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DOE OSTI2020

Sensitivity Studies, Gap Analysis, and Benchmark Experiment Optimization for Reactor Physics and Criticality Safety Applications

Many new reactor designs, such as advanced reactors and micro reactors, have materials that lack nuclear data validation. This is also true for many other applications in criticality safety and global security. Both differential and integral experiments are needed to validate cross-section data. Without this, a user cannot have confidence in the predicted results of a radiation-transport code. This work describes an approach called ARCHIMEDES (Application Relevant Critical/Subcritical HEU/Pu-based Integral Measurements for Enhancing Data and Evaluating Sensitivities) to design new criticality experiments that have similar k eff cross-section sensitivities to an application of interest. This process involves simulations to generate cross-section sensitivities to a parameter of interest (such as k eff ), a gap analysis to determine which existing benchmarks are most similar to the application, and an experiment optimization. Recently, there has been a great deal of interest in the reactor physics community on advanced reactors, micro reactors, and accelerator driven systems (ADS). This work will apply the described method to specific examples in this area. The focus of this work will be on the sensitivity study and gap analysis, while future work will include experiment design.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Sensitivity-based Experiment Design Optimization for a Molybdenum Critical Experiment

A lack of intermediate molybdenum benchmarks in the ICSBEP has been identified by LANL, Y-12, and IRSN. This lacking adversely effects criticality safety operations and leaves new differential molybdenum data unvalidated. NCERC is proposing a series of intermediate integral experiments to better the understanding of molybdenum systems. Using MCNP6.2 with the ENDF/B-VIII.0 nuclear data library a single unmoderated and four moderated system designs were identified using a sensitivity optimization method. Each proposed system was found to be at least twice as sensitive to the 95 Mo capture cross section in the URR as the sole existing intermediate molybdenum benchmark in the ISCBEP handbook. The addition of a new molybdenum sensitive intermediate system would improve future nuclear data evaluations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Multiple Critical Unresolved Region Integral Experiment (MCURIE): A Proposed Integral Critical Experimental Framework for Unresolved Region and Intermediate Energies

The Critical Unresolved Region Integral Experiment (CURIE) critical experiment was performed at the National Criticality Experiments Research Center (NCERC) at the Device Assembly Facility (DAF) at the Nevada Nuclear Security Sites (NNSS) in 2020. The objective of CURIE was to improve the quality of integral nuclear data in the uranium-235 ( 235 U) unresolved resonance region (URR) by performing benchmark integral experiments that were sensitive to the URR energy ranges. The CURIE experiment was evaluated for the International Criticality Safety Benchmark Evaluation Project (ICSBEP) handbook and the benchmark evaluation was accepted in 2022. The URR is a region within the intermediate neutron energy range (the intermediate energy ranges from 0.7 eV to 100 keV). The observed resonance structure in neutron cross sections is due to discrete energy levels in the nucleus and are characterized by resonance parameters. In the URR region, the resonance parameters are only partially resolved as the resolution of the experiment techniques becomes comparable to the average width of the resonances themselves, and the resonances are so close to one another that the structure cannot be determined empirically. The ENDF/B-VIII.0 and JEFF-3.3 nuclear data libraries define the URR as beginning at 2.25 keV and continuing until 25 keV. There are minimal intermediate neutron energy benchmarks available in the ICSBEP benchmark handbook, and aside from CURIE there are none that are highly sensitive in the URR energy region. There is a current need for additional experiments sensitive to the URR energy region. There is a new proposed subgroup for the Organization for Economic Co-operation and Development and Nuclear Energy Agency (OECD NEA) Working Party on International Nuclear Data Evaluation Cooperation (WPEC), so any new models or information will need experimental validation and testing. The NEA Working Party on Nuclear Criticality Safety (WPNCS) recent experimental needs and priority list includes intermediate energy 235 U and 238 U experiments, as does the recent Integral Experiments to Address Nuclear Criticality Safety Needs Meeting (May 2023). A variant on the original CURIE experiment called the Multiple Critical Unresolved Region Integral Experiment (MCURIE) is proposed to provide further investigation of the intermediate and URR energy region for uranium. MCURIE will utilize existing fuels at NCERC but use alternative moderators and reflectors to modify the neutron absorption, scattering, and fission spectra of the experiments, allowing for precise targeting of nuclear data sensitivities. The overall goal of MCURIE is to develop a framework for designing and performing integral benchmark experiments with high sensitivities in the intermediate and URR energy regions for nuclear data validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

On the Statistical Uncertainty of Monte Carlo-Calculated Scattering Sensitivities

Sensitivity coefficients calculated with Monte Carlo codes are widely used for nuclear data uncertainty quantification in the modeling and simulation of complex 3D reactor systems. This study systematically compares sensitivity coefficients and associated statistical uncertainties for the multiplication factor and fuel temperature reactivity across multiple Monte Carlo codes (SCALE/KENO, SCALE/Shift, MCNP, and Serpent) using simple models representing light-water reactors and advanced reactor concepts. For multiplication factor sensitivities, statistical uncertainties are generally acceptable, although scattering sensitivities show significantly larger statistical uncertainties than, for example, fission and capture reactions. Fuel temperature reactivity sensitivities show significantly larger statistical uncertainties across all reactions. Elastic scattering sensitivities are the most problematic: all Monte Carlo codes fail to resolve energy-dependent coefficients, and they produce dramatically different energy-collapsed values. Critically, the use of these sensitivity coefficients in nuclear data uncertainty propagation leads to reduced statistical uncertainties in individual uncertainty contributions. This can lead to the masking of unusable sensitivity coefficients and producing misleading uncertainty results. The findings of this study show that new or enhanced methods are needed to improve Monte Carlo elastic scattering sensitivity calculations. Additionally, this study shows the relevance of verifying sensitivity coefficients through direct perturbation calculations for individual nuclide reactions, instead of only for total cross sections as commonly done.

Bostelmann, Rike [ORNL] (ORCID:0000000165968088)↗
DOE OSTI2022

Analysis of SCALE Criticality and Sensitivity Calculations for Reflected HEU Cylinders [Slides]

The SCALE code package offers multiple nuclear data libraries supporting Monte Carlo transport, with sensitivity and uncertainty methods derived from MC transport solutions. Several libraries are multigroup, which introduce bias differing by system. Previous work has shown poor S/U results in several reflector materials: ICSBEP benchmark HMF-084 was selected to analyze biases and S/U method applicability to a variety of reflectors. Prior and ongoing work found inaccuracies in CSAS and TSUNAMI results, which were further investigated utilizing the HEU-MET-FAST-084 ICSBEP critical benchmark, chosen for its geometrical simplicity and variety of reflector materials. Perturbation of reflector thickness across various reflector materials allowed for an assortment of materials is to be tested swiftly for each sequence and method. Observation was an increasing bias of MG $k_{eff}$ relative to CE, in both direction and magnitude. IFP produced extremely reliable results. >85% of CLUTCH cases were found satisfactory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Data Assimilation using Non-invasive Monte Carlo Sensitivity Analysis of Reactor Kinetics Parameters [Slides]

Sensitivity coefficients of prompt neutron decay constant (α) and effective delayed neutron fraction (β eff ) to Pu-239 nuclear data were calculated using a newly available tool (ACEtk). Uncertainty calculations showed the following trends: (1) The prompt neutron decay constant can be used to reduce nuclear data-induced uncertainty in Pu-239(n,f) and (2) the effective delayed neutron fraction can be used to effectively reduce nuclear data-induced uncertainty in Pu-239 total fission $\tilde{v}$. Sensitivity/uncertainty analysis can be used to determine optimal experiment/detector setup to identify compensating errors in nuclear data. Upcoming work includes investigating other nuclide-reaction pairs and response sensitivities, such as Δ$\rho$, neutron leakage spectra, and reaction rate measurements to constrain nuclear data of interest.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Sensitivity Coefficients Calculated for the Prompt Neutron Decay Constant At or Near Delayed Critical

The derivation of a non-invasive prompt neutron decay constant sensitivity coefficient is provided in this work. The computation of the sensitivity coefficient derived in this work does not require modification of Monte Carlo source code and is based on capabilities available in Monte Carlo N-Particle R© Code Version 6.2. The prompt neutron decay constant sensitivity coefficients are calculated for 44-group and 252-group energy structures for specific nuclide-reaction pairs in the Jezebel benchmark experiment. The nuclide-reaction pairs investigated in this work include Pu- 239(n,f), Pu-240(n,f), and Pu-241(n,f). Physical explanations of the sensitivity profiles exhibited by the 252-group energy structure are investigated for the prompt neutron multiplication factor, mean neutron lifetime, and prompt neutron decay constant. The prompt neutron decay constant sensitivity coefficients calculated for the 44-group and 252-group energy structure of Pu-239(n,f) are compared. Lastly, the 44-group energy structure sensitivity coefficients calculated are used for nuclear-data induced uncertainty quantification of the neutron multiplication factor. This work shows that a reduction in the nuclear data-induced uncertainty of the neutron multiplication factor is possible for all nuclide-reaction pairs investigated when prompt neutron decay constant sensitivity coefficients are utilized. This is important for new critical experiment design optimization studies of measurement configurations. This work provides a basis for more detailed sensitivity analysis and uncertainty quantification of nuclide, reaction, and energy-specific cross section data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

IER-517: Molybdenum Optimized Benchmark System Demonstrating Integral Correlations (MOBY DICK)

Nuclear criticality experiments are essential to the validation of nuclear data used in simulation software. The quality of nuclear data becomes paramount as simulation software becomes more relied upon for criticality safety studies and designs of nuclear systems. To improve the quality of nuclear data, experimenters can design critical experiments that are sensitive to isotope reaction pairs in materials of interest. The efforts conducted by the Organisation for Economic Co-operation and Development - Nuclear Energy Agency (OECD-NEA) Working Party on Nuclear Criticality Safety (WPNCS) Subgroup 8: Preservation of Expert Knowledge and Judgement Applied to Criticality Benchmarks (SG8) to categorize benchmarks according to their usefulness for nuclear data validation have been of great importance. Based on the OECD studies benchmark experiments included in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook are concisely used by nuclear data evaluators, criticality safety engineers and others to validate nuclear data and simulation results. A lack of benchmarks sensitive to molybdenum in the (ICSBEP), particularly in the intermediate range, was noted by Los Alamos National Laboratory (LANL), the French Institut de Radioprotection et de Sûreté Nucléaire (IRSN), and Y-12 National Security Site prompting them to submit a joint integral experiment request to the Nuclear Criticality Safety Program (NCSP) in 2019. The request included both HEU and Plutonium systems in order to validate differential nuclear data focusing on the intermediate energy range but also includes thermal and fast configurations. This document represents the preliminary design work for a series of molybdenum integral experiments known as Molybdenum Optimized Benchmark System Demonstrating Integral Correlations (MOBY DICK).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

SCALE Lattice Physics Code Assessments of Accident Tolerant Fuel

This report highlights accident-tolerant fuel (ATF) code assessment activities performed under Project NRCHQ- 60-17-T-0017, Lattice Physics Enhancements and Assessment. ATF covers a broad range of advanced fuel and clad designs for light water reactors (LWRs) to enhance performance under several accident conditions. Several ATF concepts are anticipated to be deployed as lead test rods (LTRs) or lead test assemblies (LTAs) within the next five years. The purpose of this work is to assess the predictive capabilities of NRC neutronics codes that underpin various licensing calculations. ATF designs use different fuel and clad materials compared to standard UO 2 fuel and zirconium-alloy claddings (hereafter UO 2 -Zry). These new materials and geometrical designs need to be assessed to quantify the impact of nuclear data uncertainties on quantities of interest (QOIs) in licensing calculations and the impact of modeling approximations which may be valid for UO 2 -Zry but not for ATF. This report outlines a systematic approach for ATF neutronics code assessment which includes sensitivity and uncertainty (S/U) analysis of nuclear data, identification of experimental benchmark and gaps for code validation, investigation of modeling approximations, and code-to-code comparisons of calculated QOIs against high-fidelity reference continuous energy (CE) Monte Carlo (MC) calculations. This report focuses on the assessment of the SCALE/Polaris lattice physics code for reactor safety analysis. Polaris lattice physics calculations generate few group (FG) cross sections for PARCS full-core calculations. (Full-core analysis, spent fuel analysis, and severe accident analysis will be performed in future work.) The selected ATF concepts for this report include Cr 2 O 3 and Al 2 O 3 -Cr 2 O 3 -doped UO 2 fuel, U 3 Si 2 fuel, FeCrAl cladding, SiC cladding, and Cr-coated cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Study of a Proposed fissionTPC Measurement of 233 U(n,f)/ 235 U(n,f) Cross Section Ratio

A review of the available 233 U( n, f )/ 235 U( n, f ) cross section ratio data compared to the ENDF evaluation in the fast neutron energy range, 0.1–20 MeV, shows that discrepancies exist between some of the various measurements and the evaluation. The discrepancies vary and a function of incident neutron energy and range between 1–5%. In this document we review two potential options for performing new measurements of the cross section ratio to potentially resolve these discrepancies. The two options are compared and contrasted in terms of measurement accuracy and cost. The first option would utilize the fissionTPC, which was designed specifically to achieve measurement uncertainties of better than 1% to resolve a similar data–evaluation discrepancy in the 239 Pu( n, f ) cross section. While this would seem to be an ideal option in this case also, there are challenges. The fissionTPC is a complex instrument and the cost of maintenance and operations are significant. Furthermore, some of the fissionTPC equipment is nearing the end of its useful life which presents a risk to completion of a measurement campaign. The second option is to use a dual-fission chamber, which is the more traditional approach to these types of measurements. The cost is estimated to be about half that of a fissionTPC measurement, while the much simpler design of the detector reduces overall risk. The trade-off is the measurement uncertainty, which would be on order of 1–3% with a careful measurement and analysis. This uncertainty however may not be good enough to fully resolve the discrepancies. The objective of a new measurement would be the improvement in the ENDF evaluation with the end goal of improving the accuracy of models and simulations at the end of the nuclear data pipeline. An understanding of the sensitivity of these models to the data uncertainties would help guide the choice of measurement techniques.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Selected Uses of TSUNAMI in Critical Experiment Design and Analysis

Validation in criticality safety is performed by comparing the results of critical experiments with the calculated results from models of the experiments using the computational method to be validated. Laboratory critical experiments are controlled systems that achieve a k eff of approximately 1 and enable investigation of the parameters at which such a critical condition is achieved. For the critical experiments used in a validation to capture the biases of the materials and neutron energy spectra of interest, those materials must be included in the experiment such that they influence k eff or another observable parameter with statistical significance. This paper discusses the use of sensitivity uncertainty (S/U) methods to develop critical experiments for various purposes. S/U techniques are useful for understanding the underlying components of nuclear data which affect the k eff or another parameter of a given configuration. S/U calculations are most commonly used to compare existing experiments to applications of interest; however, S/U techniques can also be used to identify, optimize, or assess features of proposed experiments so that they can better test specific portions of nuclear data or match an application of interest. The S/U techniques discussed here are from the TSUNAMI code system. The two primary codes discussed in this work are TSUNAMI-3D, which implements the KENO criticality code to calculate the sensitivity of k eff to nuclear data, and TSAR, which calculates the sensitivity of a reactivity difference between two configurations based on their TSUNAMI-3D generated sensitivity profiles. The methods used in these tools are discussed in more detail in the SCALE manual. This paper is one of a series on the development and use of TSUNAMI tools. The other papers address development of TSUNAMI methods and a review of TSUNAMI applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Adapting CLUTCH methodology to multigroup TSUNAMI-3D for eigenvalue sensitivity calculations

The sensitivity of the eigenvalue to uncertainties in nuclear data and its evaluation are important for nuclear criticality safety. TSUNAMI-3D sequences within the SCALE code system offer several options to the user community for calculating eigenvalue sensitivity coefficients with multigroup (MG) and continuous energy (CE) 3D transport capabilities. TSUNAMI-3D sequences implement the adjoint-based perturbation theory with MG KENO code, the Contributon Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method with CE KENO code, and the Iterated Fission Probability (IFP) method with CE KENO and Shift codes. Each method has benefits and limitations depending on the problem that is run. The work presented here aims to adapt the CLUTCH method, which enables the Contributon method's mesh-free, memory-efficient approach for calculating adjoint-weighted tallies for sensitivity calculations, to the MG TSUNAMI-3D sequence. This application would eliminate the explicit adjoint KENO calculation, as well as the memory-consuming mesh flux moment tallies required by the conventional MG TSUNAMI-3D. Smaller memory footprints in the CLUTCH methodology and relatively shorter runtimes in MG KENO transport can make MG TSUNAMI-3D a viable method for some complex problems. Moreover, this adaptation allows MG sensitivity calculations with Shift, ORNL's next-generation high-performance Monte Carlo transport code, which currently does not offer any sensitivity capabilities with MG particle transport simulations. Initial implementation of the new MG TSUNAMI-3D sequence and its preliminary results with a selected critical benchmark experiment in the Verified, Archived Library of Inputs and Data (VALID) are presented in this study.

KENO↗
DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint, and the sensitivity of $k$ ∞ to perturbations in the multigroup nuclear data of a single species isotropic elastic scattering material. In the appendix, we present the multigroup nuclear data for U-235 and U-238 along with the corresponding k-eigenvalue, flux, adjoint, and sensitivity profiles, which include the sensitivity of $k$ ∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Investigation of Delayed Neutron Sensitivities for Several ICSBEP Benchmarks using MCNP

The effective delayed neutron (β$_{eff}$) is a very important parameter for reactor and criticality applications. This parameter is equal to the difference in reactivity between delayed critical ($k_{eff}$ = 1, which requires both prompt and delayed neutrons to achieve criticality) and prompt critical ($k_p$ = 1, which requires only prompt neutrons to achieve criticality). This is often referred to as the delayed critical "window" (the region of criticality between delayed and prompt critical). β$_{eff}$ is a reactor kinetics parameters and depends on the nuclides in the system that undergo fission as well as the spectral characteristics of the system. Measurements of β$_{eff}$ have been performed for many criticality experiments. The EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data) project at Los Alamos National Laboratory (LANL) aims to constrain nuclear data by using a suite of measurement types beyond $k_{eff}$. Our team has recently investigated the use of pulsed spheres for nuclear data validation. Several other measurement methods are also of interest, including β$_{eff}$ (investigated here) and reactivity coefficients (investigated in a separate work at this same meeting). One focus of our work is to determine if other methods are complimentary to the critical experiments already utilized for nuclear data validation. This is important because if a method has similar sensitivities then it will not be particularly useful for nuclear data validation as it will provide the same information as the critical experiments already being used. Here "similar" could refer to several characteristics, one being the shape of a sensitivity profile over energy. In the future, these methods will be utilized (with both existing and new experiments) in machine learning algorithms for nuclear validation, similar to what is currently done for criticality experiments. In order to use a measurement type for nuclear validation, it is necessary to obtain cross-section sensitivities for that parameter. This work looks at one approach to estimate β$_{eff}$ sensitivities by utilizing $k_{eff}$ sensitivities within Monte Carlo N-Particle ® Code Version 6.2. This is applied to several criticality benchmarks. Results are compared and the benefits and limitations of this approach are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Sensitivity of D meson azimuthal anisotropies to system size and nuclear structure

Recent experimental data at the Large Hadron Collider (LHC) confirmed that the soft sector azimuthal anisotropies in central XeXe collisions are sensitive to deformations in the wave function of the Xenon nucleus. Additionally, the CMS experiment found that D meson flow is slightly suppressed compared to other particle species when considering quark number scaling in small systems of pPb compared to PbPb. In this talk we used the D and B Mesons Modular (DAB-MOD) code coupled to Trento+v-USPhydro to calculate the R AA and v n ’s of D mesons using different energy loss models and Langevin techniques. Comparing D mesons R AA and v n in PbPb to XeXe collisions it is found that in central collisions D meson azimuthal anisotropies are sensitive to details in the nuclear structure wave function of Xenon. Additionally, we find that in mid-central collisions the smaller system size of XeXe suppresses D meson flow.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

A Review of TSUNAMI Applications

The TSUNAMI-1D and TSUNAMI-3D sequences for generating k eff sensitivity coefficients were first released in SCALE 5 in 2004. Several other tools were introduced in the same release, including primarily the TSUNAMI-IP code for uncertainty analysis and similarity assessments. The TSUNAMI sequences added capabilities for identifying important reactions and data for systems using sensitivity coefficients and also introduced new quantitative tools for rigorously assessing the similarity of systems. Over time, the capabilities of these tools have grown, and their use has expanded into other areas such as nuclear data assessment and nuclear covariance data testing. This paper discusses applications of the TSUNAMI tools for sensitivity calculations, sensitivity/uncertainty (S/U)-based validation, and nuclear data testing. This paper is one of a series of papers at this conference on the development and use of TSUNAMI tools. The other papers address the development of the TSUNAMI methods and the use of TSUNAMI for critical experiment design and optimization.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Propagating neutronic uncertainties for FFTF LOFWOS Test #13

The safety evaluation conducted for licensing a Sodium-cooled Fast Reactor (SFR) may require modeling transients with best-estimate calculation tools that must first be validated against real-world measurements. To provide the community with a valuable benchmarking opportunity for validating SFR analysis tools and methods, the International Atomic Energy Agency (IAEA) initiated a coordinated research project (CRP) in 2018 for the analysis of the Fast Flux Test Facility (FFTF) Loss of Flow Without Scram (LOFWOS) Test #13. The impact of nuclear data uncertainties on neutronics parameters was previously investigated based on the COMMARA-2.0 covariance matrix. Since the transient simulation results are very sensitive to certain reactivity coefficients, it was decided to employ rigorous uncertainty propagation methods to quantify the impact of nuclear data uncertainties on the best-estimate predication of FFTF LOFWOS Test #13. The DAKOTA code is used to propagate neutronic uncertainties through SAS4A/SASSYS-1 transient simulations, while taking into account spatial and reaction-wise correlations within these uncertainties. This study shows that the remaining discrepancies observed between the Argonne National Laboratory (ANL) best-estimate results and the experimental measurements can be partly explained by the uncertainty associated with Gas Expansion Module (GEM) worth, which contributes the majority of the overall nuclear data uncertainty on the output from the FFTF LOFWOS Test #13 transient simulation. This study also confirmed the importance of including spatial and reaction-wise correlations of nuclear data uncertainties on feedback coefficients in the uncertainty propagation to avoid under-estimating their impact during the transient simulations.

42 ENGINEERING↗