Energy principles for non-ideal MHD

Energy principles were found for the three-dimensional plasmas of arbitrary geometry with viscosity and finite Larmor radius (FLR) effects and for two-dimensional plasmas of arbitrary shape, taking into account viscosity, FLR effects and resistivity. This allows a scaling-free decision about stability in the same way as for ideal MHD (necessary and sufficient criterion). Rough estimates of growth rates can also be made. Application to tokamaks yields the results: (1) Very plausible explanation of the anomalous skin effect at the beginning of the discharge; (2) Reduction by a factor of 100 of the resistive kink or ideal internal kink growth rate of the m=1, n=1 mode by inclusion of the viscosity parallel to the magnetic field, which explains the observations; (3) Formulation of a condition allowing the use of test functions to study the stability of configurations with stagnation points and magnetic islands. Application to the high-β,l=1 stellarator allows the explanation of the stabilization of m=2 by FLR in the present experiments, but parallel viscosity could strongly destabilize plasmas of higher temperatures unless their ideal MHD stability is improved. Finally, an energy principle for all three-dimensional resistive perturbations in the tokamak scaling is given even with FLR and viscosity. Helical perturbations can always be unstable. (author)