Stability calculations for the m = 1/n = 1 mode in heliotron configurations using the three-dimensional MHD equilibrium and stability (BETA) code

Abstract

Stability against the m = 1/n =1 internal mode is investigated in a Heliotron E model configuration for both currentless and flux conserving torus (FCT) equilibria. The beta limit in the first stability region is β̄ ≤ 2%, where β̄ denotes the average beta. This is consistent with the maximum beta value obtained in Heliotron E. For β̄ ⩾ 5%, a second stability region appears. It is found that the stability is sensitive to additional vertical magnetic fields. When the magnetic axis is shifted inward, the stability degrades, whereas, when it is shifted outward, the instability disappears for the above-given range of beta values. – The stability is also examined in another heliotron configuration which has a rotational transform larger than unity for all flux surfaces. Its first stability beta limit is larger than that for Heliotron E. For this configuration, an unstable free boundary mode with m = 1/n = 1 is found. A comparison of these results with analyses based on the stellarator expansion method is given.