● Domain 03 · Nuclear Energy & Engineering
The balance must close.
Reactor analysis is not judged on average accuracy. It is judged on whether the neutron balance closes.
Menger spongeSelf-similar at every scale, the way a core is: pin inside assembly inside core. Zero volume, infinite surface area.Menger sponge · Menger (1926)
Averaged accuracy is not the currency
A surrogate can reproduce flux shapes to three figures and still miss the balance. That answer cannot enter a safety case, because it fails the first question that case asks: does production equal absorption plus leakage?
What changes
When conservation is structural the balance closes at floating point for every state the model can represent. The surrogate is then argued about on its physics rather than defended on its statistics.
Demonstration
A lattice, solved live.
Surrogate flux
A fast model's answer, two per cent out, with k fitted beside the flux rather than taken from it. The residual is the part that does not look like the solution.
Solved flux
One group diffusion under power iteration, with k taken from the balance of the field it solved for, which is what k means. The residual then closes.
Every cell of the cube, its brightness the flux it holds.
Five control rods, driven into the lattice and drawn back out. Both columns see the same rods at the same depth.
Cells where the balance does not close, stained. On the left there are many, on the right none.
The vessel, with vacuum at every face.
Conservation is structural in the solved lattice, so the neutron balance closes at floating point. What is measured is the residual of production against absorption plus leakage, taken cell by cell as the rods carry k from 1.038 through critical to 0.952. The solved lattice closes it to fifteen decimal places at every rod depth in the run; the surrogate stops at two per cent, the size of its own flux error, and stays there however long it iterates. The discretisation agrees with the analytic buckling for a bare cube, νΣf = 29.72.
Sources
Ω·∇ψ + Σtψ = ∫ Σsψ dΩ′ + S
The neutron transport equation · Duderstadt & Hamilton, Nuclear Reactor Analysis (1976)
k = production / (absorption + leakage)
The multiplication factor · Lamarsh & Baratta, Introduction to Nuclear Engineering (2001)
Is this your problem?
Tell us what has to hold, and what happens if it does not.
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