Resistive magnetohydrodynamic equations, stability and nonlocal perturbations in three-dimensional geometry

A simplified set of resistive MHD (magnetohydrodynamic) equations is derived which describes the joint effect of pressure-driven (interchange and ballooning) and current-driven (tearing) perturbations in arbitrary three-dimensional geometry. These equations are shown to contain, as special cases, several sets of previously derived equations. Stability is investigated by introducing appropriate Liapunov functionals and studying their time dependence. In particular, it is shown that toroidal configurations (tokamaks and stellarators) are always unstable (though not necessarily exponentially unstable) with respect to ballooning perturbations, and that these perturbations do not have to be radially localized, but can extend over large plasma regions. (orig.)