Critical conditions for magnetic instabilities in forcefree 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 linetying have been approximate, in the sense that they give only upper or lower bounds on the critical amount of twist (or the critical looplength) 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 forcefree 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;
 ForceFree Magnetic Fields;
 Magnetohydrodynamic Stability;
 Solar Corona;
 Solar Magnetic Field;
 Boundary Conditions;
 Boundary Value Problems;
 Linear Equations;
 Magnetic Field Configurations;
 Mathematical Models;
 Photosphere