Analytical model of hydrogen inventory saturation in the subsurface of the wall material and comparison to Reaction-Diffusion simulations

We herein introduce an analytical model of hydrogen inventory saturation in the subsurface of materials (several micrometers depth) under plasma implantation. This model is valid for materials for which the desorption process is not limited by hydrogen recombination at the surface. It is based on a simplified assumption for the implantation of both hydrogen ions and atoms (point sources) and on a stationary approach. The model provides an approximation of the density profile of mobile/interstitial hydrogen and of the density profile of hydrogen trapped at materials defects in the subsurface layer. The analytical model shows good agreement with Reaction-Diffusion simulations of deuterium implantation in tungsten at different material temperatures. For the fusion relevant materials tungsten and beryllium, it is shown that most of the inventory is found in traps. The model gives the filling ratio of traps in the subsurface at steady-state fstat,iBULK. This simple parameter indicates how the total subsurface inventory builds up during plasma exposure and provides a simple way to understand the retention dynamics observed during non-linear Reaction-Diffusion simulations.