  Stability conditions of magnetized plasma flows are obtained by exploiting
the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in
particular, by using three kinds of energy principles. First, the Lagrangian
variable energy principle is described and sufficient stability conditions are
presented. Next, plasma flows are described in terms of Eulerian variables and
the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric
equilibria, the energy-Casimir principle is expanded to second order and
sufficient conditions for stability to symmetric perturbation are obtained.
Then, dynamically accessible variations, i.e. variations that explicitly
preserve invariants of the system, are introduced and the respective energy
principle is considered. General criteria for stability are obtained, along
with comparisons between the three different approaches.
