# Tritium Diffusion¶

## Overview¶

We use 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.

## 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¶

## Description¶

Achlys models macroscopic tritium transport processes through fusion reactor materials as described in the Achlys documentation and in Delaporte-Mathurin et al (2019).

Particularly, we solve the following equations:

```
\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)
```

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) for more details.

The setup used in this particular benchmark models the experimental work of Ogorodnikova et al. (2003)

## References¶

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*, Nuclear Materials and Energy, Volume 21, 2019E.A. Hodille, X. Bonnin, R. Bisson, T. Angot, C.S. Becquart, J.M. Layet, C. Grisolia,

*Macroscopic rate equation modeling of trapping/detrapping of hydrogen isotopes in tungsten materials*, Journal of Nuclear Materials, Volume 467, Part 1, 2015O.V Ogorodnikova, J Roth, M Mayer,

*Deuterium retention in tungsten in dependence of the surface conditions*, Journal of Nuclear Materials, Volumes 313–316, 2003