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 between the upper and lower rows. The magnitude of the outermost resonant component of the RMP field (other proposed criteria are discussed herein) has been shown experimentally to correlate with mitigated ELM frequency, and to be controllable by (Kirk et al 2013 Plasma Phys. Control. Fusion53 043007). This suggests that ELM mitigation may be optimised by choosing , such that is maximised. However it is currently impractical to compute in advance of experiments. This motivates this computational study of the dependence of the optimal coil phase difference , on global plasma parameters and q95, in order to produce a simple parametrisation of . In this work, a set of tokamak equilibria spanning a wide range of (, q95) is produced, based on a reference equilibrium from an ASDEX Upgrade experiment. The MARS-F code (Liu et al 2000 Phys. Plasmas7 3681) is then used to compute 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, is a smoothly varying function of (, q95). A 2D quadratic function in (, q95) is used to parametrise , such that for given (, q95) and n, an estimate of may be made without requiring a plasma response computation. To quantify the uncertainty of the parametrisation relative to a plasma response computation, 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 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.
Chasing the multi-modal plasma response in MAST-U