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Clebsch representations in the theory of minimum energy equilibrium solutions in magnetohydrodynamics

Published online by Cambridge University Press:  13 March 2009

Hanno Rund ,
Daniel R. Wells  and
Lawrence Carl Hawkins
Hanno Rund
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Daniel R. Wells
Affiliation:
Department of Physics, University of Miami, Coral Gables, Florida 33124
Lawrence Carl Hawkins
Affiliation:
Department of Physics, University of Miami, Coral Gables, Florida 33124
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Abstract

The introduction of Clebsch representations allows one to formulate the problem of finding minimum energy solutions for a magneto-fluid as a well-posed problem in the calculus of variations of multiple integrals. When the latter is subjected to integral constraints, the Euler–Lagrange equations of the resulting isoperimetric problem imply that the fluid velocities are collinear with the magnetic field. If, in particular, one constraint is abolished, Alfvén velocities are obtained. In view of the idealized nature of the model treated here, further investigations of more sophisticated structures by means of Clebsch representations are anticipated. Preliminary results of a similar calculation utilizing a modified two fluid model are discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 20 , Issue 3 , December 1978 , pp. 329 - 344
Copyright
Copyright © Cambridge University Press 1978

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