Perfectly Matched Layer implementation for E-H fields and Complex Wave Envelope propagation in the Smilei PIC code

TL;DR

This paper presents an implementation of Perfectly Matched Layer (PML) boundary conditions for electromagnetic and complex wave envelope simulations within the Smilei PIC code, enhancing accuracy and efficiency in laser-plasma modeling.

Contribution

It introduces PML boundary conditions for both Maxwell's equations and the complex wave envelope in PIC simulations, including for the first time in the envelope wave context.

Findings

PML effectively absorbs outgoing waves across all angles and frequencies.

Implementation improves simulation accuracy and reduces computational resources.

Applicable to Cartesian and azimuthal geometries in Smilei.

Abstract

The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wave lengths. In the worst, ABC are not even possible for the set of equations and/or numerical schemes used in the simulation and reflections can not be avoided at all. Perflectly Matched Layer (PML) are layers of absorbing medium which can be added at the simulation edges in order to significantly damp both outgoing and reflected waves, thus effectively playing the role of an ABC. They are able to absorb waves and prevent reflections for all angles and frequencies at a modest computational cost. It increases the simulation accuracy and negates the need of oversizing the simulation usually imposed by ABC and leading to a waste of computational resources and power. PML for finite-difference time-domain (FDTD) schemes in Particle-In-cell (PIC) codes are presented for both Maxwell's equations and, for the first time, the envelope wave equation. Being of the second order, the latter requires significant evolutions with respect to the former. It applies in particular to simulations of lasers propagating in plasmas using the reduced Complex Envelope model. The implementation is done in the open source code Smilei for both Cartesian and azimuthal modes (AM) decomposition geometries.