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.

• Received 30 June 1977

DOI:https://doi.org/10.1103/PhysRevLett.39.943