The Plasma Response to Applied Magnetic Perturbations for ELM Control in Tokamaks

Edge Localised Modes (ELMs), a repetitive MHD instability, present a risk to ITER machine components and scientific objectives, necessitating a robust ELM mitigation strategy. The application of Resonant Magnetic Perturbations (RMPs) is an effective means of suppressing or mitigating ELMs, and a set of RMP coils will be installed on ITER. Although there are several working theories, a robust predictive theory of ELM control by RMPs is currently lacking. In previous assessments of the efficacy of the ITER RMP system, the response of the plasma to the applied RMP was typically overlooked; however it is well known that the plasma response constitutes a significant correction to the total plasma perturbation. In this thesis, the MARS-F code (Liu \textit{et al} 2000 \textit{Phys. Plasmas} \textbf{7} 3681) is used to study the linear plasma response to applied RMPs using realistic geometry and experimental parameters. The pitch aligned components and the amplified peeling response components of the RMP, both previously implicated in the ELM mitigation and suppression mechanisms, are studied. It is shown that although the pitch aligned components are strongly screened by the plasma response, they may be finite near the plasma edge, and may be driven by the amplified peeling response via poloidal harmonic coupling. RMPs can be tuned by adjusting the phase $\Delta\phi_{UL}$ between the toroidal waveforms in the upper and lower rows of RMP coils. A scheme for optimising the coil phase to maximise ELM mitigation for a given plasma equilibrium is devised for ASDEX Upgrade plasmas. A database of ASDEX Upgrade RMP experiments is assembled and used to benchmark the scheme against MARS computations, and validate it against experimental measurements. The scheme is then extended to the ITER RMP coil system.