Gyrokinetic simulation of the spontaneous toroidal rotation of plasma in a stochastic magnetic field

Since the DIII-D resonant magnetic perturbation experiment [Nucl. Fusion $\bm{59}$, 126010 (2019)] suggests that the neoclassical toroidal viscosity due to the collisional effects associated with the non-resonant magnetic perturbations is not enough to explain the observed toroidal rotation, it is of interest to investigate the toroidal rotation induced by the anomalous diffusion due to the resonant magnetic perturbations. Gyrokinetic simulation of the toroidal rotation of plasma in a stochastic magnetic field is carried out to investigate the resonant magnetic perturbations effects on toroidal rotation. The simulation results suggest that, in a stochastic magnetic field, resonant magnetic perturbations drive the plasma to toroidally rotate through the ambipolar radial electric field. It is found that this spontaneous flow driven on the time scale less than an ion-ion collision time is the parallel return flow of the $\bm{E}_r\times\bm{B}_0$ drift, which is due to the the ambipolar radial electric field induced by the non-ambipolar radial diffusion in the stochastic magnetic field. Collisional effect changes the plasma toroidal rotation from the return flow to the rigid-body flow after a few ion-ion collision times. The toroidal rotation observed in DIII-D resonant magnetic perturbation experiment [Nucl. Fusion $\bm{59}$, 126010 (2019)], can be explained by the rigid-body rotation driven by the ambipolar radial electric field generated by the stochastic magnetic field layer.