General stability analysis of forcefree magnetic fields. Part 1. General theory
Abstract
We formulate, in the framework of MHD, a simple eigenvalue problem, capable of treating the stability of forcefree magnetic fields curl B = αB in different geometries. We prove that a forcefree field surrounded by a rigid wall is stable, if the eigenvalue α corresponds to the lowest value of compatible with the geometry considered. We extend this result to the case where α is a function of position; and we recliscuss it from the viewpoint of the firstorder variation. We give various theorems and criteria for stability, for continuous as well as for admissible discontinuous or infinite displacements. A general upper limit for the growth rate is , where and and are respectively the maximum values of and υ_{A}the Alfvén velocity inthe plasma volume.
 Publication:

Journal of Plasma Physics
 Pub Date:
 February 1976
 DOI:
 10.1017/S0022377800019577
 Bibcode:
 1976JPlPh..15...15K
 Keywords:

 Boundary Value Problems;
 Eigenvalues;
 ForceFree Magnetic Fields;
 Magnetohydrodynamic Stability;
 Plasma Dynamics;
 Potential Theory;
 Boundary Conditions;
 Entire Functions;
 Field Theory (Physics);
 Lorentz Force;
 Potential Energy;
 Plasma Physics