Studies of Gyrokinetic Turbulence Models for Edge Plasmas*

Gyrokinetic computational models are developed for studying tokamak edge plasmas. A 5D $\delta f$ Eulerian gyrokinetic code which uses ($\vec{R}$, $\mu$, $v_\parallel$) coordinates has been developed and benchmarked with the GS2 gyrokinetic code in the linear, collisionless, electrostatic limit, including trapped electron dynamics. Various collisional and numerical dissipation algorithms for the ($\mu$, $v_\parallel$) velocity space formulation with nonlinear dynamics are explored. Extensions of the $ \delta f$ gyrokinetic formulation to full $F (F=F_0 + \delta f)$ are also presented. We discuss studies of turbulence and transport in the tokamak edge/scrape-off region, where $\delta f \sim F_0$ so $O\left(\rho_*^2\right)$ effects neglected for core plasma simulations, such as the parallel nonlinearity, may now be important.