ECsim-CYL: Energy Conserving Semi-Implicit particle in cell simulation in axially symmetric cylindrical coordinates

TL;DR

ECsim-CYL is a cylindrical coordinate implementation of the energy conserving semi-implicit particle-in-cell method, significantly improving computational efficiency for axially symmetric plasma simulations while maintaining accuracy and energy conservation.

Contribution

This work introduces ECsim-CYL, a novel cylindrical coordinate version of ECsim that enhances simulation speed for symmetric problems without sacrificing energy conservation or accuracy.

Findings

Retains energy conservation within machine precision.

Accurately models plasma wave spectra in cylindrical waveguides.

Successfully simulates plasma expansion in vacuum.

Abstract

Based on the previously developed Energy Conserving Semi Implicit Method (ECsim) code, we present its cylindrical implementation, called ECsim-CYL, to be used for axially symmetric problems. The main motivation for the development of the cylindrical version is to greatly improve the computational speed by utilizing cylindrical symmetry. The ECsim-CYL discretizes the field equations in two-dimensional cylindrical coordinates using the finite volume method . For the particle mover, it uses a modification of ECsim's mover for cylindrical coordinates by keeping track of all three components of velocity vectors, while only keeping radial and axial coordinates of particle positions. In this paper, we describe the details of the algorithm used in the ECsim-CYL and present a series of tests to validate the accuracy of the code including a wave spectrum in a homogeneous plasmas inside a cylindrical waveguide and free expansion of a spherical plasma ball in vacuum. The ECsim-CYL retains the stability properties of ECsim and conserves the energy within machine precision, while accurately describing the plasma behavior in the test cases.