N-dependence of ballooning instabilities

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Abstract
The critical ..beta.. for stability against ideal hydromagnetic internal ballooning modes as a function of toroidal mode number, n, is calculated for two different equilibrium sequences by use of a finite element technique (n less than or equal to 20), and a WKB formalism (n greater than or equal to 5). The agreement between the two methods is good in the overlap region 5 approx.less than or equal to n approx. less than or equal to 20. The WKB formula reduces to the 1/n correction at very high n, but is much more accurate at moderate n. The critical ..beta.. vs n curves exhibit oscillatory structure at low n, but in both sequences the lower bound on ..beta../sub c/ approx. 5%. For reactor parameters, finite Larmor radius effects are not expected to have a large effect on this ..beta..-limitation.

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