Quantifying PIC Noise Effects on Particle Velocity Moments: Comparisons of PIC and Vlasov Simulations

It is well understood that Particle-in-Cell (PIC) simulation results are affected by the inherent statistical noise of the macro-particles. While the statistical noise level of PIC method in general scales inversely with the square root of the number of particles per cell, its exact effect on the different orders of particle velocity moments obtained from simulation is less clear. This paper investigates the statistical noise effects on particle velocity moments in fully kinetic PIC simulations through comparisons of PIC and grid-based Vlasov simulations. The grid-based Vlasov method eliminates the statistical noise in PIC. We present correlated PIC and Vlasov simulations of plasma expansion and several representative instability problems, with a focus on the electron kinetics and thermodynamic in the processes. We derive the scaling of PIC statistical noise in density, velocity, temperature, and heat flux. We discuss the limitations of the different filtering schemes in PIC to suppress the numerical noise in higher order velocity moments, and the limitations of the PIC method to resolve electron thermodynamic relations.