Resistive ballooning stability of ASDEX equilibria

Abstract

Experiments on the maximum attainable beta values of ASDEX discharges show that the limits for this parameter lie in the range of theoretical predictions. In a previous publication a theoretical identification of the corresponding instabilities has been attempted. No significant correlation with global plasma instabilities could be found, but the two-dimensional MHD equilibria calculated on the basis of ASDEX experimental parameters turned out to be close to the marginal ideal ballooning limit. In the work presented here, the previous investigation on resistive ballooning modes is extended. Separatrix bounded as well as limiter controlled plasma equilibria are considered. Because of the small aspect ratio of ASDEX (A ≅ 4) all equilibrium as well as stability calculations are performed in full toroidal geometry. After the formulation of a system of four equations describing the resistive evolution of velocity and magnetic fields in the high-m stability limit in co-ordinate invariant form and its Fourier approximation in the neighbourhood of a localization field line, the resulting quasimode equations are solved, applying methods of finite-element discretization. Complex growth rates γ are found, with a positive real part for values of the toroidal mode number n below 100. Calculated values of Re {γ} ≤ 10−3/τA S−1 (with τA being the Alfvén time) are small and therefore in agreement with the experimentally observed non-disruptive behaviour at the βp limit. Thus we believe that the characteristic signatures which govern ASDEX high βp discharges can be explained by resistive ballooning modes.