Numerically derived parametrisation of optimal RMP coil phase as a guide to experiments on ASDEX Upgrade

Edge localised modes (ELMs) are a repetitive MHD instability, which may be mitigated or suppressed by the application of resonant magnetic perturbations (RMPs). In tokamaks which have an upper and lower set of RMP coils, the applied spectrum of the RMPs can be tuned for optimal ELM control, by introducing a toroidal phase difference DF between the upper and lower rows. The magnitude of the outermost resonant component of the RMP field bres 1 | |(other proposed criteria are discussed herein) has been shown experimentally to correlate with mitigated ELM frequency, and to be controllable by DF (Kirk et al 2013 Plasma Phys. Control. Fusion 53 043007). This suggests that ELM mitigation may be optimised by choosing DF = DFopt, such that bres 1 | |is maximised. However it is currently impractical to compute DFopt in advance of experiments. This motivates this computational study of the dependence of the optimal coil phase difference DFopt, on global plasma parameters bN and q95, in order to produce a simple parametrisation of DFopt. In this work, a set of tokamak equilibria spanning a wide range of (bN, q95) is produced, based on a reference equilibrium from an ASDEX Upgrade experiment. The MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is then used to compute DFopt across this equilibrium set for toroidal mode numbers n = 1-4, both for the vacuum field and including the plasma response. The computational scan finds that for fixed plasma boundary shape, rotation profiles and toroidal mode number n, DFopt is a smoothly varying function of (bN, q95). A 2D quadratic function in (bN, q95) is used to parametrise DFopt, such that for given (bN, q95) and n, an estimate of DFopt may be made without requiring a plasma response computation. To quantify the uncertainty of the parametrisation relative to a plasma response computation, DFopt is also computed using MARS-F for a set of benchmarking points. Each benchmarking point consists of a distinct free boundary equilibrium reconstructed from an ASDEX Upgrade RMP experiment, and set of experimental kinetic profiles and coil currents. Comparing the MARS-F predictions of DFopt for these benchmarking points to predictions of the 2D quadratic, shows that relative to a plasma response computation with MARS-F the 2D quadratic is accurate to 26.5° for n = 1, and 20.6° for n = 2. Potential sources for uncertainty are assessed.