MHD tilting modes for arbitrary plasma pressure and configuration

A technique developed by Rosenbluth and Bussac was used to analytically examine the ideal MHD tilting instability of nearly spherical configurations. The extension was to an arbitrary (nearly spherical) separatrix shape that differs in general from the wall shapes and to arbitrary plasma Beta and current profiles. Results show that appropriate separatrix shaping as well as peaking the current near the vortex point give a factor of 5 improvement over stability conditions for the elliptical case. Walls close fitting at the poles can yield a factor of 2 improvement at best over a wall with delta constant and the same surface area. Extension of the wall inside the separatrix is stabilizing. After everything is optimized, the wall must still be order epsilon distant from the separatrix to insure tilting stability.