Abstract
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.
Original language | English |
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Pages (from-to) | 93-118 |
Journal | Solar Physics |
Volume | 146 |
DOIs | |
Publication status | Published - 1 Jul 1993 |
Keywords
- Magnetohydrodynamic Stability
- Solar Corona
- Solar Magnetic Field
- Ballooning Modes
- Euler-Lagrange Equation
- Force-Free Magnetic Fields
- Photosphere
- Plasma Pressure
- Three Dimensional Models