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 Δ Φ between the upper and lower rows. The magnitude of the outermost resonant component of the RMP field ∣ b res 1 ∣ (other proposed criteria are discussed herein) has been shown experimentally to correlate with mitigated ELM frequency, and to be controllable by Δ Φ (Kirk et al 2013 Plasma Phys. Control. Fusion 53 043007 ). This suggests that ELM mitigation may be optimised by choosing Δ Φ = Δ Φ opt , such that ∣ b res 1 ∣ is maximised. However it is currently impractical to compute Δ Φ opt in advance of experiments. This motivates this computational study of the dependence of the optimal coil phase difference Δ Φ opt , on global plasma parameters β N and q 95 , in order to produce a simple parametrisation of Δ Φ opt . In this work, a set of tokamak equilibria spanning a wide range of ( β N , q 95 ) 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 Δ