Turbulence-driven flow dynamics in general axisymmetric toroidal geometry

This work gives the equations governing the generation of toroidally axisymmetric flows by turbulent Reynolds and Maxwell stresses in finite aspect ratio, general cross section tokamak plasmas. Inclusion of the divergence-free flow constraint in the lowest order changes the timescale for evolution of the poloidal flows driven by turbulence by substantial factors. In the pedestal region for the present-day machines, as compared to earlier cylindrical models, the timescale evaluated using a large aspect ratio circular cross section model can be two orders of magnitude longer, while the present, general geometry result can be about one order of magnitude longer. Inclusion of gyroviscosity in the calculation shows that the only lowest order radial velocity fluctuations that enter the problem are those due to fluctuating E × B flows. Toroidal and poloidal flow effects on the toroidally axisymmetric flows are inextricably coupled due to the neoclassical poloidal viscosity. Accordingly, the physics is inherently three dimensional and measurements of all three-velocity components are required to obtain the information needed to quantitatively test the theory. The parallel and angular momentum equations for the lowest order, toroidally axisymmetric flows look like radial transport equations when the turbulence is included. The turbulence terms provide the radial transport fluxes. In standard neoclassical theory, the parallel flow equation is local on each flux surface; there is no radial derivative term. However, adding turbulence gives a way, in principle, for radial transport to lead to poloidal flows that deviate from the neoclassical prediction. The inclusion of the Maxwell stress provides a mechanism for MHD fluctuations to alter the toroidally axisymmetric flows.