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

TL;DR

This paper identifies a numerical cancellation issue in hybrid particle-in-cell simulations caused by finite particle size, leading to wave dispersion errors, and suggests mesh spacing guidelines to mitigate these errors.

Contribution

It reveals a specific numerical cancellation problem in hybrid PIC schemes and provides practical mesh spacing recommendations to reduce dispersion errors.

Findings

Finite particle size causes significant wave dispersion errors.

Mesh spacing constraints can bound these errors.

Guidelines improve simulation accuracy in plasma modeling.

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 treatment of ions as finite-size particles and electrons as a grid-based fluid can cause significant numerical wave dispersion errors in the magnetohydrodynamic limit ($kd_i \ll 1$, where $d_i$ is the ion skin-depth). Practical requirements on the mesh spacing $\Delta x/d_i$ are suggested to bound these errors from above.