General methods for determining the linear stability of coronal magnetic fields

Details General methods for determining the linear stability of coronal magnetic fields General methods for determining the linear stability of coronal magnetic fields

Dec 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988apj...335..441c&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 335, Dec. 1, 1988, p. 441-455.

Astronomy and Astrophysics

Astrophysics

10

Magnetic Field Configurations, Magnetohydrodynamic Stability, Solar Corona, Solar Magnetic Field, Convergence, Eigenvalues, Equations Of Motion, Linearization, Tensors

Scientific paper

This paper develops methods for determining the ideal linear stability of arbitrary three-dimensional magnetic fields. The authors base their approach on time integration of a linearized plasma equation of motion, which can be expressed simply in Cartesian tensor notation. Since the method deals directly with eigenvalue equations, the dominant physical modes (and their growth rates) emerge naturally from the analysis. The mathematical techniques adopted - explicit and implicit shifted power methods - are developed in detail. As an illustration the authors determine (for the first time) growth rates for Gold-Hoyle force-free equilibria. It is found that the corkscrew-kink instability is surprisingly weak, the largest eigenvalue of the force operator being some two or three orders of magnitude smaller then expected dimensionally.

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