22.016
9-18-2025
Remi Delaporte-Mathurin
Joint European Torus (JET), Culham, UK
LIBRA tritium breeding experiment
Tritium contamination in a heat exchanger with FESTIM
Hydrogen gas-driven permeation experiment
ITER
Plasma: mixture of Hydrogen (D-T) and Helium
Particle bombardment
Divertor
Why should we care?
T is rare
T is expensive
€£$
Material embrittlement
T is radioactive
☢
+
+
+
Protium
Deuterium
Tritium
Molar mass: 6.032 g/mol
+
Tritium
☢
Half-life: 12 years
☢
Consumption of a 1 GWth fusion reactor (1 year)
50 kg
Cost: $30,000 per gram
→ Li6 enrichment is an option
DT fusion neutrons
Magnet
Breeding blanket
Plasma
Burns tritium
Breeds tritium (TBR)
Tritium Extraction System
Breeding Blanket
Plasma
Storage
neutrons
TBR
(constrained by technology)
Doubling time
(driven by economics)
Startup inventory
(constrained by safety)
Startup inventory
Tritium Extraction System
Breeding Blanket
Plasma
Storage
☢
Augustin Janssens. ‘Emerging Issues on Tritium and Low Energy Beta Emitters”’. en. In: (Nov. 2007), p. 100
Country | Water limit (Bq/L) |
---|---|
EU | 100 |
USA | 740 |
UK | 100 |
Canada | 7,000 |
Finland | 30,000 |
Australia | 76,103 |
Russia | 7,700 |
WHO | 10,000 |
413 pages!
1. Keep inventory at a minimum
Tritium limit in the ITER vacuum vessel: 1 kg
1. Keep inventory at a minimum
2. Reduce inventory
Heating components help releasing their tritium content (cf. Basics of H transport)
1. Keep inventory at a minimum
2. Reduce inventory
3. Avoid contamination of coolants
Metal
Tritiated environment
"Clean" environment
Permeation
1. Keep inventory at a minimum
2. Reduce inventory
3. Avoid contamination of coolants
Metal
Tritiated environment
"Clean" environment
Permeation barrier
Permeation
1. Keep inventory at a minimum
2. Reduce inventory
3. Avoid contamination of coolants
Ceramics are promising candidates:
Permeation barriers are caracterised by their PRF (Permeation Reduction Factor)
Target for breeding blankets PRF ≈ 100-1000
Luo et al Surface and Coatings Technology 2020
Kuznetsov, Alexey S. et al. “Hydrogen-induced blistering of Mo/Si multilayers: Uptake and distribution.” Thin Solid Films 545 (2013): 571-579.
Review of HIC by Sofronis
https://doi.org/10.1016/j.jngse.2022.104547
H transport
Safety
Fusion Economy
Materials
DFT
Y. Ferro et al 2023 Nucl. Fusion 63 036017
Length scale
Time scale
MD
Length scale
Time scale
DFT
potentials
Component scale modelling
Length scale
Time scale
MD
DFT
D, S, other coeffs.
Length scale
Time scale
MD
DFT
Component scale modelling
Fuel cycle modelling
Residency times, fluxes, ...
Length scale
Time scale
MD
DFT
Component scale modelling
Fuel cycle modelling
Abstraction
Even more particles
continuity approximation
Single particle
Random walk
Many particles
\( \varphi \): diffusion flux
\( D \): diffusion coefficient
\( c \): mobile hydrogen concentration
Fick's 1st law of diffusion
\( \varphi\): diffusion flux
\( D \): diffusion coefficient
\( c \): mobile hydrogen concentration
\( S\): source term
Fick's 1st law of diffusion
Fick's 2nd law of diffusion
\( \varphi\): diffusion flux
\( D \): diffusion coefficient
\( c \): mobile hydrogen concentration
\( S\): source term
Soret effect (or thermophoresis)
Stress assisted diffusion
Ziegler et al. 2010. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 268 (11): 1818–23. https://doi.org/10.1016/j.nimb.2010.02.091.
Implantation range
Implantation range & width and reflection coefficient can be computed with SRIM, SDTRIM...
Mutzke et al, SDTrimSP Version 6.00 2019
\(\Gamma_\mathrm{incident} \): incident flux (particle/m2/s)
\( f(x) \): Gaussian distribution (/m)
\(r \): reflection coefficient
H2 molecules
Metal lattice
Dissociation coefficient (H/m2/s/Pa)
Partial pressure of H (Pa)
Adsorbed H
Metal lattice
Metal lattice
Recombination coefficient (m4/s)
Concentration (H/m3)
Metal lattice
Waelbroeck model
Metal lattice
At equilibrium:
Sievert's law of solubility
Non-metallic liquid
At equilibrium:
Henry's law of solubility
Material 1
Material 2
Partial pressure and flux are continuous
Material 1
Material 2
Material 1
Material 2
Case 1:
Metal-Metal
Sievert's law
Material 1
Material 2
Case 2:
Non metal-non metal
Henry's law
Material 1
Material 2
Case 3:
Metal-Non metal
Sievert's law
Henry's law
Material 1
Material 2
Steady state concentration profile
\(x\)
\(c\)
⚠️Very little experimental validation data for interfaces
Metal
Tritiated environment
"Clean" environment
Permeation
Permeation barrier
Pressure \(P\)
High gradient = high flux
Low gradient = low flux
Pressure \(P\)
H
Trap = anything binding to H
H
Potential energy
Distance
Diffusion barrier
Energy barrier = activation energy
Trap binding energy
Trapping energy
Common assumption:
\( E_k = E_D \)
0D
Since \(n_\mathrm{trap} = n_\mathrm{free \ trap} + c_\mathrm{t} \)
0D
Total concentration of traps
0D
With diffusion
and
1 trap
N traps
McNabb & Foster model
Other models assume traps can hold more than one H
Recombination
Dissociation
Absorption
Trapping
Detrapping
Diffusion
Pre-exponential factor
Activation energy (eV/H)
Temperature (K)
Boltzmann constant (eV/H/K)
Pre-exponential factor
Activation energy (J/mol)
Temperature (K)
Gas constant (J/mol/K)
Conversion:
\( 1/T \) (1/K)
Intercept
+ Slope
Y =
X
Arrhenius parameters: