A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

TL;DR

This paper introduces a particle-in-cell algorithm based on finite element exterior calculus that preserves gauge symmetries and conservation laws, improving the accuracy and stability of plasma simulations.

Contribution

It develops a gauge-compatible Hamiltonian splitting algorithm within finite element exterior calculus, ensuring exact preservation of gauge symmetries in particle-in-cell methods.

Findings

Numerical demonstration of time invariance of the momentum map.

Accurate initialization of electric fields with fixed background charge.

Effective simulation of 1X2P phase space.

Abstract

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via the momentum map. We numerically demonstrate this time invariance of the momentum map and its usefulness in establishing precise initial conditions with a desired initial electric field and fixed background charge. The restriction of this canonical, finite element Poisson structure to the 1X2P phase space is also considered and simulated numerically.