Intrinsic rotation modulation by finite-step neutral particles in tokamaks

Toroidal rotation is a stabilizing mechanism for tokamak plasmas, and is thus a parameter of interest. Burning fusion plasmas will primarily be heated isotropically by fusion reactions, unlike present heating by neutral-beam injectors which can apply a large net toroidal torque. Therefore, it is important to understand the toroidal rotation in low applied-torque scenarios. Even in such scenarios, strong transport-driven scrape-off layer (SOL) plasma flows act as a boundary condition for the core rotation. Charge-exchanging (c.x.) SOL neutrals can theoretically transport this momentum into the confined region due to their high cross-field mobility, coupling the core rotation to this boundary layer. We show that diffusive neutral particles (infinitesimal c.x. steps) cannot drive a significant toroidal rotation within a self-consistent treatment of the plasma edge. Thus, we develop and explore an approximate analytic treatment of thermal neutral particles in the edge that maintains the effects of finite c.x. steps. The resulting equation for the neutral flux can approximately be expressed as the sum of the diffusive neutral transport terms and an effective Gaussian spreading of the flux itself due to the finite steps. The theory retains key edge features (turbulent transport, drift orbits, ion loss cone, transport-driven SOL flows, etc.) and allows arbitrary neutral densities to couple the SOL flows to the core rotation solution via the non-local finite-step neutral momentum flux.