Description
Digital twins are a key enabler for the design and optimisation of future fusion reactors. Their development relies on predictive, high-fidelity simulations that integrate multiple physical phenomena in realistic three-dimensional geometries. In particular, the modelling of radio-frequency (RF) heating systems, such as Ion Cyclotron Resonance Heating (ICRH), requires accurate solutions of Maxwell's equations in magnetised plasmas together with the capability to run efficiently in High-Performance Computing (HPC) environments and to couple with other reactor-scale physics.
Most existing ICRH tools are developed for specific configurations or focus mainly on plasma modelling, which can complicate their integration with engineering and multi-physics simulations at reactor scale. To address this, we develop a dedicated electromagnetic full-wave solver within Alya, a single-code, massively parallel finite element framework designed for large-scale multi-physics problems. This approach enables the consistent coupling of plasma and engineering solvers within the fusion-oriented framework Alya4fusion.
Within this ecosystem we present EMWAVE, a frequency-domain full-wave solver for RF wave propagation. It relies on a finite element discretisation of the Maxwell and Helmholtz equations and includes both a 2D nodal formulation and a three-dimensional version using first-order Nédélec elements to represent curl-conforming electromagnetic fields and avoid spurious modes.
The current development stage focuses on verification and validation in cold magnetised plasmas. Canonical test cases assess numerical accuracy and robustness, and the solver is benchmarked against the established ICRH code ERMES, showing excellent agreement and confirming the correctness of the formulation. Two-dimensional simulations have been performed on meshes up to approximately 120k elements, while preliminary three-dimensional tests demonstrate the correct behaviour of the edge-element formulation. Alya has previously been run with billions of elements, indicating that mesh size will not be a limiting factor when scaling to larger problems.
In this contribution, we detail the finite element formulation, the integration within Alya4fusion, and the first verification and benchmarking results against canonical cases and the ERMES code. These results establish EMWAVE as a reliable and extensible basis for large-scale RF simulations, while ongoing work targets higher-order Nédélec elements, hot plasma models, scalability studies and applications to realistic reactor configurations.