Transport-driven toroidal rotation in the tokamak edge

The edge of H-mode tokamak plasmas without external momentum input almost always rotates toroidally in the co-current direction, which has prompted a theoretical search for non-diffusive momentum transport mechanisms. In contrast to these efforts, the present work treats a model drift-kinetic ion equation for the pedestal and SOL containing only parallel free streaming, magnetic drifts, and spatially inhomogeneous but purely diffusive transport. The solution demonstrates that passing-ion orbits and spatially inhomogeneous diffusion interact to cause a variation of the orbit-averaged diffusivities that depends on the sign of $v_{\parallel}$, typically resulting in preferential transport of counter-current ions. If the plasma at the boundary with the core is allowed to rotate toroidally to annihilate toroidal momentum transport, the resulting pedestal-top rotation reaches experimentally relevant values and exhibits several features in qualitative agreement with experiment. It is almost always in the co-current direction, with a rate that is proportional to $T_{i}|_{\rm{ped-top}}/B_{\rm{pol}}L_{Te}$ for small $q\rho_{i}/L_{Te}$, thus inversely proportional to $I_{p}$ in accord with Rice scaling. It is independent of the toroidal velocity and its radial gradient, representing a residual stress. The $T_{i}|_{\rm{ped-top}}/B_{\rm{pol}}L_{Te}$ scaling implies co-current spin-up at the transition to H-mode, as $T_{i}$ increases and the gradient of $T_{e}$ steepens. Untested predictions of the model include a sensitivity of the rotation to the major-radial position of the X-point, with a more inboard X-point leading to stronger co-current rotation. Beyond intrinsic rotation predictions, comparison of heat and momentum transport reveals that neutral beam injection must be significantly unbalanced in the counter-current direction to cause zero toroidal rotation at the pedestal top.