Nuclear Engineering

The nuclear engineering subpackage provides models for tritium breeding blanket neutronics, plasma-wall interaction, erosion physics, and thermoelectric MHD effects in liquid metal divertors.

Blanket Neutronics

The blanket_neutronics module (blanket_neutronics.py) computes the tritium breeding ratio (TBR) using a 1D slab transport model with realistic albedo and neutron multiplication.

The tritium breeding ratio is defined as:

(1)\[\text{TBR} = \frac{\text{tritium atoms produced per unit time}} {\text{tritium atoms consumed per unit time}}\]

For a self-sustaining fusion reactor, \(\text{TBR} > 1.0\) is required (with margin \(\text{TBR} \geq 1.05\) to account for losses in the tritium fuel cycle).

The neutron source from D-T fusion at 14.1 MeV is:

\[S_n = \frac{1}{4} n_D n_T \langle\sigma v\rangle_{\text{DT}}\]

The module evaluates breeding performance for different blanket concepts:

  • Lithium-lead (\(\text{Pb-Li}\) eutectic) blankets

  • Ceramic breeder (\(\text{Li}_4\text{SiO}_4\), \(\text{Li}_2\text{TiO}_3\)) blankets

  • Lithium (pure liquid Li) blankets

The BreedingBlanket class computes the VolumetricBlanketReport containing TBR, neutron multiplication factor, and energy deposition profiles.

Plasma-Wall Interaction

The nuclear_wall_interaction module (nuclear_wall_interaction.py) provides the NuclearEngineeringLab class for simulating first-wall damage from the fusion neutron spectrum:

  • Displacement damage (dpa) from 14.1 MeV neutrons

  • Helium production (appm He) via \((n,\alpha)\) transmutation

  • Hydrogen production via \((n,p)\) reactions

  • Activation products and decay heat

The neutron wall loading is:

\[\Gamma_n = \frac{P_\text{fus} \times 0.8}{4\pi R \times 2\pi a \kappa}\]

where the factor 0.8 reflects the 14.1 MeV neutron fraction of the 17.6 MeV total D-T fusion energy.

PWI Erosion Model

The pwi_erosion module (pwi_erosion.py) implements the SputteringPhysics class for plasma-facing component erosion:

  • Physical sputtering yield \(Y(E, \theta)\) as a function of ion energy \(E\) and incidence angle \(\theta\)

  • Chemical sputtering for carbon-based materials

  • Self-sputtering cascade effects

  • Erosion rate computation for tungsten, carbon, and beryllium PFCs

  • Angle-energy invariant testing for physical consistency

The sputtering yield follows the Yamamura-Tawara parametrisation:

\[Y(E) = Q \cdot s_n(E) \cdot \left[1 - \left(\frac{E_\text{th}}{E}\right)^{2/3}\right] \cdot \left(1 - \frac{E_\text{th}}{E}\right)^2\]

where \(Q\) is a fitting parameter, \(s_n(E)\) is the nuclear stopping cross-section, and \(E_\text{th}\) is the sputtering threshold energy.

Divertor Thermal Simulation

The divertor_thermal_sim module models the heat flux profile on the divertor target plates using the Eich model (Eich et al., Nuclear Fusion 53, 2013):

\[q(s) = \frac{q_0}{2} \exp\!\left(\frac{S^2}{4\lambda_q^2 f_x^2}\right) \cdot \text{erfc}\!\left(\frac{S}{2\lambda_q f_x} - \frac{s - s_0}{\lambda_q}\right)\]

where \(\lambda_q\) is the SOL power width, \(f_x\) is the flux expansion factor, \(S\) is the divertor broadening parameter, and \(s\) is the coordinate along the divertor target.

TEMHD Peltier Effects

The temhd_peltier module (temhd_peltier.py) implements the TEMHD_Stabilizer for thermoelectric magnetohydrodynamic effects in liquid metal divertors.

In a liquid metal flowing perpendicular to a strong magnetic field, thermoelectric currents driven by temperature gradients generate \(\mathbf{J} \times \mathbf{B}\) forces that can either stabilise or destabilise the flow. The TEMHD effect is characterised by the thermoelectric figure of merit:

\[ZT = \frac{S^2 \sigma T}{\kappa}\]

where \(S\) is the Seebeck coefficient, \(\sigma\) is the electrical conductivity, \(T\) is the temperature, and \(\kappa\) is the thermal conductivity.

For the MVR-0.96 compact reactor design, the TEMHD liquid metal divertor is essential for handling heat loads exceeding 90 MW/m^2.