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Elements of magnetohydrodynamics with the Hall current. Part 1. Nonlinear phenomena

Published online by Cambridge University Press:  13 March 2009

P. Rosenau ,
J. A. Tataronis  and
G. Conn
P. Rosenau
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
J. A. Tataronis
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
G. Conn
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
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Abstract

The elements of magnetohydrodynamics (MHD) with the Hall current are presented. The governing partial differential equations are, like those of ideal MHD, quasi-linear, but unlike ideal MHD, are not hyperbolic. However, they do possess real characteristics which are shown to be associated with the sound wave and the surfaces ø(r, t) = const. determined by B. ∇ø = 0. Properties of weak and strong discontinuities are discussed, and comparisons are made with ideal MHD. It is shown that generalizations of dipole layers appear as a result of discontinuities in the magnetic field.

Type
Research Article
Information
Journal of Plasma Physics , Volume 21 , Issue 3 , June 1979 , pp. 385 - 399
Copyright
Copyright © Cambridge University Press 1979

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