Dancoff-Based Wigner-Seitz Approximation for the Embedded Self-Shielding Method in SCALE/Polaris
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Engineering topics
Publications and source records attributed to Holcomb, Andrew.
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This is a collection of public data produced by AMPX or curated from quality sources that the SCALE code system relies on for user problem input.
This report constitutes the requirement document that guides the development of the experimental reaction database, MEDUSAL (Machine-readable Experimental Data User App & Library), created by OECD/NEA/WPEC SubGroup 50. Experimental reaction data are usually stored in the EXFOR library in EXFOR format. With MEDUSAL, the WPEC sub-group 50 wants to go beyond the EXFOR format and database to generate a library that is (a) automatically readable, (b) comprehensive, and (c) curated.
R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.
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Conventional nuclear data evaluation methods using generalized linear least squares make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate to minimize the cost function (even for nonlinear models); the model (e.g., of neutron cross section) and experimental data (including covariance data) are without defect and prior PDFs of parameters and measured data are known perfectly. Neglect of covariance between model parameters and measured data in conventional evaluations contributes to imperfections. These assumptions are inherent to the generalized linear least squares minimization method commonly used for resolved resonance region neutron cross section evaluations but are often not justified due to the presence of non-normal PDFs, nonlinear models (e.g., R-matrix formalism), and inherent imperfections in data and models (e.g., imperfect covariance data). Here, these assumptions are removed in a mathematical framework of Bayes’ theorem, which is implemented using the Metropolis-Hastings Monte Carlo method. Most importantly, new parameters are introduced to parameterize discrepancies between the theoretical model and measured data to quantify judgement about discrepancies or imperfections in a reproducible manner. An evaluation of 233U in the eV region using the ENDF-B/VIII.0 library and transmission data (Guber et al.) is presented, and posterior parameters are compared to those obtained by conventional evaluation methods. This example illustrates the effects of removing the most harmful assumption: that of model-data perfection.
This presentation is on Bayesian evaluation framework for imperfect differential and integral data or models. This presentation includes a particular focus on common assumptions used in Bayesian ND evaluations. Additionally, this presentation highlights the benefits of a generalized form of the Bayes' theorem.
This presentation covers recent AMPX developments. Presentation highlights include the news of AMPX being openly available, link to source and configure options are included. The interconnections between AMPX and Generalized Nuclear Database Structure (GNDS) are additionally highlighted as well.
The presented R-matrix formalism could improve evaluations of resolved resonance nuclear cross section data by parameterizing direct reaction processes via an orthonormal channel mixing matrix and doorway state processes. Together, they can parameterize direct-semidirect capture. A formal similarity among the R-, K-, T- matrix formalisms was leveraged to parameterize direct and doorway processes. The advantage of this R-matrix parameterization is that it is easily extensible due to its application of projection operators directly upon the (H-E) on p. 6.
This presentation provides overviews of ENDF and GNDS reading in AMPX, AMPX covariance processing updates, thermal scattering law updates, and data libraries for SCALE 6.3.0.
Sufficient AGN-201M fuel plate material exists at Y-12 to support the development of a new, inherently safe, subcritical assembly for use in NCS training courses at ORNL. Four experiments with the ORNL subcritical assembly are possible and feasible. Future work includes the final design of the core and reflector and split table component design specifications. The ORNL Material Demonstration Facility (MDF) may be used to 3D print ORSA stand/table components and graphite reflector. Researchers will consider fuel coatings for contamination control, rather than an Al can. A visit to Y-12 will be made to determine the location of AGN fuel plates and remaining fuel transportation considerations. Final facility location will be considered
A near-final design has been completed for a new subcritical assembly at Oak Ridge National Laboratory (ORNL). This subcritical assembly will support the Nuclear Criticality Safety Program (NCSP) training and education program to augment current subcritical assembly capabilities at Sandia National Laboratories (SNL) and at the National Criticality Experiments Research Center (NCERC). Other collaborations have been proposed with the Sunrise Consortium and others. This proposed subcritical assembly uses legacy AGN-201M research reactor fuel plates that are available from the Y-12 National Security Complex. This subcritical assembly contains approximately 620 grams of 235 U as UO 2 particulates distributed homogeneously in radiation-stabilized polyethylene. The fuel plates will have a graphite neutron reflector to obtain a core multiplication, M, from 10 to 50, corresponding to a k eff of 0.9 to 0.95, respectively. The subcritical assembly will be able to support at least four experiments for the training courses: (1) the addition of fissile material to increase neutron multiplication (mass), (2) a core separation experiment (interaction), (3) the effect of adding moderators to the core (moderation), and (4) the effect of adding neutron absorbers to the core (poison/absorption). The proposed ORNL subcritical assembly will provide additional student bandwidth to support NCSP training courses and to provide for some backup capacity if nuclear facility operations are disrupted at SNL or NCERC due to some unforeseen issue. The subcritical assembly will be designed to be an inherently safe subcritical assembly—subcritical under all normal and abnormal conditions—and it will provide the capability to conduct hands-on training to support NCSP and general nuclear criticality safety (NCS) staff training and qualification goals.
A near-final design has been completed for a new subcritical assembly at Oak Ridge National Laboratory (ORNL). This subcritical assembly will support the Nuclear Criticality Safety Program (NCSP) training and education program to augment current subcritical assembly capabilities at Sandia National Laboratories (SNL) and at the National Criticality Experiments Research Center (NCERC). Other collaborations have been proposed with the Sunrise Consortium and others. This proposed subcritical assembly uses legacy AGN-201M research reactor fuel plates that are available from the Y-12 National Security Complex. This subcritical assembly contains approximately 620 grams of 235 U as UO 2 particulates distributed homogeneously in radiation-stabilized polyethylene. The fuel plates will have a graphite neutron reflector to obtain a core multiplication, M, from 10 to 50, corresponding to a k eff of 0.9 to 0.95, respectively. The subcritical assembly will be able to support at least four experiments for the training courses: (1) the addition of fissile material to increase neutron multiplication (mass), (2) a core separation experiment (interaction), (3) the effect of adding moderators to the core (moderation), and (4) the effect of adding neutron absorbers to the core (poison/absorption). The proposed ORNL subcritical assembly will provide additional student bandwidth to support NCSP training courses and to provide for some backup capacity if nuclear facility operations are disrupted at SNL or NCERC due to some unforeseen issue. The subcritical assembly will be designed to be an inherently safe subcritical assembly—subcritical under all normal and abnormal conditions—and it will provide the capability to conduct hands-on training to support NCSP and general nuclear criticality safety (NCS) staff training and qualification goals.
AMPX links Thermal Scattering Law (TSL) libraries to isotopes in the resolved resonance region. No guidance is given in the TSL files or the ENDF format if this is acceptable or advised, which can lead to several issues. This presentation discusses these issues and provides suggested solutions.
As part of the nuclear data evaluation and validation cycle, the ENDF/B-VIII.0 cross-section library released in 2018 requires testing to determine areas of improvement and deterioration. Previous work by the authors investigated the performance of 16 O, 56 Fe, and 63,65 Cu cross sections, with this study acting as an extension of the prior work. In addition to the isotopes and nuclear criticality safety benchmarks of interest to the prior work, benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook were selected for their k eff sensitivity to 1 H, C, 58,60 Ni, 182,183,184,186 W, 235,238U, or 239 Pu cross sections and were modeled in the SCALE code system maintained by Oak Ridge National Laboratory. In total, 253 benchmark configurations were selected for their sensitivities and modeled using SCALE 6.2.4 Criticality Safety Analysis Sequences (CSAS) continuous-energy Monte Carlo k eff calculations. This collection includes and expands upon the 99 benchmarks in the prior work. The AMPX-processed ENDF/B-VIII.0 library was decomposed into individual ENDF/B-VIII.0 datum libraries for each isotope of interest. Doing so allowed for the individual substitution of an ENDF/B-VIII.0 cross section in the place of ENDF/B-VII.1, determining isotope-specific effects of ENDF/B-VIII.0 relative to ENDF/B-VII.1. Full library calculations with entirely ENDF/B-VII.1 data or entirely ENDF/B-VIII.0 data were also executed. As a measure of performance, the average relative deviation was determined as the ratio of the deviation between calculated and experimental keff to the propagated calculational and experimental uncertainty. With calculated full library and isotope-specific ENDF/B-VIII.0 k eff ’s, an optimized combination of data libraries was estimated and confirmed with SCALE calculations. This showed that reverting 239 Pu, 58 Ni, 16 O, and 65 Cu cross sections to ENDF/B-VII.1 resulted in improved performance relative to the full ENDF/B-VIII.0 library. Across all 253 benchmarks, the average relative deviation was 1.29σ for the full ENDF/B-VII.1 library, 1.17σ for the full ENDF/B-VIII.0 library, and 0.97σ for the optimized combination. The reversion of 239 Pu, 58 Ni, 16 O, and 65 Cu cross sections to ENDF/B-VII.1 in the 99 benchmarks of the prior work resulted in further improved experimental agreement compared to the previously reported improvement from 16 O and 65 Cu alone. Therefore, it is suggested that applications with significant sensitivities to 239 Pu, 58 Ni, 16 O, and 65 Cu consider their choice of nuclear data library.
Conventional Bayesian optimization methods implicitly assume that the data and model being optimized are “perfect.” This assumption leads to inaccurate posterior probability distribution functions (PDFs) when applied to “imperfect” data or models. The new Bayesian optimization framework presented in this report provides a way to parameterize the effect of imperfections usually encountered in a prior PDF of generalized data or a model on the posterior PDF. The effects of imperfections are parameterized by a set of constraints imposed on the posterior expectation values of deviations between the data and the model and on their covariance matrix elements. A particular set of values for these constraints conveys an evaluator’s best estimate of the effect of imperfections on the corresponding posterior expectation values. When a prior PDF of generalized data is assumed to be normal, an expression for a posterior PDF satisfying an arbitrary set of constraints is derived analytically for linear models. An analogous iterative algorithm is given for nonlinear models. The corresponding posterior PDF should be used to estimate any posterior expectation values in the presence of imperfections parameterized by that set of constraints. A posterior PDF of a conventional Bayesian optimization method is recovered analytically when all evaluator-specified constraints are set to zero (i.e., in the absence of any imperfections). The analytical expressions derived in this report for normal PDFs and linear models were verified numerically by a Metropolis–Hastings Monte Carlo method. The methods presented herein could be applied to any kind of data or models, including differential cross-section data or integral benchmark experiments.
BMC evaluation is a tool to address imperfect data & models, non-linear models, and non-normal PDFs. ENDF-6 format does not allow non-normal parameter PDFs. Storing posterior sets allow for variance, covariance, skewness, etc. To better predict criticality, we could document non-normal parameter PDFs (i.e. asymmetric uncertainty), consider non-linear sensitivity of $\kappa$ eff to resonance parameters, and reduce uncertainty in key resonance parameters.