Plasma-wave interaction modelling in magnetic confined devices with the finite element method

Plasma-wave interaction is a broad topic that includes many different phenomena. In the Scrape-Of-Layer (SOL) of tokamak plasmas, different modes of electromagnetic waves can be found, resonances, reflections, scattering and the interaction of these fields with the wall. The study of these phenomena is important for the correct operation of future nuclear fusion reactors because electromagnetic waves are commonly used to stabilize and heat the plasma. Without the proper understanding and modelling, the integrity of the machine could be endangered (e.g., due to the creation of hot-spots caused by RF-DC sheath rectification [1]) and limit the maximum heating power that can be safely sent to the plasma.

The numerical modelling of the plasma-wave interaction in the tenuous plasma close to the tokamak walls is especially challenging due to the confluence of vast physical phenomena with complex geometries. The Finite Element Method (FEM) seems a good choice to solve the problem. But the presence of phenomena as the Lower-Hybrid Resonance (LHR) or the parasitic excitation of small wavelengths modes crates serious numerical difficulties [2,3].

This work compares different FEM approaches implemented in the open-source code ERMES [4]. Some are new, as the Local L2 projections method with bubble elements or the regularized formulation, and others are more known as the edge elements formulation with and without Lagrange multipliers stabilization. The aim is to assess their computational performance and accuracy, and which one is the most adequate in realistic situations.