The stability of arbitrary toroidal magnetohydrostatic equilibria is investigated near the limit of a vacuum magnetic field. Nonsingular expansions in powers of β ~ 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 β 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.
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A Journal of Physical Sciences: Zeitschrift für Naturforschung A (ZNA) is an international scientific journal which publishes original research papers from all areas of experimental and theoretical physics. In accordance with the name of the journal, which means “Journal for Natural Sciences”, manuscripts submitted to ZNA should have a tangible connection to actual physical phenomena.