Monte-Carlo Neutronics Methods
Monte-Carlo neutron transport follows individual particle histories through complex geometry to compute flux, heating, activation, and tritium breeding.
The Monte-Carlo idea
Neutrons born in fusion reactions travel through the machine, scattering, being absorbed, and inducing reactions. Rather than solve the transport equation directly, Monte-Carlo methods simulate a large number of individual neutron histories using random sampling of the physical probabilities, then average over histories to estimate quantities of interest with statistical error bars.
A neutron history
Each history starts at a source point with a sampled energy and direction. The code samples the distance to the next collision from the local cross-sections, moves the neutron there, samples which nuclide and reaction occurs, and updates energy and direction accordingly. Secondary particles are tracked too. The history ends when the neutron is absorbed or leaves the system.
What it computes
- Neutron and gamma flux and spectra throughout the machine
- Nuclear heating in components
- Tritium breeding rate in a breeding blanket
- Material damage indicators and activation source terms
- Shielding effectiveness and dose outside the machine
Strengths and costs
Monte-Carlo handles arbitrarily complex three-dimensional geometry and continuous-energy physics with high fidelity, which is why it is the reference method for fusion neutronics. Its cost is statistical: results in a small or well-shielded region can have large variance, requiring variance-reduction techniques to converge.
Variance reduction
Techniques such as importance weighting, weight windows, and biased sampling steer computational effort toward the regions and reactions that matter, dramatically improving the statistics of deep-penetration and rare-event tallies without biasing the answer.
For a D-T device like the Hyperion breeder, Monte-Carlo neutronics is the tool for evaluating tritium breeding and shielding, both first-order to a breeding design.