Numerical heating in particle-in-cell simulations with Monte Carlo binary collisions

The binary Monte Carlo (MC) collision algorithm is a standard and robust method to include Coulomb effects in particle-in-cell (PIC) simulations of plasmas. Here we show that the coupling between PIC MC algorithms can give rise (nonphysical) numerical heating system significantly exceeds observed when these operate independently. We argue this deleterious effect results from an inconsistency particle motion associated with collisions work performed by collective electromagnetic field on grid. This manifests as (artificial) stochastic production energy, which ultimately heats plasma particles. MC-induced impact evolution simulated for long simulation times ($\ensuremath{\gtrsim}{10}^{3}$ periods, typical parameters). describe source analytically discuss strategies minimize it.