Physics
Scientific paper
Jul 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993soph..146...93l&link_type=abstract
Solar Physics (ISSN 0038-0938), vol. 146, no. 1, p. 93-118.
Physics
7
Magnetohydrodynamic Stability, Solar Corona, Solar Magnetic Field, Ballooning Modes, Euler-Lagrange Equation, Force-Free Magnetic Fields, Photosphere, Plasma Pressure, Three Dimensional Models
Scientific paper
A necessary and a sufficient condition are derived for the ideal magnetohydrodynamic stability of any 3D magnetohydrostatic equilibrium using the energy method and incorporating photospheric line-tying. The theory is demonstrated by application to a simple class of theoretical 3D equilibria. The main thrust of the method is the formulation of the stability conditions as two sets of ordinary differential equations together with appropriate boundary conditions which may be numerically integrated along tied field lines one at a time. In the case of the shearless fields with non-negligible plasma pressure treated here the conditions for stability are necessary and sufficient. The method employs as a trial function a destabilizing 'ballooning' mode, of large wave number vector perpendicular to the equilibrium field lines. These modes may not be picked up in a solution of the full partial differential equations which arise from a direct treatment of the problem.
Hood Alan William
Longbottom Aaron W.
Melville J. P.
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