Theory of Ballooning Modes in Tokamaks with Finite Shear

We studied ballooning instabilities in tokamaks of arbitrary cross section and finite shear. These azimuthally localized, ideal magnetohydrodynamic modes have large toroidal-mode numbers, but finite variation along the field and across the flux surfaces. Stability is determined by solving a second-order ordinary differential equation on each flux surface, subject to the proper boundary conditions. Qualitative agreement is achieved with the Princeton pest stability code.