HOW MUCH ENERGY CAN BE STORED IN A 3-DIMENSIONAL FORCE-FREE MAGNETIC-FIELD

We develop simple physical arguments showing that any finite-energy force-free magnetic field occupying a half-space D (or the exterior of a "star-shaped" region) and having all its lines unknotted and tied to the boundary partial derivative D of D must have an energy which is not larger than that of the "open field" having the same flux distribution on partial derivative D. This result, which was first conjectured a few years ago by the author, has some important consequences for our understanding of the eruptive phenomena in the solar corona. In particular, it puts an absolute upper bound on the energy which can be released in a flare, and it precludes any spontaneous transition of the coronal field to an open state - thus allowing us to discard some popular models.