Validation of the current and pressure coupling schemes with nonlinear simulations of TAE and analysis on the linear stability of tearing mode in the presence of energetic particles

Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently. Numerical equivalences between these two coupling schemes are strictly verified under different approximations. First, when considering only the perturbed distribution function of energetic particles (EPs), the equivalence can be proved analytically. Second, when both the variations of the magnetic field and the EP distribution function are included, the current and pressure coupling schemes numerically produce the same result in the nonlinear simulations. On this basis, the influences of co-/counter-passing and trapped EPs on the linear stabilities of the m/n ＝ 2/1 tearing mode (TM) have been investigated (where m and n represent the poloidal and toroidal mode numbers, respectively). The results of scanning ${\beta }_{\mathrm{h}}$ of EPs show that the co-passing and trapped EPs are found to stabilize the TM, while the counter-passing EPs tend to destabilize the TM. The behind (de)stabilization mechanisms of the TM by EPs are carefully analyzed. Furthermore, after exceeding critical EP betas, the same branch of the high-frequency mode is excited by co-/counter-passing and trapped EPs, which is identified as the m/n ＝ 2/1 energetic particle mode.