Theory
Physics, mathematics, and algorithms behind Nucleide's core capabilities.
These pages explain the physics, mathematics, and algorithms that Nucleide implements. They are written for analysts and contributors who want to understand why the code behaves the way it does, not just how to call it.
When to read each page
| Page | Read if you are… |
|---|---|
| Depletion | Solving burnup chains and want to understand the Bateman equation, transmutation matrices, and CRAM. |
| Enrichment cascades | Configuring multicomponent enrichment cascades and need the MARC/SWU derivation. |
| Variance reduction | Generating MAGIC weight windows or sampling mesh-based sources. |
| Nuclear data | Looking up nuclide IDs, masses, half-lives, or converting between code-name dialects. |
| Point kinetics | Running prescribed-reactivity transients and want the PKE system, the inhour relation, and the prompt-jump approximation. |
| Tritium transport | Running 1D diffusion-trapping permeation and want the McNabb–Foster system, the surface taxonomy, and the closed-form permeation checks. |
| Gamma-ray spectroscopy | Smoothing spectra, counting peaks, calibrating energy/efficiency, X-ray lines, SDEF decay-source cards, and the SPE readers. |
| UQ-lite sampling | Seeded MVN, log-normal, and LHS sampling over caller-supplied covariance blocks, SANDY-compatible estimators, and the decay and fission-yield perturbation consumers. |
| Damage metrics | Folding multigroup fluxes into NRT-dpa and arc-dpa, gas production, and He/dpa ratios, with uncertainty propagation through the fold and coil lifetime bookkeeping. |
| Fusion neutron sources | Building D-D/D-T ring, point, lattice, and parametric tokamak sources — including fuel mixtures, the hot-tail shape, and ECRH accessibility — and want the Ballabio spectra, Bosch–Hale reactivity, and the Miller-geometry map. |
| Neutron spectrum unfolding | Recovering a spectrum from activation detector measurements with SAND-II, least-squares, or GRAVEL adjustment, including the IRDFF response pack. |
| Clearance screening | Classifying activation inventories against the EU or Spanish clearance-limit tables, plus the S1+S2 activity and decay-heat totals. |
| TBR and blanket bookkeeping | Raw TBR from caller tallies, port-penalty haircuts, energy multiplication, burn rate, and breeding margins. |
| Equilibrium data readers | Classic-netCDF wout reading, the INDATA grammar, flux-surface Jacobians, and wall-load mapping. |
Relationship to tutorials
The theory pages are companions to the tutorials. A tutorial shows you how to run a calculation; the matching theory page explains the equations and assumptions behind it.
Structure of a theory page
Each page follows the same pattern:
- Overview — what problem the method solves.
- Mathematical details — the governing equations and symbols.
- Algorithm — how Nucleide turns the math into code.
- Worked example — a small hand-verified calculation.
- Assumptions and limitations — explicit list of what is and is not handled.
- Related work beyond Nucleide — adjacent methods in PyNE, OpenMC, and the literature that Nucleide does not (yet) implement.
- References — sources are cited inline at the claims they back, with the full bibliography at the end of the page.