A second-order ordinary differential equation on each flux surface is derived for the high-mode-number limit of resistive magnetohydrodynamic (MHD) ballooning modes in tokamaks with arbitrary cross section, aspect ratio, and shear. The equation is structurally similar to that used to study ideal MHD ballooning modes computationally. The model used in this paper predicts linear instability in the high-mode-number limit, with growth rate proportional to resistivity when the pressure gradient is small compared with the critical value needed for ideal MHD stability.

• Received 25 September 1978

DOI:https://doi.org/10.1103/PhysRevLett.41.1804