Different ELM regimes at ASDEX Upgrade and their linear stability analysis

Edge localised modes (ELMs) are magnetohydrodynamic (MHD) instabilities that occur at the edge of magnetically confined fusion plasmas. They periodically expel particles and energy from the confined region. In addition to limiting the confinement, they cause high heat fluxes to the walls of the tokamak which may not be manageable in larger, next-generation devices. However, the exact nature of the instabilities that drive ELMs is still unknown. The most commonly invoked theory to explain the occurrence of ELMs is the peeling-ballooning model which posits a critical edge pressure gradient and current density. In this thesis, this model is tested against experimental data gathered at the ASDEX Upgrade (AUG) tokamak. For the first time, a broad selection of ELM scenarios is analysed with respect to ideal MHD stability using the same methodology. The comparison of experiment and theory is performed using a stability analysis chain, which consists of combining kinetic and magnetic measurements to generate self-consistent plasma equilibria with the Grad-Shafranov solver CLISTE, refining this equilibrium with the HELENA code, and, finally, determining its stability using ILSA, a linear MHD stability code. In theory the peeling ballooning model should apply to all type-I ELM scenarios. Therefore, the stability of several different type-I ELMy H-mode plasmas is analysed with respect to peeling ballooning modes. While some of them are consistent with the model, in others ELMs occur well below or above the ideal MHD stability limit. The standard type-I ELMy H-mode regime exhibits considerable variations with equilibria both well below and at the stability limit depending on the discharge. In addition, a nitrogen-seeded case in which the edge pressure gradient greatly exceeds the stability limit is identified. In another discharge, the edge pressure gradient and current density, which are on the threshold for marginal stability, relax when edge heating is applied. Contrary to the theory, as the equilibrium becomes more stable against peeling-ballooning modes, the ELM frequency actually increases. Other scenarios in which peeling-ballooning modes are not thought to be the ELM trigger are also examined. In discharges featuring type-II and type-III ELMs the edge pressure gradient and current density are well below the threshold for peeling-ballooning instabilities, consistent with expectations. This indicates that other mechanisms must be present that prevent the kinetic profiles from building up. The behaviour of the analysed type-III ELMs is consistent with the hypothesis that they are driven by resistive interchange modes. The feasibility of triggering ELMs via frozen deuterium pellets is also examined in detail. In discharges performed when the walls of AUG were protected by carbon tiles, pellets triggered ELMs whenever they were injected into an H-mode plasma. In the tungsten-walled AUG, however, it is only possible to trigger ELMs after a specific lag time has elapsed since the previous ELM. This lag time can be significantly reduced, though not eliminated, when injecting nitrogen into the divertor. In the tungsten-walled AUG, with and without nitrogen, it is possible to trigger ELMs via pellets when the pedestal pressure gradient and the edge current density are 20% below the threshold for spontaneous ELMs. Since the ELM-induced collapse of the plasma edge pressure profile is strongest in the unseeded tungsten machine and the profile recovery is slower, the lag time for successful triggering is longer. Recent extrapolations of the ITER pedestal are also tested using the peeling-ballooning model. It is found that the predictions are very optimistic, but that stability could be achieved with temperatures and densities which are 30% lower than in the extrapolations. Some of the results presented in this thesis question the validity of the peeling-ballooning theory. In many of the presented cases, ELMs occur well below the threshold for peelingballooning stability and in one case well above. The presented results indicate that the peeling-ballooning model is insufficient to fully explain the triggering of ELM instabilities. Rather, another as yet unknown trigger mechanism is required.