An integrated model for the ionization, radiation, and advection of impurities in the extended-magnetohydrodynamic code M3D-C1 is described. This implementation makes use of the KPRAD model, which calculates bremsstrahlung radiation and impurity ionization, recombination, and radiation rates using a model in which the density of each charge state is advanced separately. The integrated model presented here allows the independent evolution of electron and ion temperatures, which is necessary to accurately model cases where the electron temperature drops more quickly than the electron–ion thermal equilibration time. This model is used to simulate the disruption of a model NSTX discharge caused by the introduction of argon impurities, using physically realistic resistivity. Despite well-mixed impurities, contraction of the current channel is found to lead to magnetohydrodynamic instabilities that result in stochastization of the magnetic field, a fast thermal quench, and localized parallel electric fields that can exceed the axisymmetric values by a factor of five for brief periods.

A drift orbit model for relativistic test electrons has been incorporated into the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), in order to study the runaway electron (RE) behavior in the presence of magneto-hydrodynamic perturbations computed by MARS-F. By implementing the model directly into the MARS-F curve-linear magnetic coordinates, maximal accuracy in representing the full field perturbation is preserved. The updated code is utilized to study the high current RE beam loss in a post-disruption DIII-D plasma, revealing that a fast growing, n  =  1 (n is the toroidal mode number) resistive kink instability, at  ∼100 Gauss level, can induce significant fraction of RE loss, largely by perturbing drift orbits of REs. A  ∼1000 Gauss perturbation fully terminates the RE beam, as found in both experiment and modeling. The 3D field induced loss increases with the perturbation amplitude but decreases with the particle energy. The loss fraction is generally not sensitive to the initial particle pitch angle. The particle velocity change, due to electric field acceleration/deceleration, small pitch angle scattering, synchrotron radiation and Bremsstrahlung, further perturbs the RE trajectory but plays a minor role in prompt RE loss within microseconds time scale. Therefore, the dominant dependencies are simply the RE energy and instability strength. For comparison, a resonant magnetic perturbation field, generated by 4 kAt n  =  3 even parity I-coil currents in DIII-D and with the plasma response field included, is found to induce almost no loss for the same RE beam.

Plasma response to 3D resonant magnetic perturbations (RMPs), applied for the purpose of controlling type-I edge localized modes (ELMs) in ITER with the baseline ELM control coils, is computed using a toroidal, resistive, full magneto-hydrodynamic model. Considered are five representative ITER plasmas, designed for different phases of the ITER exploration. The plasma response, measured by the plasma boundary corrugation, is found to be similar for the two DT scenarios at full plasma current (15 MA) and full toroidal field (5.3 T) but different fusion gain factors (Q  =  5 versus Q  =  10), indicating similar ELM control performance with the same RMP coil current configuration. The other plasma scenarios, with proportionally scaled down plasma current and toroidal field, can have different plasma boundary corrugation. The key plasma parameter affecting the response is the plasma toroidal flow near the pedestal region, which significantly varies depending on the transport model assumption for the toroidal momentum. Lower pedestal flow leads to a stronger edge peeling response from the plasma and thus probably a better ELM control. The optimal coil configuration for controlling type-I ELMs is similar for all four ITER plasmas with similar safety factor but different current levels, but is significantly different for the case at half plasma current (7.5 MA) and full field (5.3 T). On the other hand, for the purpose of controlling the radial profile of the plasma toroidal rotation in ITER using 3D fields, the relative amplitude of the toroidal torque density, between the plasma core and edge region, is optimized. Generally, a strong coupling between the core and edge torques is observed, largely due to the middle row ELM control coils. The best decoupling scheme of the core-edge torque distribution thus de-emphasizes the role of the middle row coils. Optimal coil current configurations are found for the ITER 15 MA/5.3 T Q  =  10 plasma, that synergistically maximize the plasma edge-peeling response (indication for good ELM control) and the toroidal torque near the plasma edge (good for RMP field penetration through pedestal).

The toroidal Alfvén eigenmode (TAE), excited by trapped energetic particles (EPs), is numerically investigated in a tokamak plasma, using the non-perturbative magnetohydrodynamic-kinetic hybrid formulation based MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503). Compared with the fixed boundary condition at the plasma edge, a free boundary enhances the critical value of the EPs kinetic contribution for driving the TAE. Free boundary also induces finite perturbations at the plasma edge as expected. An anisotropic distribution of EPs, in the particle pitch angle space, strongly enhances the instability and results in a more global mode structure, compared with the isotropic case. The plasma resistivity is also found to play a role in the EPs-destabilized TAE. In particular, the mode stability domain is mapped out, in the 2D parameter space of the plasma resistivity and a quantity defining the width of the particle distribution in pitch angle (for anisotropic distribution). A resonance layer in the poloidal mode structure, with the layer width increasing with the plasma resistivity, appears at the large width of the particle distribution in pitch angle space. A mode conversion, from the modified ideal kink by the EPs kinetic effect to the TAE, is also observed while increasing the birth energy of EPs. Computational results suggest that the TAE mode structure can be modified by certain key plasma parameters, such as the EPs kinetic contribution, the equilibrium pressure, the plasma resistivity, the distribution of EPs, as well as the birth energy of EPs. Such modification of the eigenmode structure can only be obtained following the non-perturbative hybrid approach (Wang et al 2013 Phys. Rev. Lett. 111 145003, Wang et al 2015 Phys. Plasmas 22 022509), as adopted in this study. More importantly, numerical results show that near the marginal stability point, the dominant poloidal harmonics of the TAE overlap with each other, and are localized at the tip positions of the Alfvén continua. This kind of TAE structure in high beta plasma with unstable ideal kink is substantially different from that of the conventional TAE.