Smoothing reduces noise and eliminates grid instability in particle-in-cell simulation

Particle-in-cell (PIC) plasma simulation can be unstable when the Debye length is insufficiently resolved by the simulation grid. This may unduly increase computational expense when the plasma and fields vary on scales much larger than the Debye length. Previous work suggested that smoothing the charge density (or using larger particle shapes) allows grid cells to be only somewhat enlarged before encountering instability. Using the PIC dispersion, we calculate how much smoothing is needed to eliminate grid instability, and demonstrate success with the most common explicit, electrostatic PIC algorithm for 2000 Debye lengths per cell. We also characterize particle noise, which is increasingly detrimental as the Debye length becomes more poorly resolved. Fortunately, smoothing mitigates this noise. By reducing noise and grid instability, smoothing can significantly speed up simulations (with no fundamental physical need to resolve the Debye length) by allowing larger cells and fewer computational particles per cell.