Criteria for second stability for ballooning modes in stellarators

An expression determining how variations in the pressure gradient and average magnetic shear affect ballooning stability for a stellarator equilibrium is presented. The procedure for determining the marginal stability boundaries, for each field line, depends only on the equilibrium and a single ballooning eigenfunction calculation. This information is sufficient to determine if increasing pressure gradient is stabilizing or destabilizing and to predict whether the configuration possesses a second stable region