Toroidal modeling of energetic passing particle drift kinetic effects on tearing mode stability

Abstract

Drift kinetic effects of the neutral beam injection (NBI) induced passing energetic particles (EPs) on the linear stability of the n=1 tearing mode (with the dominant poloidal harmonic of m=2) are numerically investigated utilizing the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)], in a tokamak plasma with finite equilibrium pressure and anisotropic thermal transport. In the low plasma pressure regime, it is found that co- (counter-) passing EPs stabilize (destabilize) the tearing mode, agreeing with previous studies. However, as the plasma pressure increases beyond a critical value, it is found that co-passing EPs also destabilize the mode. An in-depth analysis reveals that the net effect of co-passing EPs is a result of competition between the stabilizing contribution from the non-adiabatic drift kinetic terms and the destabilizing contribution associated with adiabatic terms, with the latter becoming more dominant at higher equilibrium pressure. Non-perturbative magnetohydrodynamic-kinetic hybrid modeling also finds that co- and counter-passing EPs modify the tearing mode eigenfunction differently, with the counter-passing EPs enhancing the sideband harmonics. Furthermore, effects of the plasma resistivity and toroidal rotation, as well as that of the equilibrium distribution of EPs in the particle pitch angle space, are also investigated, showing asymmetric results on the tearing mode stability between the co- and counter-passing EPs. The first order finite orbit width correction is found be to stabilizing with co-passing EPs and destabilizing with counter-passing particles. Finally, drift resonances between passing EPs and the tearing mode induces finite frequency to the mode and generate finite net torques inside the plasma, due to the neoclassical toroidal viscosity and the Reynolds stress associated with 3-D perturbations.

A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

“…However, the perturbed Lagrangian with the form similar to equation (1), i.e. the terms related to magnetic field curvature or curvature drift velocity are retained, has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency large-scale magnetohydrodynamic (MHD) problems [3][4][5][6][7][8][9][10][11][12][13], particularly in the field of magnetic confinement fusion plasma research, such as shear Alfvén waves [14][15][16][17][18][19][20], the internal kink or fishbone-like mode [21][22][23][24][25][26][27][28][29][30][31][32][33][34], resistive wall modes (RWMs) [35][36][37][38][39][40][41][42][43][44], neoclassical tearing modes or neoclassical toroidal viscosity torque [45][46][47][48] and long-wave-length turbulences…”