A cancellation problem in hybrid particle-in-cell schemes due to finite particle size

Abstract The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the different spatial discretizations of ions as finite-spatial-size particles and electrons as a grid-based fluid can lead to significant numerical wave dispersion errors in the long wavelength limit ( k d i ≪ 1 , where k is the wavenumber and d i is the ion skin-depth). The problem occurs when high-order particle-grid interpolations, or grid-based smoothing, spreads the electric field experienced by the ions across multiple spatial cells and leads to inexact cancellation of electric field terms in the total (ion + electron) momentum equation. Practical requirements on the mesh spacing Δ x / d i are suggested to bound these errors from above. The accuracy impact of not respecting these resolution constraints is shown for a non-linear shock problem.