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%.