Numerical thermalization in 3D PIC simulations

A critical aim of particle-in-cell (PIC) simulations is to properly model the evolution of the velocity distribution function (VDF). Simulations with higher macroparticle weights have higher collision rates and corresponding rapid thermalization of the VDF. PIC methods are generally understood to compensate for this effect and provide a numerical solution to the collisionless Vlasov equation due to the weakened short range force. This work tests the degree to which PIC effects compensate for large particle weights in 1-D, 2-D, and 3-D. It is determined that reaching the physical collision rate, let alone the Vlasov solution, in 3D PIC simulations may often be intractable for grids that resolve the Debye length. The collision time is calculated from PIC data and compared directly with the kinetic theory of Okuda, Birdsall, and Langdon in each of the three dimensions. This effect is distinct from grid heating and ``particle noise'' in the sense that energy conserving, δf, and quiet start methods do not inherently avoid numerical thermalization.