Magnetic well and Mercier stability of stellarators near the magnetic axis

TL;DR

This paper evaluates magnetohydrodynamic stability measures like magnetic well and Mercier's criterion near the magnetic axis of stellarators, using an inverse expansion approach and confirming results with numerical simulations.

Contribution

It introduces an inverse expansion method to analyze interchange stability near the magnetic axis, extending previous flux coordinate expansions and providing analytic expressions.

Findings

Analytic expressions for magnetic well and Mercier's criterion near the axis.

Validation of analytic results with VMEC equilibrium code calculations.

Near the axis, resistive stability criterion aligns with Mercier's ideal condition.

Abstract

We have recently demonstrated that by expanding in small distance from the magnetic axis compared to the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the inverse expansion in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene, & Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.