Upstream example

Tritium breeding ratio of a lithium-lead spherical blanket with a 14 MeV point source.

How much tritium does a simple spherical lithium-lead breeder blanket produce per 14 MeV source neutron, and which lithium isotope produces most of it?

Morton reproducedOpenMCChecked 2026-10-10
Scope

A single-code fixed-source Monte Carlo case: three nested spheres (an empty inner region, a 10 cm steel first wall and a 100 cm lithium-lead breeder shell) with an isotropic 14 MeV point source at the centre and a cell tally of tritium production split by Li-6 and Li-7. It is the standard first fusion-neutronics exercise and a sanity reference, not a design geometry or a validation of any device.

Relationship to fusion

A magnetic-confinement-style breeding blanket in a spherical surrogate geometry with a DT-like source. Directly relevant to any DT blanket as a first check; not a validation of any device, and not an inertial-fusion chamber geometry.

Evidence status: Morton reproduced

A specific pinned example was run by Morton Labs with retained evidence.

Run date
2026-10-10
Environment
Docker Desktop 29.3.1 on an Apple Silicon workstation, linux/amd64 image under emulation · Official image openmc/openmc, manifest digest sha256:efe6796f94fd0c0341f8a419603f97d7d66bc8a02acdfb4bd14c589d2d51ca7b (the 'latest' tag as pushed 2025-11-22, reporting version 0.15.3) · Python 3.12.3 inside the image; 8 OpenMP threads
Versions
OpenMC 0.15.3 (sha256:efe6796f94fd…)
Nuclear data
NNDC ENDF/B-VII.1 HDF5 (bundled in the image at /root/nndc_hdf5/cross_sections.xml) · The upstream documented value used ENDF/B-VIII.0; no checksum is published for either archive, so the image digest is the pin.
Settings
run_mode fixed source · 20,000 particles × 50 batches = 1,000,000 histories (run B); 500 × 10 = 5,000 histories (run A, the upstream settings) · seed 1 · cell tally on the breeder scoring H3-production for Li6 and Li7 · model restated in Morton Labs' own script run_tbr.py (catalog/cases/openmc-pbli-sphere-tbr)
Runtime
16.845 s
docker run --rm --platform linux/amd64 -e OMP_NUM_THREADS=8 -v $PWD/run_tbr.py:/work/run_tbr.py:ro -v $PWD/evidence/run-b-high-statistics:/work/evidence -w /work openmc/openmc@sha256:efe6796f94fd0c0341f8a419603f97d7d66bc8a02acdfb4bd14c589d2d51ca7b bash -lc 'python3 run_tbr.py --out /work/evidence --particles 20000 --batches 50 --seed 1'

Outputs

TBR, run B (1,000,000 histories)
1.0188 ± 0.0011 (1σ, quadrature)
Li-6 contribution, run B
1.0150 ± 0.0011
Li-7 contribution, run B
0.00372 ± 0.00001
TBR, run A (5,000 histories, upstream settings)
1.0214 ± 0.0183 (1σ, quadrature)
Run A wall time (model.run)
1.4 s
Retained artifacts
statepoint.*.h5, summary.h5, tallies.out, model.xml, stdout.log, result.json for both runs

Comparison

The upstream workshop page documents TBR 1.0266 with a summed standard deviation of 0.0182 (5,000 histories, ENDF/B-VIII.0, a development build of OpenMC 0.15.3). Run A, at the same statistics, gives 1.0214 ± 0.0183; the difference of 0.005 is 0.2 combined standard deviations. Run B tightens the pinned value to 1.0188 ± 0.0011; its 0.008 difference from the upstream figure is 0.4 of the upstream uncertainty, so the two are statistically consistent. Any residual effect of the data library (ENDF/B-VII.1 here versus VIII.0 upstream) is below what the upstream's 5,000-history precision can resolve. Acceptance rule applied: agreement within two combined standard deviations for a stochastic quantity; met.

Limitations of this run

A smoke-level reproduction of a teaching surrogate, not validation: the spherical geometry, a single 14 MeV line and neutron-only transport are the model's simplifications, not a device. The library differs from the upstream run (VII.1 versus VIII.0), the upstream number came from an unreleased build, and no experimental benchmark is involved. Run B's 0.1 % statistical precision says nothing about systematic nuclear-data uncertainty.

Inputs
  1. Breeder: Pb 84.2 / Li 15.8 atom %, Li-6 enriched to 50 atom %, 3.272e-2 atom/b-cm
  2. First wall: Fe 95 / C 5 weight %, 7.75 g/cm3
  3. Spheres at r = 500 cm (vessel), 510 cm (first wall) and 610 cm (vacuum boundary)
  4. Isotropic point source at the origin, single 14 MeV energy line
  5. Fixed-source mode, 10 batches of 500 particles (5,000 histories)
  6. Cell tally on the breeder scoring tritium production by nuclide (Li6, Li7)
Outputs
  • Tritium breeding ratio (sum of the Li-6 and Li-7 tritium-production means) with its statistical uncertainty
  • Per-isotope contributions to tritium production
  • Documented reference from the workshop's rendered page: TBR 1.027 with a summed standard deviation of 0.018, run with a development OpenMC build and ENDF/B-VIII.0
Assumptions and limits
  • Spherical teaching surrogate, not a tokamak or inertial-fusion chamber shape
  • Single 14 MeV line rather than the 14.1 MeV DT line or a plasma-shaped spectrum
  • Neutrons only: no photons, heating, activation or depletion
  • 5,000 histories give roughly 2% statistical uncertainty on TBR; the notebook adds the two isotope uncertainties arithmetically, which overstates the combined value
  • A different nuclear data library gives a slightly different TBR; the workshop documents no pass/fail tolerance
Dependencies
OpenMC
v0.16.0 · Official release image openmc/openmc:v0.16.0 on Docker Hub (digest sha256:f714ba42bcc2209f9865b360616b6d439c16e854cd63ebbb58310ed17b181cfe); the image ships the NNDC ENDF/B-VII.1 HDF5 library with OPENMC_CROSS_SECTIONS preset. hub.docker.com ↗
Nuclear data
ENDF/B-VIII.0 (documented run) or ENDF/B-VII.1 (shipped in the image) · The workshop's documented number used the official ENDF/B-VIII.0 OpenMC HDF5 library (about 3.4 GB compressed) from openmc.org/data; no checksums are published there. openmc.org ↗
Python packages
pandas, matplotlib · Used for the tally dataframe and the geometry plot.

This case was written by Morton Labs from public sources and last checked on 2026-10-10. Spotted an error, or want something changed or removed? Email zach@mortonlabs.ai with the page address.

Sources checked for this page (5)