An Unstructured Body-of-Revolution Electromagnetic Particle-in-Cell Algorithm with Radial Perfectly Matched Layers and Dual Polarizations

TL;DR

This paper introduces a new electromagnetic particle-in-cell algorithm for complex plasma simulations on unstructured meshes in body-of-revolution geometries, utilizing dual polarizations and cylindrical perfectly matched layers for improved accuracy and flexibility.

Contribution

The paper presents a novel unstructured mesh particle-in-cell algorithm that handles dual polarizations and implements cylindrical PMLs, enhancing simulation flexibility in complex geometries.

Findings

Successfully models azimuthal currents from charged rings.

Demonstrates charge-conserving scatter and gather steps.

Validates the algorithm with numerical examples.

Abstract

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell's equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge-conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE-phi and TM-phi polarizations on the finite element (primal) mesh. A cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TM-phi polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.