Influence of toroidal equilibrium plasma rotation on m/n=2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τ R /τ V >>1, where τ R and τ V represent resistive and viscous diffusion time, respectively.), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τ R /τ V <<1), the rotation shear shows a destabilizing effect when the rotation is large.

A hybrid kinetic-magnetohydrodynamic code (CLT-K) is developed to study nonlinear dynamics of Alfvén modes driven by energetic particles (EP). A n = 2 toroidicity-induced discrete shear Alfvén eigenmode (TAE)-type energetic particle mode (EPM) with two dominant poloidal harmonics (m = 2 and 3) is first excited and its frequency remains unchanged in the early phase. Later, a new branch of the n = 2 frequency with a single dominant poloidal mode (m = 3) splits from the original TAE-type EPM. The new single m EPM (m = 3) slowly moves radially outward with the downward chirping of the frequency and the mode amplitude remains at a higher level. The original EPM remains at its original position without the frequency chirping, but its amplitude decays with time. Finally, the m = 3 EPM becomes dominant and the frequency falls into the β-induced gap of the Alfvén continuum. The redistribution of the δf in the phase space is consistent with the mode frequency downward chirping and the drifting direction of the resonance region is mainly due to the biased free energy profile. The transition from a TAE-type EPM to a single m EPM is mainly caused by extension of the p = 0 trapped particle resonance in the phase space.

In this paper, the OpenACC heterogeneous parallel programming model is successfully applied to modification and acceleration of the three-dimensional Tokamak magnetohydrodynamical code (CLTx). Through combination of OpenACC and MPI technologies, CLTx is further parallelized by using multiple-GPUs. Significant speedup ratios are achieved on NVIDIA TITAN Xp and TITAN V GPUs, respectively, with very few modifications of CLTx. Furthermore, the validity of the double precision calculations on the above-mentioned two graphics cards has also been strictly verified with m/n=2/1 resistive tearing mode instability in Tokamak.

The nonlinear evolution of the m/n = 2/1 double tearing mode (DTM) is investigated by the toroidal resistive magnetohydrodynamic code CLT. It is found that the m/n = 2/1 DTM can lead to either a core pressure crash or an off-axis pressure crash. Unlike the core pressure crash, the plasma pressure at the magnetic axis remains almost unchanged during the off-axis pressure crash. The pressure crash only occurs in the annular region during the off-axis crash, and the on-axis plasma pressure slowly reduces after the crash, which is consistent with TFTR observations. A series of simulations are carried out to investigate the influence of the radial position of the inner resonant surface r1, the magnetic shear at the inner resonance surface, and the spatial separation between the two resonant surfaces on nonlinear behaviors of DTMs. We find that r1 plays a dominant role in the nonlinear DTM behaviors. It is more likely for the DTM to lead to the core pressure crash with a smaller r1. It is also found that the magnetic shear at the inner resonant surface and the spatial separation between the two resonant surfaces can also largely influence the nonlinear evolution of the DTM. A simple theoretical formula of the transition criterion between the two pressure crashes is proposed, which agrees well with the simulation results.