2D and 3D modeling of wave propagation in cold magnetized plasma near the Tore Supra ICRH antenna relying on the perfecly matched layer technique

Abstract

A novel method to simulate ion cyclotron wave coupling in the edge of a tokamak plasma with the finite element technique is presented. It is applied in the commercial software COMSOL Multiphysics. Its main features include the perfectly matched layer (PML) technique to emulate radiating boundary conditions beyond a critical cutoff layer for the fast wave (FW), full-wave propagation across the inhomogeneous cold peripheral plasma and a detailed description of the wave launcher geometry. The PML technique, while widely used in numerical simulations of wave propagation, has scarcely been used for magnetized plasmas, due to specificities of this gyrotropic material. A versatile PML formulation, valid for full dielectric tensors, is summarized and interpreted as wave propagation in an artificial medium. The behavior of this technique has been checked for plane waves on homogeneous plasmas. Wave reflection has been quantified and compared to analytical predictions. An incompatibility issue for adapting the PML for forward (FW) and backward (slow wave (SW)) propagating waves simultaneously has been evidenced. In a tokamak plasma, this critical issue is overcome by taking advantage of the inhomogeneous density profile to reflect the SW before it reaches the PML. The simulated coupling properties of a Tore Supra ion cyclotron resonance heating (ICRH) antenna have been compared to experimental values in a situation of good single-pass absorption. The necessary antenna elements to include in the geometry to recover the coupling properties obtained experimentally are also discussed.

Simulation as a tool to improve wave heating in fusion plasmas

“…That is to say we must have an improved perfect matching layer or absorbing boundary conditions for the relevant modes, which is not the case at present (Jacquot et al 2013). The SBC description should be improved and valid, at any angle.…”

“…We can also add the displacement of the cut-off layer on the IRCH antenna-plasma coupling (Clairet et al 2004;Jacquot et al 2013) (which had not been taken into account until now), as well as the depolarisation induced by the density fluctuations in fusion devices. In general, the depolarisation mechanism should be studied in detail, by itself, applied to fusion plasmas, in order to evaluate the impact on the wave heating or on current drive efficiency.…”

SOL RF physics modelling in Europe, in support of ICRF experiments

“…PMLs are implemented as lossy inhomogeneous materials with artificial dielectric and magnetic tensors depending on plasma parameters, the stretching function and stretched coordinates. For gyrotropic media like cold plasmas, PMLs were formulated in slab [17] and cylindrical geometries [13].…”

Simulation of cold magnetized plasmas with the 3D electromagnetic software CST Microwave Studio®

“…The idea of a "Perfectly Matched Layer" (PML) was proposed in [12] and extended by many authors in specific situations. In particular, the use of PMLs for magnetized plasmas has been studied in [13] and for ICRF plasmas in [14]. A PML is an additional boundary layer put at the edge of the computation domain where perfect absorption is desired.…”