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General two-dimensional magnetohydrodynamic equilibria with mass flow

Published online by Cambridge University Press:  13 March 2009

Y. Z. Agim  and
J. A. Tataronis
Y. Z. Agim
Affiliation:
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706
J. A. Tataronis
Affiliation:
Department of Electrical Engineering, University of Wisconsin, Madison, Wisconsin 53706
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Abstract

A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations, such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that, as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasilinear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology.

Type
Research Article
Information
Journal of Plasma Physics , Volume 34 , Issue 3 , December 1985 , pp. 337 - 360
Copyright
Copyright © Cambridge University Press 1985

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References

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