Description
Plasma transport in magnetic fusion devices is governed by strongly anisotropic, multi-scale processes, leading to steep, evolving gradients throughout a discharge. While some phenomena can be approximated in two dimensions, a comprehensive understanding, especially of non-axisymmetric effects, requires fully three-dimensional simulations. These are crucial for capturing magnetic ripple from discrete coils, resonant magnetic perturbations (RMPs), localized plasma-facing components, complex wall geometries, and stellarator configurations. Such features can profoundly alter plasma confinement and introduce spatial irregularities, which are critical for next-generation devices where managing heat and particle fluxes is vital to protecting plasma-facing components. Accurately resolving these effects is computationally demanding, as the cost and memory requirements of 3D simulations scale rapidly with resolution. Adaptive mesh refinement is therefore essential, allowing resolution to be concentrated only where needed and making high-fidelity 3D plasma simulations feasible. Understanding the relationship between magnetic geometry and transport is thus key to predicting and optimizing plasma dynamics.
The contribution of this work is twofold. First, we present an $h$-adaptive mesh refinement strategy implemented in the SolEdge-HDG [1–3] finite element code. This fully automated approach enables local refinement in regions of strong transport gradients and coarsening where the solution remains smooth [4,5]. Second, we use this framework to compute two- and three-dimensional simulations in both circular limited and WEST diverted configurations. In the first part, density, temperature, heat and particle fluxes, and power deposition profiles are computed in 2D axisymmetric WEST simulations for different values of the $h$-adaptivity parameters. Results show that careful tuning of these parameters significantly impacts the computed plasma quantities. In the second part, we conduct a systematic study of 3D simulations in the circular limited configuration, incorporating magnetic ripple with various perturbation amplitudes and periods. The resulting plasma profiles are quantitatively compared to those from 3D axisymmetric cases, revealing the influence of non-axisymmetric effects on transport and confinement. These 3D ripple simulations are also qualitatively compared to WEST Langmuir probes experimental measurements. Moreover, the 3D model mitigates the density accumulation at the tangential contact point seen in 2D axisymmetric simulations, providing a more accurate representation of experimental observations and highlighting the importance of including magnetic ripple in predictive modeling.
[1] Giorgio Giorgiani, H Bufferand, G Ciraolo, Eric Serre, and P Tamain. A magnetic-field independent approach for strongly anisotropic equations arising plasma-edge transport simulations. Nuclear Materials and Energy, 19:340–345, 2019.
[2] Ivan Kudashev, M Scotto d’Abusco, A Glasser, Eric Serre, Frédéric Schwander, Hugo Bufferand, Guido Ciraolo, Philippe Ghendrih, and Patrick Tamain. Global particle buildup simulations with gas puff scan: application to WEST discharge. Frontiers in Physics, 12:1407534,
2024.
[3] M Scotto d’Abusco, G Giorgiani, JF Artaud, H Bufferand, G Ciraolo, P Ghendrih, E Serre, and P Tamain. Core-edge 2D fluid modeling of full tokamak discharge with varying magnetic equilibrium: from WEST start-up to ramp-down. Nuclear Fusion, 62(8):086002, 2022.
[4] Giacomo Piraccini, Frédéric Schwander, Eric Serre, Giorgio Giorgiani, and M Scotto D’Abusco. Spatial adaptivity in SolEdge3X-HDG for edge plasma simulations in versatile magnetic and reactor geometries. Contributions to Plasma Physics, 62(5-6):e202100185, 2022.
[5] Marcello Capasso, Ivan Kudashev, Frédéric Schwander, and Éric Serre. A $h$-adaptivity strategy for Hybridizable Discontinuous Galerkin (HDG) simulations of fluid transport models in tokamak plasma. International Journal for Numerical Methods in Engineering, 126(17):e70107, 2025.