Suppressing grid instability and noise in particle-in-cell simulation by smoothing

Smoothing short-wavelength charge density variations can stabilize explicit electrostatic particle-in-cell (PIC) plasma simulations against grid heating and cold beam instabilities, which cause unphysical heating when the Debye length is poorly resolved. We demonstrate this by solving the dispersion and by running 1D electrostatic PIC simulations, using an efficient smoothing algorithm that leverages the Poisson solve. To ensure stability, the smoothing radius must increase with the number of Debye lengths per cell. Smoothing also suppresses particle noise, which is severely exacerbated by poor resolution of the Debye length. To help determine optimal PIC configuration, we empirically characterize electric field noise, particle velocity diffusion, and unphysical energy exchanges in 1D PIC simulation, as a function of Debye-length resolution, smoothing, and particles per cell. We also show how PIC noise causes test particles to exhibit misleading behavior. Since smoothing reduces the effective resolution, the optimal cell size is less than the desired resolution but can be much greater than the Debye length, reducing computational expense.