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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.
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Dobrott et al. (1977) studied this question.
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