Resonant magnetic perturbations (RMP) have extensively been demonstrated as a plausible technique for mitigating or suppressing large edge localized modes (ELMs). Associated with this is a substantial amount of theory and modelling efforts during recent years. Various models describing the plasma response to the RMP fields have been proposed in the literature, and are briefly reviewed in this work. Despite their simplicity, linear response models can provide alternative criteria, than the vacuum field based criteria, for guiding the choice of the coil configurations to achieve the best control of ELMs. The role of the edge peeling response to the RMP fields is illustrated as a key indicator for the ELM mitigation in low collisionality plasmas, in various tokamak devices.

Extensive modelling efforts of the plasma response to the resonant magnetic perturbation fields, utilized for controlling the edge localized mode (ELM), help to identify the edge-peeling response as a key factor, which correlates to the observed ELM mitigation in several tokamak devices, including MAST, ASDEX Upgrade, EAST, and HL-2A. The recently observed edge safety factor window for ELM mitigation in HL-2A experiments is explained in terms of the edge-peeling response. The computed plasma response, based on toroidal single fluid resistive plasma model with different assumption of toroidal flows, is found generally larger in ELM suppressed cases as compared to that of the ELM mitigated cases, in ASDEX Upgrade and DIII-D. The plasma shaping, in particular, the plasma triangularity, contributes to the enhanced plasma response. But the shaping does not appear to be the sole factor-other factors such as the (higher) pedestal pressure and/or current can also lead to increased edge-peeling response.

Sustained mitigation and/or suppression of the type-I edge localized modes (ELMs) have been achieved in EAST H-mode plasmas, utilizing the resonant magnetic perturbation (RMP) fields, produced by two rows of magnetic coils located just inside the vacuum vessel. Systematic toroidal modelling of the plasma response to these RMP fields, with various coil configurations (with dominant toroidal mode number n=1, 2, 3, 4) in EAST, is for the first time carried out by using the MARS-F code [Liu Y et al 2000 Phys. Plasmas 7 3681], with results reported here. In particular, the plasma response is computed with varying coil phasing (the toroidal phase difference of the coil currents) between the upper and lower rows of coils, from 0 to 360 degrees. Four figures of merit, constructed based on the MARS-F computations, are used to determine the optimal coil phasing. The modelled results, taking into account the 2 plasma response, agree well with the experimental observations in terms of the coil phasing, for both the mitigated and the suppressed ELM cases in EAST experiments.This study provides a crucial confirmation of the role of the plasma edge peeling response in the ELM control, complementing similar studies carried out for other tokamak devices.

Toroidal computation of the plasma response to the n  =  2 (n is the toroidal mode number) resonant magnetic perturbation field, based on an H-mode plasma in DIII-D, is carried out for the purpose of investigating the role of the ideal versus resistive plasma response models while scanning the plasma safety factor (q) at the edge. Both response models, implemented in the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), show significant amplification of the kink-peeling response in certain q-windows. A longstanding issue addressed in this work is the sensitivity of the q-window versus smoothing of the X-point geometry of the plasma separatrix. For this purpose, scan of the safety factor in 2D space (q95, qa) is carried out, where the q-value at 95% of the equilibrium poloidal flux, q95, is scanned by varying the total plasma current, whilst the edge safety factor qa is varied by gradually smoothing the X-point geometry at fixed total plasma current. Transition to the edge-peeling amplification domain is well described by simple analytic curves relating q95 and qa in the (q95, qa) space. These analytic curves not only help to quantify the sensitivity of the q95-window versus qa variation, but also establish the q95 window in the asymptotic limit of infinite qa (i.e. in the presence of true X-points). The ‘resonant’ q95 values (3.6, 4.05, 4.5) are found to roughly exhibit 1/n periodicity at infinite qa. Both ideal and resistive plasma response models, as well as the computed field at different pick-up locations, yield the same analytic curves describing transition to strong edge-peeling response. Detailed analysis of the computed plasma response and comparison with experiments are also performed.

Magnetic coil design study is carried out, for the purpose of mitigating or suppressing the edge localized modes (ELMs) in a EU DEMO reference scenario. The coil design, including both the coil geometry and the coil current requirement, is based on criteria derived from the linear, full toroidal plasma response computed by the MARS-F code (Liu et al 2000 Phys. Plasma 7 3681). With a single midplane row of coils, a coil size covering about 30°–50° poloidal angle of the torus is found to be optimal for ELM control using the n  >  2 resonant magnetic perturbation (RMP) field (n is the toroidal mode number). For off-midplane coils, the coils’ poloidal location, as well as the relative toroidal phase (coil phasing) between the upper and lower rows of coils, also sensitively affects the ELM control according to the specified criteria. Assuming that the optimal coil phasing can always be straightforwardly implemented, following a simple analytic model derived from toroidal computations, it is better to place the two off-midplane rows of coils near the midplane, in order to maximize the resonant field amplitude and to have larger effects on ELMs. With the same coil current, the ex-vessel coils can be made as effective as the in-vessel coils, at the expense of increasing the ex-vessel coils’ size. This is however possible only for low-n (n  =  1–3) RMP fields. With these low-n fields, and assuming 300 kAt maximal coil current, the computed plasma displacement near the X-point can meet the 10 mm level, which we use as the conservative indicator for achieving ELM mitigation in EU DEMO. The risk of partial control coil failure in EU DEMO is also assessed based on toroidal modeling, indicating that the large n  =  1 sideband due to coil failure may need to be corrected, if the nominal n  >  1 coil configurations are used for ELM control in EU DEMO.