Structure and stability of constant-alpha force-free fields

Abstract

The author presents an expression for the magnetic helicity in spherical and planar geometries with inhomogeneous boundary conditions, and applies it to constant-α fields. The relations between helicity, energy, α, and the volume of the force-free region are described. If the volume is increased indefinitely with fixed helicity, the field approaches the potential state. The field of minimum α for a given helicity is stable to all fixed-boundary helicity-preserving perturbations.