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Thermal neutron scattering cross sections for amorphous carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm{sup 3}. From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical optical peak at 0.25 eV for the ideal graphite disappears for amorphous carbon, in good agreement with the expected structure. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Deployment of neural-network-based neutron microscopic cross sections in the Griffin reactor physics application

The capability to utilize neural networks to predict macroscopic and microscopic cross section parametric spaces has been developed for the Griffin reactor physics application. The LibTorch interface enables Griffin's MOOSE-based materials to interact with LibTorch-trained models, allowing for the evaluation of complex macroscopic or microscopic cross section spaces, which are then used to evaluate the neutronic properties of the Griffin finite element model. This study benchmarks traditional ISOXML-formatted tabulation libraries against neural network-based models for 279 nuclides on 20,160 grid points for zero-dimensional and two-dimensional reactor models. Benchmark metrics include the fundamental mode eigenvalue, fission and absorption rates, and various temperature coefficients of reactivity (isothermal, fuel, and moderator). From the perspective of storage space, the complete set of LibTorch models uses 11 MB on disk, compared to the 10 GB for the ISOXML multigroup library that covers the same grid space. For the two-dimensional performance case considered in Griffin, the Torch model uses 97% less RAM than the reference ISOXML dataset while runtime increases by a factor of 3 when using the LibTorch model compared to the ISOXML dataset with multi-linear interpolation. The LibTorch model consistently yields errors within 0.01% for most analyzed quantities except for the temperature coefficients of reactivity where the maximum discrepancies are up to 0.3 $\frac{pcm}{K}$. Due to the neural network attempting to best predict quantities with no regard for a positive or negative bias for any given quantity, predictions may experience random fluctuations, resulting in both positive and negative errors. Future work will entail both depletion and coupled transient analysis to determine the predictive capabilities of Griffin with neural network-based cross sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Enhancement of sub-thermal neutron flux through cold polyethylene

Total thermal neutron cross section measurements serve as the primary means of validation for thermal neutron scattering kernels, an important quantity for neutron transport calculations. In an effort to improve the quality of thermal neutron scattering kernels, researchers at Rensselaer Polytechnic Institute (RPI) designed and constructed a polyethylene based cold moderation system to enhance neutron flux below 10 meV when coupled with the Enhanced Thermal Target (ETT) at the RPI Gaerttner LINAC. The final design yielded an increase in sub-thermal neutron flux (below 10 meV) by a factor of 4.5 for a moderator temperature of 37.5 K relative to the ETT alone. A further increase to a factor of 6 is expected after a minor geometry modification and decrease in polyethylene temperature to 25 K. This novel capability will be used to conduct total thermal neutron cross section measurements from 0.0005–10 eV for different materials including moderator materials.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Thermal Neutron Scattering Cross Sections for Graphitic Amorphous Carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm 3 . From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical features and the optical graphitic peak at 0.25 eV for the ideal graphite DOS disappear for graphite-like amorphous carbon, which shows good agreement with the expected structure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Neutrons in MINERvA and the Antineutrino Multi-Neutron Production Cross Section

Neutrinos are among a handful of particles in the Standard Model of particle physics whose properties have not yet been fully measured. Neutrino oscillations, discovered in the late 1990s, still have yet to be fully characterized. Early evidence suggests that neutrinos and antineutrinos may undergo neutrino oscillations differently. So, multiple collaborations are building and operating kTon-scale particle detectors to try to measure this CP violation in the neutrino sector of the Standard Model. Measuring neutrino and antineutrino energies is essential to characterizing oscillation phenomena. But neutrons interfere with (anti)neutrino energy measurements because they are hard to detect in (anti)neutrino detectors. Furthermore, there are very few measurements of neutrons produced by (anti)neutrinos in the energy range of interest to accelerator-based oscillation experiments. The MINERvA collaboration initially tried to fill this gap by measuring the rate of neutron-induced activity i n plastic. The data deviated significantly from leading model predictions, but it could not be determined which models needed to be tuned. MINERvA’s first neutron counting result also cannot be compared to future models because it was not suitable for unsmearing. This thesis first expands upon MINERvA’s first foray into neutron detection at higher antineutrino energy. Neutron detection efficiency is enhanced by advances in analysis algorithms. Then, an unsmeared cross section for producing two or more neutrons is measured. Existing antineutrino interaction models again over-predict the rate of neutron production by antineutrinos. Preliminary neutron production rate measurements in MINERvA’s iron and lead targets suggest that models are also over-predicting neutron production in heavier nuclei.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Stellar s-process neutron capture cross sections on 78,80,84,86 Kr determined via activation, atom trap trace analysis and decay counting

We present a detailed account of neutron capture experiments of astrophysical relevance on 78,80,84,86 Kr (n, γ) reactions at the border between weak and main s process. The experiments were performed with quasi-Maxwellian neutrons from the Liquid-Lithium Target (LiLiT) and the mA-proton beam at 1.93 MeV (2-3 kW) of the Soreq Applied Research Accelerator Facility (SARAF). The setup yields high-intensity approximate to 40 keV quasi-Maxwellian neutrons (3-5 x10 10 n/s) closely reproducing the conditions of s-process stellar nucleosynthesis. A sample of 100 mg of atmospheric, pre-nuclear-age Kr gas contained in a Ti spherical shell was activated in the LiLiT neutron field. The abundances of long-lived Kr isotopes ( 81,85g Kr) were measured by atom counting via atom trap trace analysis (ATTA) at Argonne National Laboratory and low-level counting (LLC) at University of Bern. This work is the first measurement of a nuclear cross section using atom counting via ATTA. The activities of short-lived Kr isotopes ( 79,85m,87 Kr) were measured by gamma-decay counting with a high-purity germanium detector. Maxwellian-averaged cross sections for s-process thermal energies are extracted. By comparison to reference values, our nucleosynthesis network calculations show that the experimental cross sections have a strong impact on calculated abundances of krypton and neighboring nuclides, in some cases improving agreement between theory and observations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Calculation of the Thermal Neutron Scattering Cross-Section of Solids Using OCLIMAX

The thermal neutron scattering cross-section of a solid depends on the energy (or wavelength) of the incident neutrons. Devising a method to calculate the energy dependence from first principles, without the approximations built in the scattering theory, has been a major undertaking in nuclear engineering. Here, we demonstrate such a calculation method using the program OCLIMAX. In this work, our approach eliminates various approximations and limitations involved in a regular calculation with the LEAPR module of NJOY code, and the results are compared with available experimental and theoretical data. It is also demonstrated how additional insight can be obtained from the calculated full dynamical structure factor. The results reported here show the great potential and excellent platform provided by OCLIMAX for future development in the study of neutron thermalization in solid materials for different applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bayesian Monte Carlo Evaluation Framework for Imperfect Data and Models [Abstract]

Nuclear data evaluation methods conventionally 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 for minimization of a cost function (even for non-linear models); and that both the model (of, e.g., neutron cross section) and experimental data (including their covariance data) are perfect. These assumptions are inherent to the well-known generalized linear least squares (GLLS) minimization method commonly used for evaluations of resolved resonance region (RRR) neutron cross sections. However, these assumptions are often not justified due to the presence of non-normal PDFs, non-linear models (e.g. R -matrix formalism), and inherent imperfections in data and models (e.g. discrepant data sets, discrepancies between the previous evaluation and newly measured data, or imperfect covariance data). We remove the said assumptions in a mathematical framework of Bayes’ theorem, and implement it using the Metropolis-Hastings Monte Carlo method. Parameters of a new kind are introduced to parameterize inherent imperfections, e.g. , any discrepancies between the theoretical model and measured data. These new parameters enable evaluators to quantify their expert judgement about any discrepancies or imperfections in a reproducible manner. We demonstrate the framework with an ongoing evaluation of 233 U in the eV region using the ENDF-B/VIII library and transmission data measured by Guber, et al. , and compare the posterior parameters to those obtained by conventional evaluation methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Uncertainty Analysis for a Criticality Benchmark [Slides]

This presentation discusses how KRUSTY was analyzed with LANL’s MCNP neutron transport code, Monte Carlo N-Particle. In the Monte Carlo method, neutrons are born in fission events and fly around the geometry having events (e.g., scatter, capture, fission, escape) according to the natural probabilities. “Natural probabilities” are given as neutron cross sections , which are measured and evaluated nuclear data. One of the goals of the benchmark project is to improve the nuclear cross sections (and the codes that use them). In this work, the response of interest is called k eff , which describes the neutron multiplication in a near critical system. Like most quantities, k eff is not measured directly; it is only inferred. In summation, MCNP results for k eff matched the measurements extremely well. The evaluated uncertainties are asymmetric and smaller than 0.00100 (e.g., + 0.00080 / – 0.00062). The largest uncertainties are due to alignment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Uncertainty Analysis for a Criticality Benchmark [Slides]

This presentation discusses how KRUSTY was analyzed with LANL’s MCNP neutron transport code, Monte Carlo N-Particle. In the Monte Carlo method, neutrons are born in fission events and fly around the geometry having events (e.g., scatter, capture, fission, escape) according to the natural probabilities. “Natural probabilities” are given as neutron cross sections , which are measured and evaluated nuclear data. One of the goals of the benchmark project is to improve the nuclear cross sections (and the codes that use them). In this work, the response of interest is called k eff , which describes the neutron multiplication in a near critical system. Like most quantities, k eff is not measured directly; it is only inferred. In summation, MCNP results for k eff matched the measurements extremely well. The evaluated uncertainties are asymmetric and smaller than 0.00100 (e.g., + 0.00080 / – 0.00062). The largest uncertainties are due to alignment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Uncertainty Quantification and Sensitivity Analysis of Non-Nuclear Advanced Controls Testbed Reactor Mockup

The research presented in this report describes our progress in applying stochastic methods and uncertainty quantification, parametric study, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated with Griffin, with the goal of developing a reduced order (surrogate) model which can be rapidly sampled while perturbing multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums, which are controlled by a hybrid proportional, integral and derivative (PID) controller, actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time and $\beta$ from a transient Griffin simulation executed with the improved quasi-static method to provide the kinetic parameters) as inputs to functions which control the CD rotation angle. Using a number of stochastic method approaches, we developed a dual purpose training-surrogate model of the NTP system using polynomial regression. The trained model can be rapidly sampled while simultaneously perturbing various input parameters of the model, such as coefficients on the PID control, or temperature (directly affect the neutron cross section). The surrogate model delivers accurate results orders-of-magnitude faster (minutes, not days) than the base model. Once the base model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs and their effect on the output. For example, coefficients used in the PID control system may vary due to some physical interference, or there may be uncertainty in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters and operational boundaries can be determined. The goal of this work is to support development of an advanced control system to operate CDs in a functioning NTP system.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence

The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [ β eff ] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

147 Sm Neutron Capture Cross Section and Resonances

Measurement of ( n,γ ) cross sections measurements are of high importance to many fields such as radiochemical diagnostics, technical nuclear forensics, nuclear physics and astrophysics, nuclear criticality safety, advanced reactors, and isotope production. For these applications an accurate characterization of the resonances in the resolved resonance region is important. In the energy range of the resonance region neutron capture, and scattering are possible so the total resonance width Γ is the sum of the gamma and neutron widths Γ = Γ γ +Γ n .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Reduced-order modeling for efficient cross section library development in high-temperature gas reactor pebble-bed depletion analysis

Accurate modeling of running-in and equilibrium conditions in pebble-bed reactors (PBRs) requires precise microscopic multigroup neutron cross sections. In Griffin, deterministic neutronics calculations rely on multivariate interpolation over large cross section libraries, resulting in significant memory usage and performance bottlenecks. This work, together with a companion paper on Griffin integration, explores reduced-order models (ROMs) to replace interpolation with lightweight surrogates. Several ROM techniques are benchmarked, with deep neural networks (DNNs) demonstrating superior memory efficiency, scalability, and predictive accuracy. A total of 295 DNNs were trained to build a comprehensive isotope library, integrated into Griffin through a custom LibTorch interface for depletion analysis. Initial results demonstrate that DNN-based ROMs drastically reduce memory demands while preserving accuracy, enabling finer tabulations and additional state variables without overhead. In conclusion, the framework also supports online cross section generation and real-time DNN updates through transfer learning, improving fidelity by capturing self-shielding and evolving nuclide compositions during burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

R-Matrix Analysis of the Neutron-Induced Cross Sections on 143 Nd Measured at LANSC [Slides]

An established use of R-Matrix codes is being implemented at LANSCE. There are unique features accessible with detectors at LANSCE that can be used to perform more complete R-Matrix analysis. Further, Spin separation is a powerful technique that can be applied in DANCE measurements. Additionally, a unique method to measure transmission with DICER is being undertaken. Transmission and capture data were analyzed in this work. The study can be extended to other channels. The results of the 143 Nd data are presented in this work. New resonances found in this work: 21 compared to ENDF/B-VIII.0 and JEFF-3.3, and 24 compared to JENDL-5. Wrong spin assignment in 23 resonances in ENDF/B-VIII.0, 25 in JEFF-3.3 and 26 in JENDL-5. The 143 Nd and 147,149 Sm have been analyzed. Exciting future for new measurements and analysis!

97 MATHEMATICS AND COMPUTING↗

Analysis of the time-of-flight neutron scattering cross-section data for light water measured at the SEQUOIA spectrometer, Spallation Neutron Source (SNS)

Thermal neutron scattering cross-section data for light water available in the major nuclear data libraries observes significant differences especially at reactor operating temperatures. During the past few years there has been a renewed interest in reviewing the existing thermal scattering models and generating more accurate and reliable thermal scattering cross sections using existing experimental data and in some cases based on Molecular Dynamics (MD) simulations. There is a need for performing new time-of-flight experiments at high temperatures and pressures, to have a better understanding of the physics involved in the scattering process that could help improve the existing TSL data.Lack of experimental thermal scattering data for light water at high temperatures led to a new measurement campaign within the INSIDER project at the Institut de radioprotection et de sûreté nucléaire (IRSN). Double differential scattering cross section for light water have been measured at the SEQUOIA spectrometer based at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory, United States. Several measurements have been carried out at different temperatures and pressures corresponding to liquid light water. Measurements at five different incident neutron energies Ei (8, 60, 160, 280 and 800 meV) have been carried out to help exploring different regions of the frequency spectrum. This paper presents the analysis of the dynamic structure factor and the derived frequency spectrum of light water. The analysis of the experimental data would provide one with better confidence, the behavior of thermal scattering cross sections for light water at high temperatures, knowledge of which is very important for the design of novel reactors as well as existing pressurized water reactors.

Jaiswal, V↗