Toroidal Gyrofluid Equations for Simulations of Tokamak Turbulence
Authors: M. A. Beer and G. W. Hammett
A set of nonlinear gyrofluid equations for simulations of tokamak turbulence are derived by taking moments of the nonlinear toroidal gyrokinetic equation. The moment hierarchy is closed with approximations that model the kinetic effects of parallel Landau damping, toroidal drift resonances, and finite Larmor radius effects. These equations generalize the work of Dorland and Hammett [Phys. Fluids B 5 , 812 (1993)] to toroidal geometry by including essential toroidal effects. The closures for phase mixing from toroidal rB and curvature drifts take the basic form presented in Waltz, et al. [Phys. Fluids B 4 , 3138 (1992)], but here a more rigorous procedure is used, including an extension to higher moments, which provides significantly improved accuracy. In addition, trapped ion effects and collisions are incorporated. This reduced set of nonlinear equations accurately models most of the physics considered important for ion dynamics in core tokamak turbulence, and is simple enough to be used in high resolution direct numerical simulations.