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DOE OSTI2022

SCALE 6.2.4 Validation: Radiation Shielding

For safe and reliable use of computer codes by the community, accuracy must be clearly evaluated. In particular, the nuclear reactor engineering and licensing field needs accurate tools for radiation shielding modeling. Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) is one such tool, with built-in variance reduction methods distributed within the SCALE code, and its validity is demonstrated in this report for the released version 6.2.4. Representative benchmarks corresponding to shielding analysis are selected for the validation study. Typical experimental results analyzed from those benchmarks include neutron fluxes, detector count rates, detector energy response functions, neutron and gamma doses, foil neutron activation rates and activities, neutron leakage fluxes, and skyshine dose rates. Thousands of points of comparison between experiment and calculation are presented in this work. Other than rare outliers typically explained by either a lack of information or large uncertainties in the experiment conditions, material, or dimensions, MAVRIC agrees well with the experiment results. MAVRIC is also compared to Monte Carlo N-Particle (MCNP) calculations when available, and both codes generally produce good agreements within estimated uncertainties. The selected benchmarks are obtained from reliable sources such as the International Criticality Safety Benchmark Evaluation Project Handbook (ICSBEP Handbook), the Shielding Integral Benchmark Archive & Database (SINBAD), and other shielding validation work found in the literature. Additional datapoints and benchmarks will be added to future versions of this report to incrementally expand the shielding validation suite incrementally.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2021

Distributed, Intelligent Edge-Sensing for a Smarter Grid

The electric grid is undergoing major transformations and developments resulting in unprecedented levels of volatility, uncertainty, and stress on grid infrastructure. Smart sensors and methods aiding in advanced visibility and situational awareness are key for tackling these issues. In this work, a decentralized architecture is proposed, where sensing, local computation and control capability are embedded in the edge devices, communicating with a set of trusted 'data mules' in a 'delay-tolerant' manner, while functioning autonomously. This system has been designed and implemented as an overall platform – called Global Asset Monitoring, Management and Analytics (GAMMA) Platform intended to provide the backbone for a global array of sensors and actuators. Further, as a building block for advanced current sensing solutions, a smart, low-cost ‘clip-on’ current sensor based on PCB-embedded Rogowski coil has been developed. The sensor hosts a novel signal conditioning stage allowing an 'auto-tuning' feature, resulting in a universal current sensor design for measuring a wide range of currents, including faults for smart grid applications. Finally, the research proposes a method to instrument and monitor key parameters for the most common electric utility asset – the pole-top distribution transformer. The work done in this research enables scalable, edge-intelligent sensing solutions for monitoring grid infrastructure, allowing utility operators to gain advanced visibility in an economical way.

Kulkarni, Shreyas Bhalchandra↗

DOE OSTI2018

The Impact of Nuclear Reaction Rate Uncertainties on the Evolution of Core-collapse Supernova Progenitors

We review properties of core-collapse supernova progenitors with respect to the composite uncertainties in the thermonuclear reaction rates by coupling the probability density functions of the reaction rates provided by the STARLIB reaction rate library with MESA stellar models. We evolve 1000 models of 15${M}_{\odot }$ from the pre-main sequence to core O-depletion at solar and subsolar metallicities for a total of 2000 Monte Carlo stellar models. For each stellar model, we independently and simultaneously sample 665 thermonuclear reaction rates and use them in a MESA in situ reaction network that follows 127 isotopes from 1 H to 64 Zn. With this framework we survey the core mass, burning lifetime, composition, and structural properties at five different evolutionary epochs. At each epoch we measure the probability distribution function of the variations of each property and calculate Spearman rank-order correlation coefficients for each sampled reaction rate to identify which reaction rate has the largest impact on the variations on each property. We find that uncertainties in the reaction rates of ${}^{14}{\rm{N}}{({\rm{p}},\gamma )}^{15}{\rm{O}}$, triple-α, ${}^{12}{\rm{C}}{(\alpha ,\gamma )}^{16}{\rm{O}}$, 12 C( 12 C,p) 23 Na, 12 C( 16 O, p) 27 Al, 16 O( 16 O,n) 31 S, 16 O( 16 O, p) 31 P, and 16 O( 16 O,α) 28 Si dominate the variations of the properties surveyed. We find that variations induced by uncertainties in nuclear reaction rates grow with each passing phase of evolution, and at core H-, He-depletion they are of comparable magnitude to the variations induced by choices of mass resolution and network resolution. Yet, at core C-, Ne-, and O-depletion, the reaction rate uncertainties can dominate the variation, causing uncertainty in various properties of the stellar model in the evolution toward iron core-collapse.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Primary $\gamma$-ray intensities and $\gamma$-strength functions from discrete two-step $\gamma$-ray cascades in radiative proton-capture experiments

Background: Reaction rates of radiative capture reactions can play a crucial role in the nucleosynthesis of heavy nuclei in explosive stellar environments. These reaction rates depend strongly on $\gamma$-ray decay widths in the reaction products, which are, for nonresonant capture reactions at high excitation energies, derived from the $\gamma$-ray strength function and the nuclear level density. Recently, the ratio method was applied to primary $\gamma$ rays observed from ($\textit{d, p}$) reactions and nuclear resonance fluorescence measurements to extract the dipole strength in atomic nuclei and to test the generalized Brink-Axel hypothesis. Purpose: The purpose of this work is to apply the ratio method to primary $\gamma$-ray intensities of the 63,65 Cu($\textit{p},\gamma$) reactions to extract $\gamma$-ray strength information on the nuclei 64,66 Zn. Here, the impact of spin distribution, total $\gamma$-ray decay widths, level densities, and width fluctuations on the application of the ratio method will be discussed. Additionally, by comparing the relative $\gamma$-ray strength at different excitation energies, conclusions on the validity of the generalized Brink-Axel hypothesis can be made. Method: The radiative proton capture reaction measurements have been performed at the HORUS $\gamma$-ray spectrometer of the University of Cologne at one excitation energy for each reaction. Primary $\gamma$-ray intensities have been determined by normalizing secondary $\gamma$-ray transitions in two-step cascades using their absolute branching ratio. The ratio method was applied to the measured primary $\gamma$-ray intensities as well as to previous measurements by Erlandsson et al. at different excitation energies. Results: The relative strength function curve for 64 Zn from our measurement shows no significant deviation from the previous measurement at a different excitation energy. The same is true for 66 Zn where both measurements were at almost the same excitation energy. Absolute $\gamma$-strength function values have been obtained by normalizing the relative curves to quasiparticle random phase approximation calculations because of the absence of experimental data in the respective energy region. Conclusion: The generalized Brink-Axel hypothesis, i.e., the independence of the strength function on the excitation energy, seems to hold in the studied energy region and nuclei. The method to obtain primary $\gamma$-ray intensities from two-step cascade spectra was shown to be a valuable and sensitive tool although its uncertainties are connected to the knowledge of the low-energy level scheme of the investigated nucleus. The scaling in the ratio method should be taken with care, because the relative strength is not a simple sum of $f_{E1}$ and $f_{M1}$ but a somewhat complex linear combination dependent on the excitation energy of the nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Bose enhancement, the Liouville effective action, and the high multiplicity tail in p – A collisions

In the framework of dense-dilute CGC approach we study fluctuations in the multiplicity of produced particles in p-A collisions. We show that the leading effect that drives the fluctuations is the Bose enhancement of gluons in the proton wave function. We explicitly calculate the moment generating function that resums the effects of Bose enhancement. We show that it can be understood in terms of the Liouville effective action for the composite field which is identified with the fluctuating density, or saturation momentum of the proton. The resulting probability distribution turns out to be very close to the gamma-distribution. In conclusion, we also calculate the first correction to this distribution which is due to pairwise Hanbury Brown-Twiss correlations of produced gluons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Analytic Thermal Model of an Optical Fiber Based Gamma Thermometer and its Application in a University Research Reactor

This paper describes and validates, by comparison with numerical modeling results, an analytical model of thermal transport in an optical fiber based gamma thermometer (OFBGT) that is appropriate for use in university research reactors. The maximum temperature difference between the thermal mass and the outer sheath ( Δ T ) for the OFBGT design that we have considered is approximately 50 ∘ C , for the OFBGT in the Central Irradiation Facility of the Ohio State University Research Reactor (OSURR) with the reactor operating at full power (450 kW). The maximum value of Δ T that is predicted by the analytic model for the OFBGT design is smaller by approximately 1.1 °C than the value of Δ T which is predicted by the numerical model, for the same OFBGT design, but including all the details of the design. We have used the analytical model of thermal transport in an OFBGT to determine a normalized Modulation Transfer Function M T F ′ ( k ) ) for the OFBGT. We conclude that MTF ′ ( k OSU ) > 0.99 , where k OSU is the spatial frequency for the axial dependence of the reactor power distribution in the

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

S -factor and scattering-parameter extractions from ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}{ \rightarrow }^{7}\mathrm{Be}+\gamma $

Previous studies of the reaction ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ have mainly focused on providing the best central value and error bar for the S factor at solar energies. Experimental measurements of this capture reaction at higher energies, the ${}^{3}\mathrm{He}$–${}^{4}\mathrm{He}$ scattering phase shifts, as well as properties of ${}^{7}\mathrm{Be}$ and its excited state, have been used to constrain the theoretical models employed for this purpose. Here we show that much more information than was previously appreciated can be extracted from angle-integrated capture data alone. We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ to perform the extrapolation. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic properties of ${}^{7}\mathrm{Be}$ and its excited state, and short-distance contributions to the E1 capture amplitude. We extract the multi-dimensional posterior of all these parameters via a Bayesian analysis that uses capture data below 2 MeV. We find that properties of the ${}^{7}\mathrm{Be}$ ground and excited states are well constrained. The total S factor $S(0)\,={0.577}_{-0.016}^{+0.015}$ keV b, while the branching ratio for excited- to ground-state capture at zero energy, ${Br}(0)={0.406}_{-0.011}^{+0.013}$, both at 68% degree of belief. This S(0) is broadly consistent with other recent evaluations, and agrees with the previously recommended value $S(0)=0.56\pm 0.03\,\,\mathrm{keV}$ b, but has a smaller error bar. We also find significant constraints on ${}^{3}\mathrm{He}$–${}^{4}\mathrm{He}$ scattering parameters, and we obtain constraints on the angular distribution of capture gamma rays, which is important for interpreting experiments. The path forward for this reaction seems to lie with better measurements of the scattering phase shifts and S(E)'s angular dependence away from zero energy, together with better understanding of the asymptotic normalization coefficients of the ${}^{7}$Be bound states' wave functions. Lastly, data on these could further reduce the uncertainty on S(0).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

Dark Energy Surveyed Year 1 results: calibration of cluster mis-centring in the redMaPPer catalogues

Abstract The centre determination of a galaxy cluster from an optical cluster finding algorithm can be offset from theoretical prescriptions or N-body definitions of its host halo centre. These offsets impact the recovered cluster statistics, affecting both richness measurements and the weak lensing shear profile around the clusters. This paper models the centring performance of the redMaPPer cluster finding algorithm using archival X-ray observations of redMaPPer-selected clusters. Assuming the X-ray emission peaks as the fiducial halo centres, and through analysing their offsets to the redMaPPer centres, we find that ${\sim } 75\pm 8 {{\ \rm per\ cent}}$ of the redMaPPer clusters are well centred and the mis-centred offset follows a Gamma distribution in normalized, projected distance. These mis-centring offsets cause a systematic underestimation of cluster richness relative to the well-centred clusters, for which we propose a descriptive model. Our results enable the DES Y1 cluster cosmology analysis by characterizing the necessary corrections to both the weak lensing and richness abundance functions of the DES Y1 redMaPPer cluster catalogue.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Center-of-Mass Corrections in Associated Particle Imaging

Associated particle imaging (API) utilizes the inelastic scattering of neutrons produced in deuterium-tritium (DT) fusion reactions to obtain 3-D isotopic distributions within an object. The locations of the inelastic scattering centers are calculated by measuring the arrival time and position of the associated alpha particle produced in the fusion reactions, and the arrival time of the prompt gamma created in the neutron scattering event. While the neutron and its associated particle move in opposite directions in the center-of-mass (COM) system, in the laboratory system the angle is slightly less than 180°, and the COM movement must be taken into account in the reconstruction of the scattering location. Furthermore, the fusion reactions are produced by ions of different momenta, and thus the COM velocity varies, resulting in an uncertainty in the reconstructed positions. In this article, we analyze the COM corrections to this reconstruction by simulating the energy loss of beam ions in the target material and identifying sources of uncertainty in these corrections. Here we show that an average COM velocity calculated using the ion beam direction and energy can be used in the reconstruction and discuss errors as a function of ion beam energy, composition, and alpha detection location. When accounting for the COM effect, the mean of the reconstructed locations can be considered a correctable systematic error leading to a shift/tilt in the reconstruction. However, the distribution of reconstructed locations also have a spread that will introduce an error in the reconstruction that cannot be corrected. In this article, we will use the known stopping powers of ions in materials and reaction cross sections to examine the reconstruction uncertainties. We also discuss the impact of this effect on our API system.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

A Lumped Stochastic Model of Coupled Neutronic Assemblies

The objective of the present work is to apply the Harris ansatz to coupled assemblies in a lumped setting, i.e., ignoring the neutron phase dependence, which hitherto has not been considered. A Master equation for the single-time joint distribution of neutron number in each assembly, accounting for transfer of neutrons from one assembly to another via leakage transition probabilities and intercept or view factors is derived from which equations for the mean and variance in each assembly are developed. Because of the neutronic coupling, it is necessary to additionally compute the correlation function between pairs of assemblies which gives an expanded set of moment equations to solve. The reactivity of each assembly is allowed to vary with time, although a formal mechanism that is responsible for reactivity coupling between assemblies is not considered or proposed. Following Harris, it is then hypothesized that the number distribution in each assembly is a gamma distribution with assembly-specific mean and variance computed exactly from the moment equations. Illustrative numerical results are presented for the moments of a system of four coupled assemblies under various reactivity and neutronic coupling scenarios. The gamma distribution is then used to compute the probability that the neutron population exceeds a threshold value in any assembly. The report concludes with a discussion of recommended further work on this problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

C 12 ( n , n 1 ′ γ ) partial γ -ray cross section measured using the GENESIS array

Improved neutron inelastic scattering cross sections have repeatedly been identified as a top priority nuclear data need, important for basic science and a range of applications in nuclear energy, stockpile stewardship, and proliferation detection. For the C 12 ( n , n ′ γ ) reaction in particular, recent measurements have unveiled some structural discrepancies, demonstrating incongruities among themselves and in relation to the ENDF/B-VIII.0 nuclear data evaluation. To help resolve these disagreements, a measurement was performed at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory using a broad-spectrum neutron beam and a 99.8% pure natural carbon target. The Gamma Energy Neutron Energy Spectrometer for Inelastic Scattering (GENESIS) was employed to measure energy-differential γ -ray emission spectra as a function of incident neutron energy in the energy range of 5.5 to 16.7 MeV. The C 12 partial γ -ray cross sections were extracted at 63 ∘ , 122 . 5 ∘ , and 150 ∘ with respect to the incoming neutron beam and integrated using angular distribution data available in the literature. The data show agreement with a recent literature measurement and evaluation from 11 to 15 MeV, but indicate a larger cross section for incident neutron energies between 5.5 and 8.5 MeV. The measured relative angular distributions are also reported and were found to agree with evaluation. Published by the American Physical Society 2025

Gordon, J. M. (ORCID:0009000789886897)↗

DOE OSTI2019

Enabling a Decentralized Smart Grid Using Autonomous Edge Control Devices

As a large number of distributed devices are connected to the modern smart grid, the traditional centralized connectivity models fail to provide economic value. These models have relied on sending data to the cloud for processing and receiving commands to exert control actions, resulting in an ‘on-demand system’ with high bandwidth, low latency and an overload of data on the cloud. For realizing a decentralized system, there is a strong need to embed intelligence at the ‘edge of the network’. These intelligent devices, capable of sensing, local data processing and exerting control actions, report only actionable information to the cloud, acting as an edge control node. The system can then function autonomously, without constant cloud inputs, tolerating longer delays in communication, making the overall system ultra-low cost. The Global Asset Monitoring, Management and Analytics (GAMMA) Platform is a novel ultralow- cost, secure platform that operates through a Bluetooth based delay tolerant network. It relies on so-called ‘data mules’ to bridge the last mile connectivity gap in an inherently secure way. Due to this model, the platform requires no in-country certifications, does not rely on a dedicated backhaul technology and is immune to technology migration. This architecture also addresses some gaps identified in traditional IoT-based solutions in remote areas and sparse connectivity. A functional unit of the edge computing node has been built, taking into account various constraints like costs, customizations, data storage, cybersecurity and power management. Here, the platform has been built, deployed and has demonstrated distributed smart grid applications like power quality sensing, automated metering infrastructure and utility asset monitoring.

42 ENGINEERING↗

DOE OSTI2019

GADRAS-DRF Version 18 User's Manual

The Gamma Detector Response and Analysis Software Detector Response Function (GADRAS-DRF) application computes the response of gamma-ray and neutron detectors to incoming radiation and provides analysis on measured spectra. This manual provides step-by-step procedures to acquaint new users with the use of the application. The capabilities include characterization of detector response parameters, plotting and viewing measured and computed spectra, analyzing spectra to identify isotopes, estimating source energy distributions from measured spectra, and creating inject data. GADRAS-DRF can compute and provide detector responses quickly and accurately, giving users the ability to obtain usable results in a timely manner (a matter of seconds or minutes).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Uranium Holdup Monitoring with Compton Imaging as Function of Depth and Mass

Material Control and Accountability (MC&A) programs track masses of materials flowing through production processes, where some material remains in process equipment as holdup. Quantification of these masses using gamma emissions typically involves usage of a well characterized radiation detector and assumptions of geometric configuration to constrain detection efficiencies, where the Generalized Geometry Holdup (GGH) method is often used. Uncertainties on the order of ±50% are observed, where the difficulties arise based on the asymmetric and gradient distributions of material that do not fall within the bounds of GGH. Gamma imagers provide a possible means to improve this geometric knowledge. This work describes the process used in creating a series of mass standards to aid the development of imaging algorithms for quantification.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Three-State Majority-vote Model on Scale-Free Networks and the Unitary Relation for Critical Exponents

Abstract We investigate the three-state majority-vote model for opinion dynamics on scale-free and regular networks. In this model, an individual selects an opinion equal to the opinion of the majority of its neighbors with probability 1 − q , and different to it with probability q . The parameter q is called the noise parameter of the model. We build a network of interactions where z neighbors are selected by each added site in the system, a preferential attachment network with degree distribution k − λ , where λ = 3 for a large number of nodes N . In this work, z is called the growth parameter. Using finite-size scaling analysis, we obtain that the critical exponents $$\beta /\bar{\nu }$$ β / ν ¯ and $$\gamma /\bar{\nu }$$ γ / ν ¯ associated with the magnetization and the susceptibility, respectively. Using Monte Carlo simulations, we calculate the critical noise parameter q c as a function of z for the scale-free networks and obtain the phase diagram of the model. We find that the critical exponents add up to unity when using a special volumetric scaling, regardless of the dimension of the network of interactions. We verify this result by obtaining the critical noise and the critical exponents for the two and three-state majority-vote model on cubic lattice networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

$\gamma$-ray angular correlations, distributions and linear polarization in tracking arrays

With $\gamma $-ray tracking arrays, the angular correlation and, especially, the linear polarization of $\gamma $ rays can be measured with high precision. However, because of the complexity of these spectrometers, measuring angular distributions is more involved. The techniques and associated formalisms were developed and established in the 1950s. The experimental setups of that era were relatively simple when compared to the advanced $\gamma $-ray tracking arrays available today. This paper aims to review and refine these techniques, unify the nomenclatures and, specifically, adapt them for use with the newest tracking arrays. In addition, new methods for producing the required response functions for these arrays are introduced.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Methodology for inferring reactor core power distribution from an optical fiber based gamma thermometer array

Here, a 4-step data analytic methodology has been devised for the purpose of inferring the distribution of power in a reactor core, based on the response of an array of optical fiber based gamma thermometers (OFBGTs). This data analytic methodology is crucial for the development of a system of OFBGTs for the purpose of calibrating local power range monitors in boiling water reactors. Such a system would be an improvement to the present calibration system in boiling water reactors, in terms of safety, efficiency, and permanence. The first step of this methodology is to establish an energy balance method. In this method, one uses MCNP to determine response functions, which allow one to convert from gamma thermometer response to power. The gamma thermometers and the reactor core are segmented, such that each gamma thermometer segment provides an estimate of power for each reactor core segment. The estimates of power for the reactor core segments (hereafter referred to as fuel assembly segments) are calculated based on the measured response of the gamma thermometers. The second step of the methodology is to employ a weighting scheme to combine the estimates of the power of the various fuel assembly segments, based on the response of the various OFGBT segments and the incremental dose rates of the various fuel assembly segments to the OFBGT segments. The third step is to iteratively calculate the estimates of the power of the fuel assembly segments, until a convergence criterion is met, which indicates that the calculation has converged. The fourth and final step of the methodology is to estimate the uncertainty of the power for each fuel assembly segment. The mathematical basis for this step is not the focus of this paper. We have used a 3-D homogeneous reactor model to demonstrate the data analytic methodology; and have found that the data analytic methodology operates as intended.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

RadSim: Math, Utility & RTK

This package includes three parts, (1) gov.llnl.math, (2)gov.llnl.utility and (3)gov.llnl.rtk, which are utilized in the development of Radiation Detector Simulator (RadSim) project. RadSim is being developed to provide the capability to: (1) simulate radiation source emissions, (2) interpolate results from radiation transport tools into a common format to prepare incident flux, and (3) model radiation detector response to rapidly produce synthetic radiation measurement templates. RadSim is targeted for open-source release, which will enable researchers and industry partners to model gamma-ray detectors response to simulated flux from the transport tool of their choice. The techniques and implementation will be entirely transparent, which will allow for improvements and boutique modifications by future researchers beyond the lifespan of this specific project. The first tool of the package, gov.llnl.math, includes classes and functions to define and perform basic math operations. Some of the example features available in the package include defining statistical distributions and performing algebra and matrix operations, all of which are already accessible on publicly available software packages such as MATLAB and ROOT. The second package gov.llnl.utility includes tools commonly used to enable optimization and readability of various data structures such as Java lists and external xml files. Lastly, the gov.llnl.rtk package includes classes and functions to implement methods commonly used in radiation physics, such as data structures to represent and characterize photon spectra and tools to apply well-defined and published methods to calibrate a given spectra.

Cheung, Hoi Sing↗