Numerical thermalization in 3D particle-in-cell simulations

Numerical thermalization in multidimensional particle-in-cell (PIC) codes poses challenges for accurate simulation of low temperature plasma sources. While 1D PIC simulations often have a low rate of numerical thermalization due to some degree of kinetic blocking, multidimensional PIC simulations employing the commonly used cloud-in-cell (CIC) scheme and a well-resolved Debye length will likely have a numerical collision rate which is more rapid than true Coulomb collisions between electrons. The rate of numerical collisions in 2D PIC was empirically estimated by Hockney [1] many years ago and we have recently analytically calculated the drag and diffusion coefficients of the Fokker-Planck form of the numerical collision operator for a test electron macroparticle in a thermal electron background. [2] A similar analysis has been lacking for 3D PIC, which we have investigated here.



[1] R. W. Hockney, "Measurements of collision and heating times in a two-dimensional thermal computer plasma," (1971) Journal of Computational Physics 8, 19-44.



[2] S. Jubin, A. T. Powis, W. Villafana, D. Sydorenko, S. Rauf, A. V. Khrabrov, S. Sarwar and I. D. Kaganovich, "Numerical thermalization in 2D PIC simulations: Practical estimates for low-temperature plasma simulations," (2024) Physics of Plasmas 31, 023902.