Fluid Moment Transport Equations In Tokamak Plasmas

Transport equations for tokamak plasmas are usually obtained by first taking flux-surface averages of the collisional Braginskii equations. Then, {\it ad hoc} terms are added for: neoclassical effects on the parallel Ohm's law (trapped particle effects on resistivity, bootstrap current); fluctuation-induced transport; heating, current-drive \& flow sources and sinks; small non-axisymmetries; etc. However, tokamak plasmas are usually not in collisional regimes. We have begun developing self-consistent second order in gyroradius fluid-moment-based transport equations, including poloidal and toroidal mass flow equations, in nearly axisymmetric single-ion-species tokamak plasmas. The derivation begins from fluid moments of the plasma kinetic equation, incorporates constraints from faster processes (compressional Alfven waves, sound waves, poloidal flow damping) and includes: neoclassical effects through kinetically-determined parallel viscosity and heat flux closures, fluctuation-induced transport through ensemble averages, paleoclassical effects through transforming from laboratory to poloidal flux coordinates, neoclassical toroidal viscosity (NTV) induced by slight magnetic field non-axisymmetries, and the effects of sources and sinks.