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Reduced-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Abstract – Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING

The total neutron cross section of liquid and solid ammonia

Ammonia is a material of interest for future neutron moderators at high-power sources due to its high hydrogen density, low melting point, and resistance to polymerization in an intense radiation field. Its performance in such applications cannot currently be calculated due to the absence of suitable computer models for the interaction of neutrons with ammonia under relevant conditions. In an effort to develop suitable scattering kernels for computer simulations of moderator performance, we have conducted a series of Density Functional Theory and Molecular Dynamics calculations of the molecular-level thermal properties of ammonia at various temperatures within both the solid and liquid phases. In this paper, we compare computer calculations for the energy-dependent total neutron cross section of ammonia, based on these models, to experimental measurements of those cross sections at temperatures of 221 K, 180 K, and 35 K. The experimental data were collected over an energy range from 0.1 meV to 10 eV using time-of-flight techniques at the Low Energy Neutron Source (LENS) facility at Indiana University. This comparison provides a first validation in the development of thermal scattering libraries for Monte Carlo source design simulations based on liquid and solid ammonia. In conclusion, we also provide some insights into where additional development of tools for creating such models may be needed.

Ammonia

Advanced Cross Section Library Generation using Reduced Order Models

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING

Tables of Neutron Thermal Cross Sections, Westcott Factors, Resonance Integrals, Maxwellian Averaged Cross Sections, Astrophysical Reaction Rates, and r-process Abundances Calculated from the ENDF/B-VIII.1, JEFF-3.3, JENDL-5.0, BROND-3.1, and CENDL-3.2 Evaluated Data Libraries

We present calculations of neutron thermal cross sections, Westcott factors, resonance integrals, Maxwellian-averaged cross sections, astrophysical reaction rates, and solar system r-process abundances using the latest data from the major evaluated nuclear libraries for 849 ENDF target materials. The recent release of ENDF/B-VIII.1 library, progress in 252 Cf(SF) evaluation, extensive analysis of newly-evaluated neutron reaction cross sections, neutron covariances, and improvements in data processing techniques motivated us to calculate the nuclear industry and neutron physics parameters, produce s-process Maxwellian-averaged cross sections and astrophysical reaction rates, extract r-process abundances, systematically calculate uncertainties, and provide additional insights on currently available neutron-induced reaction data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Effects of shape/phase transition regions on neutron capture cross sections

Abstract A recent study found a new, purely empirical correlation between two-neutron separation energies and neutron capture cross sections in keV neutron energy regimes. In shape/phase transition regimes, such as that near A= 150, S $$_{2n}$$ 2 n values show an anomaly—a flattening of the normal near linear decrease with neutron number. This paper addresses two questions: (1) Using this new correlation, is this anomaly in S $$_{2n}$$ 2 n values sizeable enough to produce an observable effect in capture cross sections? and (2) Can the correlation be used to quantitatively reproduce the cross sections in the transition region? It is found that the answer to both questions is in the affirmative. Possible relations to the r -process are briefly discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Finite-Geometry Corrections for Neutron Scattering Cross Section Measurements

In this report, we describe the corrections necessary for neutron scattering cross section measurements in experiments which use finite-geometry scattering samples. A new Geant4 based framework was developed to calculate these corrections which has been benchmarked against a well-measured test case. This framework also calculates the outgoing neutron energy dependence of the correction factors, which is crucial when resolving individual final states in the scatterer is not possible.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Neutron Scattering Cross Sections: (n,n′), (n,n′γ), and (n,γ) Measurements (Final Technical Report)

This technical report discusses the outcomes from a grant to the University of Dallas in collaboration with the University of Kentucky, the United States Naval Academy and Mississippi State University to measure neutron cross sections and to provide educational opportunities in nuclear science for undergraduate and graduate students and postdoctoral scholars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Measurement of the 73 As ⁢(𝑛,𝛾) cross section at thermal neutron energies

A measurement of the thermal neutron capture cross section of 73 As (t 1/2 = 80.3 d) was performed utilizing the University of Missouri Research Reactor. Two sealed quartz tubes containing 73 As were prepared and characterized before being irradiated for ≈1 week. The resulting production of 74 As was quantified with γ-ray spectroscopy. Monitor foils of Fe, Zr, and Mo were irradiated alongside the 73 As samples to assess the thermal and resonance region neutron fluxes. In conclusion, the thermal 73 As ⁢(𝑛,𝛾) cross section was determined to be 56.1 ± 8.9 b based on the average of the two 73 As samples and represents the first neutron-induced reaction cross section measured on 73 As.

and nuclear chemistry

Investigating Gadolinium-Lined Sodium-Iodide Neutron Detectors for Mobile Applications

For enhancing the effectiveness of nonproliferation efforts in neutron detection, most portable instruments rely on 6 Li scintillators, 10 B-based detectors, or gas-filled 3 He proportional counters. Additionally, gamma-ray detectors based on scintillators and semiconductors are often employed for search applications to find radioactive material in the field. These systems typically include dedicated detectors along with separate high voltage supplies and processing electronics for the gamma-ray and neutron detectors. Ideally, a portable radiation detection system should be lightweight, compact, and cost-effective. In the field, scintillators can serve a dual purpose: (1) detecting gamma-rays and (2) detecting neutrons. Gamma-ray detection with scintillators is based on the interaction of gamma-rays within the scintillating material, whereas neutron detection depends indirectly on neutron capture events. These capture events generate conversion electrons and gamma-rays, which can interact with the scintillator. For enhancing neutron capture, the scintillator can be surrounded by neutron absorber materials with a high neutron cross section. The resulting secondary electrons and gamma-rays from neutron interactions, depending on the absorber material used, can then be analyzed to detect the presence of neutron sources. Similarly, semiconductor-based detectors can be employed along with neutron absorbers as liners for neutron detection. 158 Gd has a significantly larger neutron cross section than 3 He, commonly used in gas-filled proportional counters, as shown in Figure 1. For thermal (0.025 eV) neutrons, the absorption cross section of 158 Gd is 10,000 times greater than that of 3 He (refer to Figure 1). This feature makes naturally occurring gadolinium, which consists of 24.8% 158 Gd, a promising neutron absorber material for use in combination with gamma-ray detectors–yielding a hybrid detector–for neutron detection.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P

Extraction of neutron-capture cross sections on 92 Zr using the charge-exchange Oslo method

The 93 Nb (𝑡, 3 He ) reaction at 115 MeV/nucleon was studied to demonstrate that nuclear level densities and 𝛾-ray strength functions can be extracted from charge-exchange reactions at intermediate energies using the Oslo technique. The matrix of excitation energy in 93 Zr, reconstructed from the (𝑡, 3 He ) reaction, versus the energy of 𝛾 rays emitted by the excited 93 Zr nuclei, was obtained in an experiment with the S800 Spectrograph operated in coincidence with the GRETINA 𝛾 -ray detector. The extracted level density and 𝛾 -ray strength function obtained by applying the Oslo method to this matrix were used to estimate the 92 Zr⁢(𝑛,𝛾) ⁢93 Zr cross section by combining the new results with other experimental data and theoretical calculations for 𝐸⁢1 and 𝑀⁢1 strength functions at higher energies. Good agreement with direct measurements of the 92 Zr⁢(𝑛,𝛾)⁢ 93 Zr cross section was found. The contribution from the upbend in the extracted 𝛾-ray strength function was important to achieve the consistency, as the neutron-capture cross section without this contribution is significantly below the direct measurements otherwise. Since charge-exchange reactions at intermediate energies have long been used for extracting Gamow-Teller strengths, the successful demonstration of the charge-exchange Oslo method enables experiments in which (𝑛,𝛾) cross sections and Gamow-Teller strengths can be measured simultaneously, which is of benefit for astrophysical studies.

90 ≤ A ≤ 149

Measuring the Multi-Neutron Antineutrino Cross Section at Low Charged Hadron Energy in MINERvA

Current and future accelerator neutrino oscillation experiments need neutrino interaction models with smaller systematic uncertainties to resolve much of delta CP phase space. Final state interactions (FSI) and scattering off of correlated nuclei (2p2h) are poorly understood processes that currently contribute large uncertainties to leading models. These processes have proven difficult to study because they often produce relatively low energy nucleons. Protons up to about 100 MeV are below the detection threshold of some accelerator neutrino detectors, and neutrons are usually discounted as undetectable. This poster presents a measurement of the multi-neutron antineutrino cross section at low available energy using the MINERvA detector at Fermilab. This interaction channel is particularly sensitive to FSI and 2p2h interactions. A sideband-driven background constraint that greatly reduces uncertainties on the result will be presented. The measured cross section is compared to GENIE v3 models with different FSI treatments and the SuSA model's 2p2h predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Non-Neutron Transmutation of Used Nuclear Fuel (Final Report)

The primary goal of this study is to develop a national facility concept for transmuting long-lived fission products (LLFP) to substantially reduce the disposal impact by minimizing the need for a geologic-timescale repository. As a charter for this study, the national transmutation facility was required to reduce the radiotoxicity and decay heat of LLFP isotopes by at least 90% relative to their values at discharge from a commercial LWR, while consuming less than 10% of the reactor's energy. The identified LLFP isotopes are Se-79, Zr-93, Tc-99, I-129, Sn-126, and Cs-135, whose radiotoxicity is about 99% of the total radiotoxicity of all fission products at 1,000 years. Approximately ~72 kg of LLFPs is discharged every year from a 1,000 MWe commercial or advanced nuclear reactor. First, LLFP transmutation options with non-neutron beams (photons and protons) were explored. The study concluded that LLFP transmutation is feasible with high-energy, high-intensity photons or protons, but impractical on an engineering scale due to low transmutation rates and the high energy requirements to produce the desired photon or proton beams. As alternatives, LLFP transmutation options with neutrons from fission, fusion, and spallation reactions were additionally explored. The transmutation options using advanced critical reactors are attractive only for selective LLFP isotopes because the production rates of several LLFP isotopes (Zr-93, Sn-126, and Cs-135) from fission reactions are larger than the transmutation rates. The transmutation options with only spallation neutrons are favorable to transmute all LLFP isotopes, but as a tradeoff, the net transmutation rates are reduced. The national transmutation facility concept was developed following an exploration of transmutation options using various incident particles. The proposed national LLFP transmutation comprises a dedicated molten-salt reactor (MSR), a proton accelerator, and a spallation neutron-based transmuter. The MSR power was set at 300 MWt and 120 MWe, with the thermal power approximately 10% of that of a commercial 1,000 MWe PWR. The electricity generated by the MSR powers the accelerator and transmuter. The accelerator produces 1 GeV, 30 mA protons, which are introduced into the spallation neutron-based transmuter. The spallation neutron-based transmuter consists of a central spallation target and LLFP target pins merged in a heavy water tank. The six LLFP isotopes are separated into two groups. Tc-99, I-129, and Se-79, having larger neutron cross sections, belong to group A, while Zr-93, Sn126, and Cs-135, having smaller neutron cross sections, belong to group B. Then, for effective transmutation, LLFPs in groups A and B are transmuted in the dedicated MSR and in a spallation neutron-based transmuter, respectively. The estimated capital cost of the national transmutation facility is approximately $\$$3.1B, and its annual O&M cost is expected to be ~$\$$182M. Radiotoxicity and decay heat of LLFPs were calculated and compared with those of the original LLFPs. It was assumed that the targets were made with elementwise LLFP rather than isotopic LLFP, owing to the potentially high cost of isotopic separation from used nuclear fuels. The decay heat of LLFPs can be reduced by more than 90% using a single national transmutation facility. However, radiotoxicity decreases by 79–84%, which does not meet the transmutation performance requirement, primarily because Cs-135 is produced rather than depleted. Thus, to meet the design requirement, Cs-135 should be separated from other Cs isotopes and irradiated in a spallation neutron-based transmuter. Then, radiotoxicity decreases by ~92%.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

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

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