Linear stability of force‐free equilibria

A sufficient stability criterion, applicable to all force‐free equilibria of magnetized plasmas surrounded by a rigid conducting shell, is found. Magnetic field lines may penetrate the shell, vacuum regions may exist inside the shell, and no assumptions on topology—or symmetry—are required. Stability is determined from the sign of the minimum of a functional. This minimum value depends on certain constraints that are adjustable. In one extreme of the range of adjustment, the known stability criterion of ideal magnetohydrodynamics (MHD) is recovered; in the other extreme the criterion approaches that of Taylor equilibria. In this range the constraints relevant for tearing modes are identified. A procedure for evaluating the minimum of the functional, believed suitable for numerical implementation, is given.