N-dependence of ballooning instabilities

Abstract

The critical β for stability against ideal hydromagnetic internal ballooning modes as a function of the toroidal mode number, n, is calculated for two different equilibrium sequences by use of a finite-element technique (n ≤ 20), and a WKB formalism (n≥ 5). The agreement between the two methods is good in the overlap region 5 ≤ n ≤ 20. The WKB formula reduces to the ‘1/n correction’ at very high n, but is much more accurate at moderate n. The critical- β -versus-n curves exhibit oscillatory structure at low n, but in both sequences the lower bound on βC is set by n = ∞ modes at about βC ~ 5%. Show more