Numerical thermalization in one- and two-dimensional particle-in-cell simulations with Monte-Carlo collisions

Numerical thermalization induced by discrete-particle effects was observed in particle-in-cell (PIC) simulations1, which show that the thermal relaxation time scales with ND2 and ND for one-dimensional (1D) and two-dimensional (2D) models2, respectively. The parameter ND denotes the number of particles in a Debye length (1D) or a Debye square (2D). However, it was found recently that the thermal relaxation time is anomalously shortened to scale with ND while adding the Monte-Carlo collisions in a 1D PIC simulation.3,4 In this work, we examine the numerical thermalization in two-dimensional ES PIC simulations with the consideration of electron-ion collision and electron-neutral collision.4 Our results show that the thermal relaxation time is less sensitive to the collision frequency as compared to the 1D cases, and the thermal relaxation time remains to scale with ND as predicted by the theoretical analysis using the Balescu-Lenard-Landau kinetic theory 5.