Linear and quasi-linear plasma response to resonant magnetic perturbations during ELM mitigation in HL-3

Active mitigation of edge-localized modes (ELMs)with the n=1 (n is the toroidal mode number) resonant magnetic perturbation (RMP) has recently been achieved for the first time on the HL-3 tokamak. The linear and quasi-linear plasma responses to RMP fields are numerically investigated by utilizing the MARS-F [Liu et al., Phys. Plasmas 7, 3681 (2000)] and MARS-Q [Liu et al., Phys. Plasmas 20, 042503 (2013)] codes. The linear results show that RMP induces a strong edge-peeling response which facilitates the ELM mitigation. A −50° phase shift for the n=1 coil current between the upper and lower rows of the RMP coils presents the optimal coil phase. MARS-Q quasi-linear results show that: (i) without involving perturbation mode near the plasma edge, the applied RMP has minor side effects on both the toroidal momentum and radial particle transport in this HL-3 case; (ii) allowing weak perturbation mode together with RMP produces finite flow damping and density pump-out level comparable to experiments; and (iii) the modeled flow damping and density pump-out is not very sensitive to the assumed resistivity model (Spitzer vs uniform resistivity). We found that both the neoclassical toroidal viscosity and resonant electromagnetic torques play important roles in the plasma toroidal momentum transport in HL-3.