Tritium Desorption

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.

Authors

• Mikkel Lykkegaard

• Anne Reinarz

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.

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:

\[\begin{split} \begin{align} \frac{\partial C_{m}}{\partial t} &= \nabla \cdot \left( D \left(T \right) \nabla C_{m} \right) - \sum \frac{\partial C_{t,i}}{\partial t} + S_{ext} \\ \frac{\partial C_{t,i}}{\partial t} &= \nu_m \left(T\right) C_m \left(n_i - C_{t,i} \right) - \nu_i\left(T\right) C_{t,i} \\ \rho_m C_p \frac{\partial T}{\partial t} &= \nabla \cdot \left(k \nabla T \right) \end{align} \end{split}\]

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).