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Astron. Astrophys. 339, 887-896 (1998)


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A complete solar coronal loop stability analysis in ideal magnetohydrodynamics

I. Non-force-free cylindrical equilibria

R.A.M. Van der Linden * 1 and A.W. Hood 2

1 Center for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
2 School of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews KY16 9SS, UK

Received 31 March 1998 / Accepted 12 August 1998

Abstract

A procedure is introduced to perform a complete ideal MHD stability analysis of one-dimensional cylindrical equilibrium models for coronal loops, including the important effect of line-tying. The stability is completely determined by calculating the critical (marginally stable) length for the onset of ideal MHD instabilities for every azimuthal wave number m. The analysis consists of the combination of a WKB method to determine the critical length of intermediate to high (infinite) values of m with a numerical code (using bicubic finite elements) for the low to intermediate values of m. As before it is found that for large enough m the critical length can be expressed as [FORMULA]. It is also demonstrated that in general either the [FORMULA] or the [FORMULA] mode has the shortest critical length, the former being the first to become unstable for nearly force-free magnetic fields, the latter for strongly non-force-free fields. Therefore, a stability analysis of these two modes will normally suffice, with perhaps a need for some more numerical calculations near the point where the modes cross over. The combination of these two tools provides a complete stability assessment.

Key words: MHD – plasmas – Sun: corona – Sun: magnetic fields

* Postdoctoral Research Fellow of the Flemish Fund for Scientific Research

Send offprint requests to: R.A.M. Van der Linden

© European Southern Observatory (ESO) 1998

Online publication: October 22, 1998

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