Numerical thermalization in 2D PIC: Timescales and potential for mitigation in modeling low temperature plasma discharges

Numerical thermalization in particle-in-cell (PIC) simulations has been studied extensively. It is a process that is closely related to the fluctuation spectrum of the simulation; it results in relaxation of the particle velocity distributions as they are driven towards a Maxwellian by the numerical collision operator. This is analogous to Coulomb collisions in a real plasma. For most 2D setups, numerical thermalization rates are inversely proportional to the number of particles per cell. We provide a practical guide for estimating these effects in 2D PIC simulations for a variety of low temperature plasma applications, including example simulations of capacitively coupled plasma (CCP) discharges, inductively coupled plasma (ICP) discharges, beam plasmas, and hollow cathode discharges. In addition to thermalization timescale estimates, we discuss potential methods of mitigating the effects of numerical thermalization.