Non-harmonic behavior induced by the particle-in-cell (PIC) scheme for cold plasma oscillations

Summary form only given. In a linearly perturbed cold plasma, particles exhibit harmonic motion about their equilibrium positions at the plasma frequency. A ID electrostatic model is used to investigate the non-harmonic behaviors caused by the particle-in-cell (PIC) scheme. Simulations in two periodic ID PIC codes, varying the number of particles and grid cells indicate that for two particles, non-harmonic behavior is observed when charge is weighted to the same grid. The error is due to the reduction of the electric field at the common grid node. A down shift of the plasma frequency is also observed. The critical closest distance to avoid significant numerical errors in PIC simulations differs for odd and even numbers of grid cells due to the charge weighting scheme. The error is reduced, but still present in many particle simulations where the long range Coulomb force dominates.