Calculation of neoclassical toroidal viscosity in tokamaks with broken toroidal symmetry

A new numerical simulation to evaluate neoclassical toroidal viscosity (NTV) in tokamak configurations with a small perturbation field is developed using the δf Monte Carlo method. The numerical scheme solves the guiding-centre distribution function in non-axisymmetric plasmas according to the drift-kinetic equation, and evaluates the NTV directly from the pressure anisotropy by utilizing the Fourier spectrum expression of the magnetic field in Boozer coordinates. As a first benchmark, the accuracy of the viscosity calculation is demonstrated in a helical configuration of LHD. The convergence of the calculation and dependence of the viscosity on perturbation field amplitude are also tested in a simple tokamak configuration with model perturbation field, which proves the reliability of the simulation. Next, the basic properties of NTV as dependence of the viscosity on collision frequency and magnetic shear are investigated in a multi-helicity perturbation model field and compared with a bounce-averaged analytic formula. It is found that the clear 1/ν and superbanana-plateau dependences cannot be seen in the FORTEC-3D simulation, and the toroidicity of the magnetic field makes a toroidal coupling effect, which enhances NTV if the perturbation has (m, n) and (m ± 1, n) Fourier components simultaneously, where m and n are the poloidal and toroidal numbers of the perturbation field. Local magnetic shear is also found to affect the amplitude of the viscosity.