# Tritium Desorption ## Overview We use [Achlys](https://github.com/aurora-multiphysics/achlys) to model the macroscopic transport of tritium through fusion reactor materials using the Foster-McNabb equations. Achlys is built on top of the [MOOSE Finite Element Framework](https://mooseframework.inl.gov/). ## Authors - [Mikkel Lykkegaard](mailto:mikkel@digilab.co.uk) - [Anne Reinarz](mailto:anne.k.reinarz@durham.ac.uk) ## Run ``` docker run -it -p 4242:4242 linusseelinger/model-achlys:latest ``` ## Properties Model | Description ---|--- forward | Achlys Tritium Diffusion ### forward Mapping | Dimensions | Description ---|---|--- input | [5] | E1, E2, E3: The detrapping energy of the traps. n1, n2: The density of the intrinsic traps. output | [500] | Flux of tritium across the boundary as a function of time in atomic fraction. Feature | Supported ---|--- Evaluate | True Gradient | False ApplyJacobian | False ApplyHessian | False Config | Type | Default | Description ---|---|---|--- None | | | ## Mount directories Mount directory | Purpose ---|--- None | ## Source code [Model sources here.](https://github.com/UM-Bridge/benchmarks/tree/main/models/achlys) ## Description Achlys models macroscopic tritium transport processes through fusion reactor materials as described in the [Achlys documentation](https://aurora-multiphysics.github.io/achlys/module/introduction.html) and in [Delaporte-Mathurin et al. (2019)](https://doi.org/10.1016/j.nme.2019.100709). Particularly, we solve the following equations: $$ \begin{align} \frac{\partial C_{m}}{\partial t} &= \nabla \cdot \left( D \left(T \right) \nabla C_{m} \right) - \sum \frac{\partial C_{t,i}}{\partial t} + S_{ext} \\ \frac{\partial C_{t,i}}{\partial t} &= \nu_m \left(T\right) C_m \left(n_i - C_{t,i} \right) - \nu_i\left(T\right) C_{t,i} \\ \rho_m C_p \frac{\partial T}{\partial t} &= \nabla \cdot \left(k \nabla T \right) \end{align} $$ where $C_m$ is the concentration of mobile particles, $C_{t,i}$ is the concentration of particles at the $i$th trap type and $T$ is the temperature. Additionally, the evolution of the extrinsic trap density $n_3$ is modelled as $$ \frac{dn_{3}}{dt} = (1 - r) \phi \left[ \left(1-\frac{n_3}{n_{3a,max}}\right)\eta_a f(x) + \left(1-\frac{n_3}{n_{3b,max}}\right)\eta_b\theta(x) \right] $$ This takes into account additional trapping sites that are created as the material is damaged during implantation. Please see [Hodille et al. (2015)](https://doi.org/10.1016/j.jnucmat.2015.06.041) for more details. The setup used in this particular benchmark models the experimental work of [Ogorodnikova et al. (2003)](https://doi.org/10.1016/S0022-3115(02)01375-2).