Some New Variational Properties of Hydromagnetic Equilibria

Abstract

Earlier variational formulations of problems in hydromagnetic equilibrium are extended by partially relaxing some of the boundary conditions. The resulting natural boundary conditions reflect situations of physical interest. Part of the analysis is done in the large and yields a simple intuitive condition which must be satisfied by an equilibrium which is free to move at its ends (the magnetic lines are not ``tied''). Applications are made to stability theory.