How much energy can be stored in a three-dimensional force-free magnetic field?

Abstract

Simple physical considerations indicate that the energy of any finite-energy, force-free magnetic field occupying a half-space, and having all its lines unknotted and tied to the half-space boundary, will not be larger than the energy of the 'open field' which has the same half-space boundary flux distribution. Attention is given to the consequences of this view for the solar corona's eruptive phenomena; an upper bound on the energy which a flare can release is implied, and any spontaneous transition of the coronal field to an open state is precluded.