Continuum Kinetic Modeling of the Tokamak Plasma Edge*

The problem of edge plasma transport provides substantial challenges for analytical or numerical analysis due to (a) complex magnetic geometry including both open and closed magnetic field lines \textbf{B}, (b) steep radial gradients comparable to ion drift-orbit excursions, and (c) a variation in the collision mean-free path along \textbf{B }from long to short compared to the magnetic connection length. Here, the first 4D continuum drift-kinetic transport simulations that span the magnetic separatrix of a tokamak are presented, motivated in part by the success of continuum kinetic codes for core physics and in part by the potential for high accuracy. The calculations include fully-nonlinear Fokker-Plank collisions and electrostatic potential variations. ~The problem of intrinsic toroidal rotation driven by ion orbit loss is addressed in detail.~ The code, COGENT, developed by the Edge Simulation Laboratory collaboration, is distinguished by a fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasma transport and the complex magnetic X-point divertor geometry with high accuracy. Previously, successful performance of high-order algorithms has been demonstrated in a simpler closed magnetic-flux-surface geometry for the problems of neoclassical transport and collisionless relaxation of geodesic acoustic modes in a tokamak pedestal, including the effects of a strong radial electric field under H-mode conditions.