Neoclassical toroidal plasma viscosity (NTV) torque induced by non-axisymmetric magnetic perturbation in the collisionless regimes in tokamaks is modelled by solving the bounce-averaged drift kinetic equation numerically. The detailed comparison between the numerical and the analytic solutions of NTV is discussed in this paper. In different asymptotic limits of the collisionless regimes, the numerical solutions are in good agreement with the analytic results. The numerical results are different from the analytic results calculated from the smoothly connected formula in the transit regimes. The pitch angle scattering is especially important in the regime. The final difference between the numerical and the analytic results can be up to a factor of 2 near the transition between the non-resonant and resonant regimes. This reveals the importance of the boundary condition of the pitch angle space. The sign of the electric field is found to be important in the calculation of the NTV torque. It shows that the effect of the resonant particles makes the NTV torque more important for the lower collisionality and lower rotation cases, which are the International Thermonuclear Experimental Reactor relevant conditions. It also shows that the electron NTV torque is important in the low collisionality case. This numerical method can be applied for modelling the NTV torque in different collisionality regimes and their transitions in tokamaks without additional approximations.
Calculation of neoclassical toroidal viscosity with a particle simulation in the tokamak magnetic braking experiments