The plasma response to the n = 1, 2, 4 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields, and the consequences on the fast ion confinement, are numerically investigated for a reference high-pressure plasma in HL-2M, by utilizing the linear resistive magnetohydrodynamic code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). The best coil current configurations, in terms of the coil phasing between the upper and lower rows of coils for controlling type-I edge localized modes (ELMs) in HL-2M, are identified as −130, −30, 180 degrees for the n = 1, 2, 4 fields, respectively, based on the edge peeling-tearing plasma response criterion. The plasma is found to substantially amplify the applied vacuum RMP field with the best coil phasing for the reference HL-2M equilibrium. The overall field amplification factor, defined as the peak-to-peak ratio of the poloidal spectra for the total field perturbation including the plasma response and the vacuum field alone, is about five for all n’s. The amplification, however, does not occur with the worst coil phasing for ELM control. This field amplification due to the high-pressure plasma response, together with the plasma screening of the resonant radial field components in the core region, have several consequences on the fast ion confinement in HL-2M during ELM control with RMP. (i) Three-dimensional fields including the plasma response, and with the best coil phasing, substantially enhance the distortion of fast ion orbits compared to the vacuum field approximation. With the n = 1 RMP, the plasma-response-induced enhancement of the orbit distortion reaches a factor of four when measured in terms of the canonical toroidal angular momentum. (ii) With the best coil phasing, the plasma response widens the stochastic region for the particle orbits on the Poincaré plane. (iii) The orbit islands, including the plasma response, remain as large as the vacuum counterparts in the plasma core where strong screening of the resonant field components occur. All these effects lead to enhanced fast ion transport (and loss) in the high-pressure HL-2M plasma, when the best RMP spectrum is applied to control ELMs.

Based on the non-perturbative approach, the hybrid code MARS-K is applied to study fishbone (FB) instabilities driven by trapped fast ions in a toroidal plasma with q profile nearly being flat or non-monotonic. We explore the dependency of the FB with variation in the fast ion distribution, thermal particle kinetic effects, safety factor (q) profile and plasma resistivity. When the safety factor minimum value is larger than unity (i.e. ), the mode can be excited by isotropic or anisotropic fast ions, with the latter strongly enhancing the mode growth rate. The mode frequency increases with increasing , and is more easily triggered in a equilibrium with two q = 1 surfaces, compared with the case with one or no q = 1 surface. Kinetic contributions from transit resonance of passing fast ions and from bounce resonance of trapped fast ions strongly enhance mode instability. The passing thermal ions induced Landau damping has a strong stabilization effect. Furthermore, in such a weak, even reversed magnetic shear plasma, the radial mode structure of FB mode monotonically decreases to zero at q = 1 flux surface instead of a step-like function, and it depends on the kinetic contributions from particles. In addition, the plasma resistivity significantly stabilizes the mode near the marginally unstable point.

Transport and loss of beam injected energetic-particles (EPs) due to three-dimensional (3D) perturbations, associated with the external kink (XK) instability and fishbone-like mode (FLM), are numerically investigated utilizing the guiding center following code ORBIT for static toroidal plasmas in HL-2A. The perturbation structure for the XK is computed by the MARS-F code and then mapped to the Boozer coordinates as defined in ORBIT. The simulation shows that the EP profile experiences a significant change in the middle of the plasma column, when the XK-induced radial magnetic field perturbation amplitude, normalized by the equilibrium field, exceeds a threshold value of about 10−2. The EP transport is found to be dominated by a diffusion process instead of convection. Furthermore, by scanning the perturbation frequency as a free parameter while maintaining the XK mode structure (thus mimicking the FLM as observed in DIII-D and JT-60U tokamaks), redistribution and loss of EPs are found to be substantially enhanced due to strong resonances between the FLM and EPs, when the mode frequency exceeds a threshold value of ~2 kHz for the case considered. For either XK or FLM, the response of passing EPs to the perturbation is dominant due to the assumed tangential neutral beam injection. Most lost EPs due to these instabilities are initially passing particles but are eventually lost through trapped orbits.

The kinetic effects of thermal particles and fast ions on internal kink (IK) mode are numerically investigated by the MHD-kinetic hybrid code MARS-K. It is shown that either thermal particles or fast ions have stabilizing influence on IK. However, the former can not fully stabilize IK, and the later can suppress the IK. In addition, the synergistic effect from thermal particles and fast ions induces more stronger damping on IK. The kinetic effects from particles significantly raise the critical value of poloidal beta ( β p crit ) for driving IK in the toroidal plasma. This implies a method of controlling IK or sawtooth in the high-β p discharge scenario of tokamak. It is noted that, at the q = 1 rational surface, mode structure becomes more sharp due to the self-consistent modification by particles’ kinetic effect.

A new damping model on the resistive wall mode (RWM) instability is studied, via the turbulence induced plasma viscosity (in short, turbulent viscosity). In a cylindrical plasma, the synergistic effect on suppressing the RWM is investigated between this new damping mechanism and the plasma flow. An eigenmode formulation is derived based on magneto-hydrodynamic (MHD) theory, where the momentum equation is extended by including the turbulent viscosity term with a proportionality coefficient χ. Numerical results show that, in the absence of plasma flow, increasing χ decreases the RWM growth rate but does not fully stabilize the mode. However, in the presence of sufficiently fast plasma flow, turbulent viscosity can lead to full suppression of the RWM, when χ exceeds a critical value. Similarly, at a given χ value, the plasma flow can fully suppress the mode when the flow velocity exceeds a threshold value. In particular, turbulent viscosity significantly reduces the threshold value of the flow velocity required for full stabilization of the RWM.