A Spectral Symplectic Algorithm for Cylindrical Electromagnetic Plasma Simulations

TL;DR

This paper introduces a novel symplectic electromagnetic algorithm for plasma simulations that prevents numerical instabilities and artificial heating, advancing the accuracy of plasma modeling.

Contribution

It presents the first self-consistent electromagnetic macroparticle algorithm derived via a map formalism, improving stability and physical fidelity.

Findings

Prevents numerical renkov instabilities

Reduces artificial plasma heating

Ensures correct dispersion relations

Abstract

Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend the symplectic approach to plasmas, which have focused primarily on discrete Lagrangian mechanics. In this paper, we derive a a symplectic electromagnetic macroparticle algorithm using the map formalism. The resulting algorithm is designed to prevent numerical instabilities such as numerical \v{C}erenkov, which result from incorrect dispersion relations for the fields, as well as the artificial heating of plasmas, which arise from the non-symplectic nature of conventional particle-in-cell algorithms. This is the first self-consistent electromagnetic algorithm derived using a map-based approach.