Validation of ERMES 20.0 finite element code for MAST Upgrade O-X mode conversion

TL;DR

This work addresses the need for validated, high-fidelity electromagnetic wave modeling of EBW-related O–X mode conversion in fusion plasmas. It adopts a controlled slab benchmark and compares a frequency-domain FEM code, ERMES 20.0, against multiple FDTD solvers, focusing on field profiles, energy flux, and reflection coefficients. The study demonstrates excellent agreement between ERMES 20.0 and FDTD results across two FE formulations (EDG and RME), with stability achieved via a damping approach and parameter choice that harmonizes the formulations. The findings establish ERMES 20.0 as a reliable tool for simulating cold-plasma wave interactions in fusion contexts, with planned extensions to include warm and hot plasma effects for enhanced predictive capabilities in devices like MAST Upgrade.

Abstract

This study presents the validation of the frequency-domain finite element code ERMES 20.0, benchmarked against Finite Difference Time Domain (FDTD) solvers. The simulations focus on Ordinary-Extraordinary (O-X) mode conversion in the Electron Bernstein Wave (EBW) regime of the MAST Upgrade experiment. Validation is performed in terms of mode conversion efficiency and wave propagation characteristics. Several finite element formulations are tested and compared with the FDTD results. The simulations demonstrate excellent agreement between the different approaches, confirming the accuracy and robustness of ERMES 20.0 for modeling cold plasma wave interactions.

Figures (9)

• Figure 1: Benchmark scenario #6 from Seemann. A Gaussian beam in O-mode polarization at $f_{0} = 28\,\text{GHz}$ is launched into a cold magnetized plasma at the optimal angle $\theta_{opt} = 47.3\text{\textdegree}$. The colour map represents the plasma electron density profile $n_{e}$ defined by equation \ref{['nedensity']} for $z\,>\,z_{0} = 0.15\,\text{m}$. A uniform magnetic flux density of $|\,\mathbf{B}\,| = 0.85\,\text{T}$ is applied to the plasma.
• Figure 2: FEM model of benchmark \ref{['benchmark']}. Colour map shows the module of the electric field for $k_{0}L_{n}\,=\,25$.
• Figure 3: Impact of different values of the electron collision frequency $\nu$ on the simulation results for the EDG and RME formulations. The colour map represents the module of the complex electric field for $k_{0}L_{n} = 25$.
• Figure 4: Reflection coefficient, as defined in \ref{['Reflection-Definition']}, for the EDG and RME formulations. The value between brackets represents the electron collision frequency $\nu$.
• Figure 5: Module of the imaginary part of the electric field calculated by ERMES 20.0 in the cold plasma region for $k_{0}L_{n} = [2,\,25]$ and an electron collision frequency of $\nu = 10^{9}\,\text{Hz}$. The real part of the electric field exhibits a similar module distribution and is therefore not shown.