Note on the use of Yee-lattices in (semi-) implicit Particle-in-cell codes

TL;DR

This paper proposes a modification to implicit particle-in-cell algorithms by replacing the Yee-lattice with a staggered mesh, significantly reducing magnetic field divergence and improving physical accuracy.

Contribution

It introduces a staggered mesh arrangement in implicit PIC codes to enhance divergence-free magnetic field representation, improving simulation fidelity.

Findings

Magnetic field divergence is reduced by several orders of magnitude.

The modified algorithm maintains stability and accuracy.

Improved physical realism in PIC simulations.

Abstract

A modification of the implicit algorithm for particle-in-cell simulations proposed by Petrov and Davis [2011] is presented. The original lattice arrangement is not inherently divergence-free, possibly leading to unphysical results. This arrangement is replaced by a staggered mesh resulting in a reduction of the divergence of the magnetic field by several orders of magnitude.