Description
The plasma wall interaction in a fusion device can be modeled as a collisionless problem. When modeling this low-density region, conventional particle-in-cell codes suffer from statistical error originating from under sampling the velocity space. In contrast, the Vlasov approach utilizes a distribution function in phase space thereby directly solving for the entire velocity space eliminating this statistical error. We are presenting a new finite-volume, 3D-3V Vlasov-Poisson code, kobra, equipped with adaptive mesh refinement (AMR) to reduce computational costs.
We use a second order Runge-Kutta scheme together with a linear approximation with flux limiter to advect the distribution function in phase space. While the Vlasov equation is solved on the full phase space, the Poisson equation is solved on a reduced, coordinate space grid using a multigrid technique compatible with AMR. We have validated our code by reproducing the analytic damping and growth rates of established electrostatic benchmarks: the two (1d1v) and four (2d2v) dimensional two-stream instability and strong and weak Landau damping [1,2,3,5,7].
To model the plasma wall interaction, we consider the transition from the core plasma which is charge neutral towards the wall. Therefore, we employ a fixed charge neutral inflow of plasma incident on a wall. At this wall boundary we consider a floating potential set by the total charge absorbed by the wall. First, we reproduce the steady state electrostatic plasma sheath (as this is a low dimensional 1d1v problem) given in [6]. Then, we move to simulate the Chodura sheath (1d3v) by imposing a constant external magnetic field [3]. Furthermore, we demonstrate computational speedup with AMR on all simulations.