On Magnetohydrodynamic Stability in the Low Pressure Limit

The stability of arbitrary toroidal magnetohydrostatic equilibria is investigated near the limit of a vacuum magnetic field. Nonsingular expansions in powers of ß ~ p/B2 are considered to all orders. Order by order minimization of the energy variaiton shows that any orders are positive semidefinite in the nullspace of all lower orders if either the vacuum field has shear or (for an identically vanishing rotational number) the interchange stability condition is satisfied. The question of sufficiency for stability at low ß of these conditions is discussed. While sufficiency of shear can be refuted by considering localized modes, this question remains open for the interchange stability condition.