THE STABILITY OF A LINE-TIED FORCE-FREE MAGNETIC-FIELD IN AN UNBOUNDED REGION OF SPACE

Sufficient criteria of linear ideal magnetohydrodynamic stability are derived for a three-dimensional nonlinear force-free magnetic field B occupying an infinite region Ω, which is either a half-space or an "exterior domain"; all the field lines of B are assumed to be firmly rooted in the boundary ∂Ω of Ω (line-tying condition), but their topological pattern may be otherwise quite arbitrary. Roughly speaking, a field characterized by a length scale Λ is found to be stable if α0 Λ < O(1), where α0 is a number measuring the magnitude of the force-free function α = B-2 (B·∇XB). The stability criteria established here have some important astrophysical applications (solar corona, magnetosphere of a compact object, etc.), which are briefly discussed. © 1990 American Institute of Physics.