Resistive wall mode stabilization in toroidal geometry

The possibility of stabilizing ideal magnetohydrodynamical (MHD) instabilities by resistive walls and slow plasma rotation (rotation frequencies comparable to resistive tearing growth rates) was proposed recently by Finn [Phys. Plasmas 2, 3782 (1995)] on the basis of cylindrical theory. In the present paper we analyze toroidal effects (pressure gradients and favorable averaged curvature) [Glasser et al., Phys. Fluids 18, 875 (1975)] on this “resistive window.” It is found that in toroidal geometry the resistive window for the distance of the wall from the plasma scales as S−1/3 (S is the ratio of resistive to Alfvénic time scales) and thus becomes very small in large tokamaks. Other differences between toroidal and cylindrical theories of resistive wall mode stability are discussed.