified MHD shocks

Published online by Cambridge University Press:  13 March 2009

G. P. Zank and
G. W. Webb
G. P. Zank
Affiliation:
Bartol Research Institute, The University of Delaware, Newark, Delaware 19716, U.S.A.
G. W. Webb
Affiliation:
Department of Planetary Sciences, University of Arizona, Tucson, Arizona 85721, U.S.A.
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Abstract

The multi-dimensional structure of weak, energetic-particle-modified shocks is investigated by means of appropriate perturbation techniques. The time-dependent shock-structure equation is found to be a generalized form of the well-known one-dimensional Burgers equation, whose steady state, in the absence of cosmic rays, is shown to be related to an equation modelling steady transonic flow in several dimensions. The time-dependent (1 + 2)- and (1 + 3)-dimensional Burgers equations are integrated exactly by means of Hirota's technique for one-shock solutions. On the basis of the exact solutions, a discussion relating the various length scales associated with the shock is presented.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 44 , Issue 1 , August 1990, pp. 91 - 101
Copyright
Copyright © Cambridge University Press 1990

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