A Modified Perfectly Matched Layer Implementation for Use in Electromagnetic PIC Codes

Absorption of charged particles in Perfectly-Matched-Layers by optimal damping of the deposited current

“…By contrast, in the present paper, we first focus on the fields of individual particles, before moving on to more complex, physically-relevant simulations. We show that, when an individual particle exits the simulation domain, it can produce a spurious electrostatic field (as observed in [4,5]), but also a spurious electromagnetic radiation (section I). We propose a set of modified PML equations which, under certain conditions, suppress both of these effects, and allow individual particles to cleanly exit the simulation domain (section II and section III).…”

“…However, in the original formulation of the PMLs, the presence of charged particles was not considered. In practice, a number of numerical issues can occur when charged particles reach the PML region, which can then undesirably affect the simulation at large [4,5]. While there is a large body of work on PMLs in general, the issue of charged particles reaching the PML has attracted relatively little attention.…”

“…Historically, solutions to this issue have been proposed and studied in the context of microwave devices, whereby an electron beam passes through the simulation domain, and interacts with electromagnetic modes in a cavity or a waveguide [4][5][6][7]. For instance, in [4], the authors observed that spurious electrostatic fields can build up at the boundary of the simulation domain, if charged particles are simply removed from the simulation as soon as they enter the PML region. (Note that, by default, this is how charged particles are treated in many PIC codes with PMLs.)…”

“…In order to mitigate this issue, the authors proposed to apply numerical diffusion to these fields, by using a Marder-type divergence-cleaning algorithm [8], which causes these fields to decay over time. This does prevent the build up of spurious fields, but is only effective over timescales longer than the characteristic diffusion time, which is limited by stability constraints [4]. Alternatively, instead of removing the particles, some algorithms [5,6] allow them to propagate into the PML region, and to use the corresponding current density as a source term in the PML equations.…”

Perfectly Matched Layer (PML) for Computational Electromagnetics

“…Finally, in the domain of electromagnetics, use of the PML ABC has been reported in particle in cell (PIC) finite difference calculations where moving charged particles are taken into account [76].…”