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

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 (kdi≪1, where k is the wavenumber and di 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 Δx/di 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. •A novel “cancellation” numerical error is identified for the hybrid particle-in-cell (PIC) scheme.•A semi-discrete dispersion relation is derived that shows the error is due to different discretization of ions and electrons.•The errors in the dispersion relation are validated against numerical simulations.•A dramatic example of these errors is given for a non-linear electromagnetic shock problem.