Low-n stability calculations for three-dimensional stellarator configurations

Abstract
A set of reduced magnetohydrodynamic (MHD) equations to study linear stability in general toroidal configurations is presented. The equations are derived by applying the averaging method to an equilibrium represented in a straight‐field‐line coordinate system. They permit the calculation of the low‐n stability of fully three‐dimensional (3‐D) equilibria for stellerator configurations with either a planar or a helical magnetic axis. Numerical solutions are shown to agree well with marginal stability boundaries given by the classical stellerator expansion when average stellarator equilibria with a planar magnetic axis are used as input.