Status of Continuum Edge Gyrokinetic Code Physics Development

We are developing an edge gyro-kinetic continuum simulation code to study the boundary plasma over a region extending from inside the H-mode pedestal across the separatrix to the divertor plates. A 4-D (ψ, θ, ε, μ) version of this code is presently being implemented, en route to a full 5-D version. A set of gyrokinetic equations[1] are discretized on computational grid which incorporates X-point divertor geometry. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. A fourth order upwinding algorithm is used for particle cross-field drifts, parallel streaming, and acceleration. Boundary conditions at conducting material surfaces are implemented on the plasma side of the sheath. The Poisson-like equation is solved using GMRES with multi-grid preconditioner from HYPRE. A nonlinear Fokker-Planck collision operator from STELLA[2] in (ν#parallel#,ν#perpendicular#) has been streamlined and integrated into the gyro-kinetic package using the same implicit Newton-Krylov solver and interpolating F and dF/dt|coll to/from (ε, μ) space. With our 4D code we compute the ion thermal flux, ion parallel velocity, self-consistent electric field, and geo-acoustic oscillations, which we compare with standard neoclassical theory for core plasma parameters; and we study the transition from collisional to collisionless end-loss. In the real X-point geometry, we find that the particles are trapped near outside midplane and in the X-point regions due to the magnetic configurations. The sizes of banana orbits are comparable to the pedestal width and/or the SOL width for energetic trapped particles. The effect of the real X-point geometry and edge plasma conditions on standard neoclassical theory will be evaluated, including a comparison of our 4D code with other kinetic neoclassical codes (such as NCLASS[3] and XGC[4]) and experiments