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Astron. Astrophys. 339, 887-896 (1998)
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]](img1.gif)
. It is also demonstrated
that in general either the ![[FORMULA]](img2.gif)
or the
![[FORMULA]](img3.gif)
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
This article contains no SIMBAD objects.
Contents
- 1. Introduction
- 2. Marginal stability equations
- 3. Application of the WKB method
- 4. Numerical solutions and comparison with WKB results
- 5. Summary and discussion
- Acknowledgements
- Appendix A: a brief description of the MALTS code
- References
© European Southern Observatory (ESO) 1998
Online publication: October 22, 1998
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