It is pointed out that the range of mode numbers n for which high-n, ballooning-mode theory is valid is more restricted when the shear is weak. A new theory valid for weak shear and intermediate mode number is outlined. Combined with the standard theory, this analysis shows that the growth rate of high-n instabilities is linear in 1/n at large n but in equilibria with weak shear there may be intermediate values of n for which the growth rate is an oscillatory function of 1/n, with amplitude and period proportional to 1/n2.
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Hastie et al. (1981) studied this question.
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