Energy principle for 3-d resistive instabilities in shaped-cross-section Tokamaks

An energy principle for 'helical' incompressible perturbations in shaped cross-section plasmas is derived in the Tokamak scaling ( epsilon identical to ka approximately=B perpendicular to /B z <<1). Two models for the resistivity are used. The resistivity is assumed to be transported either by the fluid or by the magnetic surfaces. In the first case generalized rippling and tearing modes are discovered, while in the latter case the rippling is cancelled in a self-consistent way. The Euler equation for the tearing modes generalizes the previously derived equation for two-dimensional perturbations. It is pointed out that the energy principle cannot be extended to higher orders in epsilon .