Numerical effects on energy distribution functions in particle-in-cell simulations with Monte Carlo collisions: choosing numerical parameters

Particle-in-cell simulations with Monte Carlo collisions are expected to calculate the velocity distribution functions of charged species correctly, even if these distribution functions have exotic features such as gross anisotropy in velocity space, marked departures from a Maxwell–Boltzmann distribution, or failure of the local field approximation. Correct computation of the electron energy distribution function, in particular, is crucial in chemically complex plasmas, where radicals produced by electron impact processes usually have a dominant role. In such cases, accurate calculation of the rate constants for electron impact processes is a major motivation for the use of a kinetic simulation procedure, such as the particle-in-cell method. Like any numerical procedure, the particle-in-cell algorithm has limitations, and one of these limitations is that velocity space diffusion can distort the particle energy distribution functions. This paper presents examples of some conditions where such numerical distortion of particle energy distribution functions is important, and draws conclusions with implications for the choice of numerical parameters for particle-in-cell simulations. In particular, we show that the number of particles per cell that is required varies significantly with the conditions (as much as three orders of magnitude), and can sometimes be very large indeed. We suggest a heuristic for selecting the number of particles per cell, derived from the examples we discuss. (paper)