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Sensitivity and uncertainty · TSUNAMI and Serpent · computed in your browser
Load TSUNAMI sensitivity data files or Serpent sensitivity output and this page computes the nuclear-data uncertainty of k by the sandwich rule, the nuclides and reactions it comes from, and the similarity index ck between the files, with this site's ENDF/B-VIII.1 covariances in SCALE's 56 groups (AMPX and NJOY routes), an ENDF/B-VII.1 library, or a COVERX file of your own. It does the first-order calculations of the NEA's NDaST in a web page.
Your files stay on your computer. The page reads them in your browser and never uploads them; it only downloads, from this site, the covariance data of the nuclides it needs, and your browser blocks it from contacting any other server. How your files stay private: technical details.
Most of this work, including this page, was generated with AI (Claude, Anthropic) under the direction of Ian H; it has not been independently reviewed. Its arithmetic (su-core.js) was compared with the ICSBEP uncertainty paper: for 120 sampled configurations it gives the paper's uncertainties with all three libraries to within 0.00002 percentage points. Its Serpent reader was compared with SAUNA's on SAUNA's example files (see the notes).
_sens0.m), any group structure; plain text or .gz
Drop sensitivity files here or
Read on your computer; nothing is uploaded (how).
The nuclides are those of the loaded files. Covariances between two nuclides that use different libraries are left out.
Load sensitivity files and press Calculate.
Uncertainty. The relative variance of k is the first-order sandwich rule, (Δk/k)2 = S C ST, with S the sensitivities in the covariance library's groups and C the relative covariance matrix, as in SCALE's TSUNAMI-IP and the NEA's NDaST. Each nuclide–reaction pair is reported once, as the signed square root of its variance term in % Δk/k (a pair of two different reactions counts both orderings) and as its share of the variance; negative terms reduce the variance. The by-nuclide table adds the terms within each nuclide, and lists terms between two nuclides as pairs. The statistical uncertainties of the sensitivities are not propagated.
Groups. Only the region-integrated profiles of a file are used. They are collapsed to the library's groups; a bin of the file that straddles a library boundary is split in proportion to lethargy (the same rule spreads a bin over finer library groups). Profiles that map to the same nuclide and reaction are added.
Serpent files. The page reads the k-eff sensitivities (ADJ_PERT_KEFF_SENS, all latent generations) of Serpent 2's _sens0.m output for the material “total” (the sum over the listed materials if there is none), following the Serpent reader of SAUNA. With sens pert xs allmt each reaction comes with its MT number; the parts of a sum that the file also lists are left out (the inelastic levels MT 51–91, whose sum MT 4 is listed, and likewise first- to fourth-chance fission, MT 19–21 and 38, and the level-resolved (n,2n), (n,p), (n,d), (n,t), (n,³He) and (n,α) reactions), and thermal scattering (MT 1002 and 1004) is added to elastic scattering, as TSUNAMI reports it for bound scatterers. With sens pert xs all (summed reaction modes), elastic and S(α,β) scattering become MT 2, inelastic MT 4, n,xn MT 16, fission MT 18, and capture, which is all absorption except fission, MT 102 (n,γ); that is wrong for nuclides whose absorption is mostly (n,p), (n,t) or (n,α), such as He-3, Li-6, B-10 and N-14, which the file list then names: use allmt for them. Total ν̄ is MT 452 and total χ MT 1018 (Serpent's χ sensitivities are already constrained to sum to zero); the total cross section, prompt and delayed ν̄ and χ, and scattering moments are left out. A ZAI (10000 Z + 10 A + I) becomes the SCALE ID 1000 Z + A, plus 1000000 for a metastable state. The file holds no k. On SAUNA's example files (MET1000_FC, 56 groups) with the same ENDF/B-VII.1 covariances, the page gives SAUNA's uncertainty over the same reactions to 0.00001 percentage points; its total, 1.100 % Δk/k against SAUNA's 1.097 %, differs because the page leaves out MT 251 and the prompt and delayed ν̄ and χ terms, and uses prompt-ν̄ covariances for total ν̄ where a nuclide has no other (next paragraph). SCALE's own SDF of the same model gives 1.133 % with the page and 1.129 % with SAUNA, from the ν̄ rule alone.
Reactions. MT 1 (total), 3 (non-elastic), 101 (capture sum), 455 (delayed ν̄) and 456 (prompt ν̄) are left out, as in SCALE's own sandwich calculations, since they duplicate other reactions. Where a nuclide has a covariance for prompt ν̄ (456) but none for total ν̄ (452), the 456 data stand for 452. A covariance between two reactions counts once, whichever way round the library stores it.
Threshold artefacts. In a few groups that straddle a reaction threshold, the processed libraries give relative standard deviations of 102 to 108 (10,000 % and more), relative to a group cross section that is nearly zero. They multiply whatever sensitivity a file has there, so numerical noise of 10−10 in a Monte Carlo profile can add several % Δk/k. With the option on (the default), the rows and columns of every such group (relative standard deviation above 100) are set to zero; the results list the groups. The rule is the one described in the CANDU-6 paper (Section 2.3).
Nuclide IDs. The SCALE IDs of bound scatterers (e.g. 1901 or 1001001 for hydrogen) take the covariances of their nuclide, as do other 7-digit IDs from 2000000 up, read as forms of the nuclide in their last six digits; bound carbon (6312, 3006000, graphite) is natural carbon. Elements and isotopes follow an option of the NEA's NDaST, with the abundance threshold you set in the covariance panel (default 90 %): an element the library has no covariance for takes the covariance of its most abundant isotope when that isotope's abundance reaches the threshold (natural carbon takes C-12, 98.9 %, and vanadium V-51, 99.75 %, in the ENDF/B-VIII.1 libraries), and an isotope the library has no covariance for, of an element it has, is added to the elemental sensitivity (sensitivities add linearly), so that ENDF/B-VII.1 and SCALE's library use their natural-carbon covariances. IDs that cannot be placed are listed with their largest |sum of profile|.
Mixed libraries. When some nuclides use another library, the variance is the sum over the libraries of each library's sandwich over the nuclides assigned to it. A covariance between two nuclides assigned to different libraries, such as U-235 fission × U-238 capture in the ENDF/B-VIII.1 libraries, is dropped.
Similarity. ck = Sa C SbT / (σa σb) is the correlation between the nuclear-data errors of k of two systems (B.L. Broadhead et al., “Sensitivity- and Uncertainty-Based Criticality Safety Validation Techniques”, Nucl. Sci. Eng. 146 (2004) 340–366); ck ≥ 0.9 is the usual threshold for a benchmark to count as similar to an application. It is shown as a matrix for up to 40 files, and against one chosen file for any number.
Covariance data. The ENDF/B-VIII.1 libraries are release v1.2 of this site's 56-group libraries, processed by the AMPX and NJOY routes; every matrix can be seen in the covariance explorer. NJOY's ERRORR mis-processes the R-matrix (LRF=7) resonance-parameter covariances of Cl-35, Ca-40, Cu-63, Cu-65, Rh-103 and W-182, -183, -184 and -186 (paper, section 4.3); use the AMPX route for files that contain them. The ENDF/B-VII.1 library is the 56-group library of SAUNA (A. Ryzhkov, MIT licence, licence text), converted to the same format. A COVERX file you load is read in your browser and stays there.
Related pages. The same arithmetic produced the uncertainties of 2,843 ICSBEP configurations and the CANDU-6 similarity study, which gives 0.81 % Δk/k for the cooled cell with the AMPX route; the covariance paper describes the libraries.