Ideal and resistive pressure gradient driven instabilities in Heliotron DR

A stability code called RESORM, which solves the reduced MHD equations as an initial-value problem, has been developed. With this code, resistive instabilities in toroidal stellarator/heliotron configurations have been studied. The code can also be applied to ideal instabilities by assuming zero resistivity. Currentless equilibria with a pressure profile of p ∝ (l – Ψ)2 in the Heliotron DR plasma are investigated by applying this code as well as the STEP code originally developed by Anania and Johnson. The critical beta value for stability against the ideal global mode obtained with both codes is β0 ≃ 1.2% (β0 is the beta value at the magnetic axis); however, the Mercier criterion obtained with the STEP code indicates β0 = 0.7%. With the RESORM code it is found that the resistive modes become unstable when β0 < 1.2%, with substantial growth rates, since the magnetic Reynolds number is not large in Heliotron DR (S ∼ 105). In the region where the Mercier mode is stable (β0 < 0.7%), the growth rate is proportional to S−1/3; in the Mercier unstable region (β0 > 0.7%) the S-dependence of the growth rate is different because of the effect of the ideal instability. The effect of the magnetic axis shift on the ideal and the resistive MHD stability is also studied with the two codes. The calculated values are compared with the experimental beta limit in Heliotron DR and good agreement between these results is found.