Growth of Axisymmetric Instabilities in ASDEX Upgrade

Modern tokamaks, operating with elongated plasmas, are unstable against vertical displacement. In the presence of conducting walls, this instability assumes the characteristics of a resistive wall mode (RWM), amenable to feedback stabilization. On ASDEX Upgrade (AUG), estimates of the growth rates, entering into the definition of safe operating regimes and into feedback parameter settings, were so far based on a rigid displacement (RD) model. However, for highly triangular plasmas this model was found to predict growth rates that were too small. A code package originally developed for general ideal magnetohydrodynamic (MHD) RWMs (NEMEC/CAS3D/STARWALL) and also capable of handling three-dimensional passive stabilizing loops (PSLs) was therefore applied to the n = 0 case for a large data sample of possible AUG equilibria. The comparison with the previously used rigid vertical displacement model showed that the latter gives a consistently lower limit to the growth rates for typical AUG parameters. A statistical analysis of the RD results brings out the stabilizing effect of triangularity. This stabilizing effect disappears, however, if generalized displacements are taken into account, like in the full MHD resistive wall model. The mode acquires a strong m = 2 component, which allows it also to elude partly the stabilization by the PSL. At low elongation, large triangularity produces even significant additional destabilization, with the mode predominantly m = 2, confined to the outer plasma layers, like predicted in references [see Rosen et al., Phys. Fluids, 18, 482 (1975) and Becker and Lackner, Proc. 6th Int. Conf. Plasma Physics and Controlled Nuclear Fusion Research, Vol. II, p. 401 (1977)]. These results explain the tendencies observed in AUG and will be taken into account in future analyses.