Grid-point requirements for direct kinetic simulation of weakly collisional plasma plume expansion

Abstract

Direct kinetic solvers enable high-fidelity simulation of multiscale plasmas in a number of applications including space physics and propulsion, materials processing, astrophysics, and nuclear fusion. While they eliminate the statistical noise associated with particle-in-cell methods, they are associated with higher dimensionalities. Thus, a detailed understanding of grid-point requirements is required to design efficient meshes so that direct kinetic solvers can be feasibly employed in general settings without compromising on predictivity. The grid-point requirements of a direct kinetic solver employing the Vlasov-Poisson-BGK equations are characterized using an electrostatic and weakly collisional plasma plume expansion model problem, which is unsteady and spatially inhomogeneous with significant deviations from equilibrium. It is demonstrated that at least two to four points per the appropriate Debye length and thermal velocity are necessary to resolve macroscopic density gradients and thus the lowest-order macroscopic quantities, with more stringent requirements for higher-order quantities. Local charge separation and the distribution function itself require at least an additional order of magnitude in resolution for comparable accuracy, as they require the resolution of gradients in the distribution function. Collisions impede plume expansion and introduce secondary flow and field structures, but do not significantly relax the grid requirements despite their smoothing action in velocity space. While specific numerical requirements necessarily depend on the solver, plasma configuration, and collision model, trends in the variation of the elucidated grid-point requirements with the quantity of interest and plasma collisionality can be generalizable across problems with comparable physics. Knowledge of similarly derived trends can contribute to efficient direct kinetic simulation of unsteady and spatially inhomogeneous plasmas of a variety of configurations and collisionalities.