We have recently demonstrated that by expanding in small distance from the magnetic axis compared with 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 the 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 and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

中文翻译：

---

仿星器在磁轴附近的磁阱和 Mercier 稳定性

我们最近证明，与主半径相比，通过在距磁轴较小的距离内扩展，可以有效地生成具有低新古典传输的仿星器形状。为了扩展这种新设计方法的实用性，我们在此评估在同一扩展内磁流体动力学互换稳定性的测量。特别是，我们评估了磁井、Mercier 准则和任意形状磁轴附近的电阻互换稳定性。与以前使用磁通坐标扩展的磁轴附近互换稳定性的工作相比，这里我们使用“逆扩展”，其中磁通坐标是自变量。在准对称情况下，给出了磁阱和稳定性判据的简化表达式。分析结果显示与 VMEC 平衡代码的计算一致。最后，我们表明在轴附近，Glasser、Greene 和 Johnson 的电阻模式稳定性标准与 Mercier 的理想条件大致一致。