A numerical method for calculating the driven current of neutral beam injection in tokamaks

The current driven by neutral beam injection in tokamak is calculated, and the slowing-down distribution function of the fast ion is obtained by the backward Euler iteration method, including the pitch angle scattering collision. This study reveals that when the pitch-angle cosine is small, the trapped fast-ion current significantly contributes to the total driven current, particularly when the neutral beam is injected perpendicularly. In such cases, the current densities of passing and trapped ions are of the same order of magnitude, with the trapped fast-ion current contributing over 10% to the total neutral beam-driven current. This results in a parabolic profile of the total current in the radial direction, promoting the formation of a negative shear equilibrium structure in the core of the tokamak plasma. The numerical approach was validated against the NUBEAM code while considering electron shielding effects and applied to calculate the neutral beam-driven current in multiple tokamaks. The influence of pitch-angle cosine and neutral beam injection power on the driven current was studied at different radial positions.