Resistive ballooning modes in W7-AS and W7-X

'Critical' pressure gradients due to resistive ballooning modes and their growth rates were computed for the W7-AS stellarator and for a HELIAS configuration with W7-X parameters, and the two configurations were compared. The results are based on the evaluation of a fourth order magnetic differential equation along closed magnetic field lines. The numerical procedure applying a variational approach uses the 'Garching resistive ballooning code', GARBO, which was originally developed for the stability analysis of axisymmetric plasmas. Concerning purely growing modes, this analysis shows that the favourable stability properties of W7-X, already optimized with respect to ideal ballooning modes, persist in the resistive regime: the destabilizing effect of resistivity is largely compensated by the stabilizing contribution of plasma compression. As a consequence, the ideal beta limit continues only moderately shifted in the resistive case and likewise ideal ballooning stable equilibria (up to β0 ≈ 5%) do not become resistively unstable. The situation is different for W7-AS. Greater resistive effects (in comparison with W7-X) are found in a configuration that is already ideally much more unstable. A basic feature in resistive calculations is the occurrence of overstable modes. These modes no longer show a stability threshold and, for realistic values of pressure and resistivity, linear instability is obtained for W7-AS as well as for W7-X, with growth rates and oscillation frequencies in the kilo-Hertz range