Perfectly Matched Layers for time-harmonic transverse electric wave propagation in cylindrical and toroidal gyrotropic media

In this paper we implement the stretched-coordinate Perfectly Matched Layer (PML) technique in [28] to emulate full power absorption outside the simulation domain for time-harmonic electromagnetic wave propagation in presence of gyrotropic dielectric tensor and curved geometry relevant for magnetized plasma devices. We recall the PML formulation as an artificial inhomogeneous lossy medium, following the stretching into the complex plane of a general system of three orthogonal curvilinear coordinates. We apply the general method in cylindrical and toroidal geometries. We then assess this technique in a simple case combining gyrotropy and coordinate curvature. Our test problem analytically quantifies the reflection of Transverse Electric (TE) cylindrical eigenmodes in a gyrotropic medium by a radial PML in cylindrical geometry. The obtained reflection coefficient involves wave, PML and geometric parameters at the PML location. The new coefficient generalizes the one obtained earlier with Cartesian coordinates, and becomes equivalent when the effects of the local cylindrical curvature at the PML (stretched) location can be neglected. These curvature effects are outlined and the limitations they impose on the properties of the PML are quantified as a function of the relevant parameters. Peculiarities related to the gyrotropy are also highlighted. Finite element calculations of the test problem in two-dimensional cylindrical geometry are exploited to verify these properties numerically. Indications are finally given on how to choose the PML parameters in order to obtain a minimal wave reflection at given numerical cost, taking into account errors associated with the numerical scheme.