FESTIM, a modelling code for hydrogen transport in materials for nuclear fusion applications

Rémi Delaporte-Mathurin (CEA, 🇫🇷)
Etienne Hodille (CEA, 🇫🇷)
Floriane Leblond (CEA, 🇫🇷)
Jonathan Mougennot (LSPM, 🇫🇷)
Yann Charles (LSPM, 🇫🇷)
Christian Grisolia (CEA, 🇫🇷)
James Dark (LSPM, 🇫🇷)
Thursday session 1 (Zoom) (13:00–14:40 GMT)
This talk won a prize: Best talk by a PhD student or undergraduate
View slides (pdf) (available under a CC BY 4.0 license)

The principle of nuclear fusion is to fuse two hydrogen nuclei to form a helium nucleus and a neutron, releasing incredible amounts of energy in the process. To achieve these fusion reactions, extremely high temperatures are required: more than 10 times the temperature of the Sun's core. The very hot fuel in the plasma is magnetically confined within a chamber called a tokamak. Eventually, hydrogen ions will hit the reactor walls and penetrate in the materials.

In order to simulate hydrogen transport in complex components (multi-material, multidimensional geometries…), a finite element modelling code relying on FEniCS called FESTIM has been developed [1]. FESTIM solves a set of transient Macroscopic Rate Equations (MRE) which accounts for the diffusion (based on Fick's law) and trapping/detrapping of hydrogen isotopes in materials (based on McNabb and Foster's equations [2]) coupled to transient heat transfer.

This talk showcases the use of FESTIM and FEniCS to model key tokamak components such as actively cooled plasma facing components and how results crucial for the International Thermonuclear Experimental Reactor (ITER) [3] operations are extracted from it [4]. The code was verified using the method of manufactured solutions and validated against experimental results. FESTIM was also benchmarked with other codes from the fusion community and with the commercial simulation suite Abaqus.


  • [1] Rémi Delaporte-Mathurin, Etienne A. Hodille, Jonathan Mougenot, Yann Charles, Christian Grisolia. Finite element analysis of hydrogen retention in ITER plasma facing components using FESTIM, 2019. [DOI: 10.1016/j.nme.2019.100709]
  • [2] A. McNabb and P. K. Foster. A new analysis of the diffusion of hydrogen in iron and ferritic steels, Transactions of the Metallurgical Society of AIME 227, 618–627, 1963.
  • [3] ITER website. www.iter.org
  • [4] Rémi Delaporte-Mathurin, Etienne Hodille, Jonathan Mougenot, Gregory De Temmerman, Yann Charles, Christian Grisolia. Parametric study of hydrogenic inventory in the ITER divertor based on machine learning, Scientific Reports 10, 2020. [DOI: 10.1038/s41598-020-74844-w]