Relaxation of toroidal discharges

A generalized energy principle is derived, based on the invariance of a volume integral K rather than perfect plasma conductivity, and including finite plasma pressure. It is found that the permissible (special) equilibria are a subset of those allowed in ideal MHD. Moreover, finite pressure severely restricts the possibility of symmetric configurations. Thus axisymmetric toroidal discharges, such as Tokamaks and pinches with weak but finite pressure, are shown not to exist within the special equilibria. An integral function is derived to permit the further study, by variational methods, of the stability of the special equilibria to perturbations which are K-invariant. A physical mechanism is proposed in outline for self-generated field reversal in pinches.