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 ∆Φ between the upper and lower rows. The outermost resonant component of the RMP field b1res (numerous other criteria have also been devised, as discussed herein) has been shown experimentally to correlate with mitigated ELM frequency, and to be controllable by ∆Φ (Kirk et al 2013 Plas. Phys. Cont. Fus. 53 043007). This suggests that ELM mitigation may be optimised by choosing ∆Φ = ∆Φopt, such that b1res is maximal. However it is currently impractical to compute ∆Φopt in advance of experiments. This motivates this computational study of the dependence of the optimal coil phase difference ∆Φopt, on plasma parameters βN and q95, in order to produce a simple parametrisation of ∆Φopt. In this work, a set of tokamak equilibria spanning a wide range of (βN , q95) is produced, based on a reference equilibrium from an ASDEX Upgrade RMP experiment. The MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is then used to compute ∆Φopt 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, ∆Φopt is a smoothly varying function of (βN , q95). A 2D quadratic function in (βN , q95) is used to parametrise ∆Φopt, such that for given (βN , q95) and n an estimate of ∆Φopt may be made, without requiring a plasma response computation. In order to quantify the uncertainty of the parametrisation relative to a plasma response computation, ∆Φopt is also computed using MARS-F for a set of validation points. Each validation 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 computed ∆Φopt for these validation points to ∆Φopt computed with the 2D quadratic, shows that relative to a plasma response computation with MARS-F the 2D quadratic is accurate to 26.5 degrees for n = 1, and 20.6 degrees for n = 2. Potential sources for uncertainty are then assessed