Stability of certain families of ideal magnetohydrodynamic equilibria

The equations of ideal magnetohydrodynamic equilibria posses a number of symmetries that may be used to generate a family of hitherto unknown equilibria if there exists a foliation of the original one by magnetic surfaces. In addition to the possibility of producing analytic equilibria from old ones, this family is studied to find among its members those with minimal energy, those lasting longer under slightly resistive conditions, and those linearly stable. It is shown that in general none of these properties implies any other, thus clarifying the difference among these concepts.