Intrinsic toroidal rotation driven by turbulent and neoclassical processes in tokamak plasmas from global gyrokinetic simulations

Gyrokinetic tokamak plasmas can exhibit intrinsic toroidal rotation driven by the residual stress. While most studies have attributed the residual stress to the parallel-momentum flux from the turbulent $\boldsymbol{E}\times\boldsymbol{B}$ motion, the parallel-momentum flux from the drift-orbit motion (denoted $Π_\parallel^D$) and the $\boldsymbol{E}\times\boldsymbol{B}$-momentum flux from the $\boldsymbol{E}\times\boldsymbol{B}$ motion (denoted $Π_{E\times B}$) are often neglected. Here, we use the global total-$f$ gyrokinetic code XGC to study the residual stress in the core and the edge of a DIII-D H-mode plasma. Numerical results show that both $Π_\parallel^D$ and $Π_{E\times B}$ make up a significant portion of the residual stress. In particular, $Π_\parallel^D$ in the core is higher than the collisional neoclassical level in the presence of turbulence, while in the edge it represents an outflux of counter-current momentum even without turbulence. Using a recently developed ``orbit-flux'' formulation, we show that the higher-than-neoclassical-level $Π_\parallel^D$ in the core is driven by turbulence, while the outflux of counter-current momentum from the edge is mainly due to collisional ion orbit loss. These results suggest that $Π_\parallel^D$ and $Π_{E\times B}$ can be important for the study of intrinsic toroidal rotation.