Lagrangian stability of fluids and multifluid plasmas

Weber’s transformation is used to show how Lin’s constraint should be replaced if fluid equations are derived from Hamilton’s principle. The same technique is used to derive a three-circulation theorem and a generalization of Ertel’s theorem for perfect multifluid plasmas. The Hamiltonian and Lagrangian formulation of the equations for fluid and electromagnetic potentials is given, with a discussion of their multivaluedness and their gauge and time dependence for static magnetohydrodynamic equilibria. The linear stability of these equilibria is shown to depend on the weight of a single negative eigenvalue of the internal energy variation, compared with all other (positive) contributions to the ‘‘energy’’ functional.