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General stability analysis of force-free magnetic fields. Part 1. General theory

Published online by Cambridge University Press:  13 March 2009

Jan Krüger
Jan Krüger
Affiliation:
Seminarie voor Wiskundige Natuurkunde, Rijksuniversiteit Ghent, Krijgslaan 271, S9, B-9000 Ghent, Belgium
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Abstract

We formulate, in the framework of MHD, a simple eigenvalue problem, capable of treating the stability of force-free magnetic fields curl B = αB in different geometries. We prove that a force-free field surrounded by a rigid wall is stable, if the eigenvalue α corresponds to the lowest value of compatible with the geometry considered. We extend this result to the case where α is a function of position; and we recliscuss it from the viewpoint of the first-order variation. We give various theorems and criteria for stability, for continuous as well as for admissible discontinuous or infinite displacements. A general upper limit for the growth rate is , where and and are respectively the maximum values of and υAthe Alfvén velocity inthe plasma volume.

Type
Research Article
Information
Journal of Plasma Physics , Volume 15 , Issue 1 , February 1976 , pp. 15 - 30
Copyright
Copyright © Cambridge University Press 1976

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References

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