Variational principles for equilibrium states with plasma flow

A new constant of the motion is utilized to formulate a variational principle for plasma equilibria with general flow fields. Two additional variational principles are derived from the original one. None of these formulations leads to a stability criterion if the velocity is not parallel to the magnetic field since the functionals used, the first of which being the energy, do not possess in this case a minimum but only stationary points. It is shown that other stability criteria already reported in the literature also suffer from the same deficiency. It is suggested that the lack of a minimum is due to the presence of ballooning modes.