Critical conditions for magnetic instabilities in force-free coronal loops
Abstract
The remarkable magnetohydrodynamic stability of solar coronal loops has been attributed to the anchoring of the ends of loops in the dense photosphere. However, all the previous analyses of such line-tying have been approximate, in the sense that they give only upper or lower bounds on the critical amount of twist (or the critical loop-length) required for the breakdown of stability. The object of the present paper is to remove these approximations and determine the exact value for the critical twist. When it is exceeded the magnetic field becomes kink unstable and a flare may be initiated. A simple analytic stability calculation is described for an idealised loop. This is followed by the development of a general numerical technique for any loop profile, which involves solving the partial differential equations of motion. It is found, for example, that a force-free field of uniform twist possesses a critical twist of 2.49 , by comparison with the previous bounds of 2, for stability, and 3.3, for instability.
- Publication:
-
Geophysical and Astrophysical Fluid Dynamics
- Pub Date:
- 1981
- DOI:
- 10.1080/03091928108243687
- Bibcode:
- 1981GApFD..17..297H
- Keywords:
-
- Coronal Loops;
- Force-Free Magnetic Fields;
- Magnetohydrodynamic Stability;
- Solar Corona;
- Solar Magnetic Field;
- Boundary Conditions;
- Boundary Value Problems;
- Linear Equations;
- Magnetic Field Configurations;
- Mathematical Models;
- Photosphere