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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Formulation of the density eigenvalue problem in neutron transport for relevant engineering applications

A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

P{sub N} source expansion nodal method in MPACT for boiling water reactors

This paper describes the one-node P{sub N}-Source Expansion Nodal Method (SENM) axial solver for the 2D/1D method recently implemented in MPACT to support Boiling Water Reactors (BWR) analysis. Since the BWR has a more complicated design and strong burnable absorber, the existing PN-Nodal Expansion Method (NEM) axial solver in MPACT may not be sufficient to accurately represent the intranodal flux and source profiles for BWRs. The one-node P{sub N}-SENM has been implemented in this work to reduce the axial spatial discretization error for BWRs. From numerical results, we verify that the P{sub N}-SENM can improve the accuracy of the pin power prediction, and confirm that P{sub N}-SENM can use more than a 1.5 times larger axial mesh size than P{sub N}-NEM to have similar accuracy for the BWR GE14 3D assembly problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

The MP{sub N} method: a new angular discretization method based on piecewise polynomial interfaces fluxes

In transport calculations, it is well known how S{sub N} method is extremely inefficient in problems where the particle physics is dominated by streaming. The ray-effect eventually produced by the insufficient angular discretization, appears to be extremely persistent with respect to the refinement of the angular quadrature. The MP{sub N} method, that relies on continuous angular representation, offers a robust remedy to such an issue. MP{sub N} is based on the decomposition of the unit sphere into solid angles and on a piecewise continuous definition of interface fluxes, which are expanded in polynomials in each solid angle. This allows propagating more than one angular degree of freedom simultaneously while maintaining unaltered the block-diagonal pattern of the displacement plus removal operator. The method is therefore well suited for the flux resolution by means of a conventional sweep algorithm. Furthermore, unlike the S{sub N} method, MP{sub N} does not rely on discrete directions and, thus, on an angular quadrature formula, but rather constructs a set of linear equations solving for the angular moments of the flux for all discrete solid angles within the sweep. MP{sub N} shows an error convergence rate higher than S{sub N} at the expense of an increased size of the coefficient matrices, so of the computational cost. Although MP{sub N} is not free from ray-effect, the latter is effectively mitigated and less persistent with respect to the increase of the angular refinement order. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Investigation of methods for targeted search of dominant higher modes in subcritical systems

The reactor physics modeling of subcritical systems requires a substantially different approach from that of a critical reactor due to the presence of the so-called higher modes. Earlier investigations showed that the dominant higher modes lie in the inner part of the eigenvalue spectrum, making the conventional eigenvalue searches unfeasible and calling for a targeted search. This paper investigates the possibility of targeted and multitudinous eigenvalue calculation by testing the Krylov-Schur and the Dynamic Modes Decomposition (DMD) method for simple, analytically tractable problems. While the DMD method clearly showed its efficiency in a one-group homogeneous problem, modal analysis of a three-dimensional reflected reactor in two-groups approximation demonstrated that the increasing complexity poses challenges for both methods. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Investigating the AGN-201M research reactor's unique dominance ratio

The AGN-201M reactor is a small, thermal spectrum reactor located at the University of New Mexico (UNM). It is moderated by polyethylene, reflected by graphite, with fuel comprised of uranium microspheres embedded in polyethylene plates that are separated by an aluminum baffle. The dominance ratio of a multiplying system is the ratio of the first higher-mode eigenvalue to the fundamental, k{sub 1}/k{sub 0}. It is a key parameter in characterizing the rate of convergence, analyzing system stability, and determining how tightly coupled the system's neutron fission is. The purpose of this paper is to investigate the system's unusually low dominance ratio of 0.632. This investigation varied the reactor's physical parameters, such as the fuel geometry, fuel density, and reflector thickness, and examined their impact on the reactor's dominance ratio. Additionally, this study examined neutronically similar systems in hopes of identifying common causes for systems with low dominance ratios. The reason why the dominance ratio of the reactor is small compared to larger thermal reactors was determined to be because of its significantly smaller geometry and the composition of the fuel plates. The reflector's effect on the dominance ratio is small in comparison to the other factors, but was found to have a non-zero effect. Furthermore, the AGN-201M was found to have a significantly lower dominance ratio than systems in which it shares a very high (c{sub k} >95%) degree of neutronic similarity.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

LA17-V-InverseRadTransportProblem-PD2Kb. Final Project Report

In the inverse radiation transport problem, a radiation signal emanating from an unknown object is used to reconstruct geometric and material parameters of the object , e.g., the mass of special nuclear material (SNM), the isotopic composition of the SNM (e.g., the enrichment of 235U), the thickness of shielding, etc. The inverse radiation transport problem is one of the most fundamental and important in the emergency response mission, and has been addressed in previous NA-22 and NA-42/84 investments by using derivative-free optimization methods. Our project was aimed at (i) consolidating previous work by applying polynomial chaos expansion (PCE) for reducing significantly the number of forward model simulations required by derivative-free optimization methods; (ii) developing a general-purpose framework and stand-alone software for solving the inverse radiation transport problem by applying a new “predictive modeling” methodology (predictive modeling of coupled multi-physics systems, PM_CMPS) which enables the fusing of experimental and computational information; and (iii) developing several benchmarks (for unscattered gamma rays) for demonstrating the quantification of non-Gaussian features (e.g., skewness and kurtosis, which characterize asymmetries and long tails) of response distributions by deterministically and efficiently propagating parameter uncertainties (covariances and higher-order moments, where available) using high-order sensitivities computed by the recently developed comprehensive adjoint sensitivity analysis methodology (C-ASAM). With regard to (i), application of PCE, the most significant accomplishment of this project was an implementation of PCE into INVERSE that significantly reduced computation time for the DiffeRential Evolution Adaptive Metropolis (DREAM) and Differential Evolution (DE) methods. For inverse transport problems with measurements of neutron leakage, neutron multiplication, and neutron-induced gamma-rays, the solution times for the DREAM and DE methods were reduced by factors of 30-300, reducing run times from hours to minutes while maintaining the same accuracy as the standard (non-PCE) DREAM and DE. Speedups were further improved by exploring sparse grid quadrature sets using the Toolkit for Adaptive Stochastic Modeling and Non-Intrusive ApproximatioN (Tasmanian) toolset. An initial exploration of sparse grids indicated that further speedups factors of 5-10 are obtainable. The implementation of PCE in INVERSE is not in a form that users can easily access. With regard to (ii), solving the inverse problem using a predictive modeling paradigm, the most significant accomplishment of this project were the derivation and implementation of adjoint-based second derivatives in neutron and photon transport theory. There are two codes that compute these derivatives. SENSPG computes them for uncollided gamma rays and SENSMG computes them for neutron leakage. SENSMG is open-source code available on github. Other significant accomplishments included a stand-alone code, MULTI-PRED, that implements the predictive modeling paradigm, along with a detailed manual. The code was implemented in the existing INVERSE code for inverse problems, but a head-to-head comparison of inverse methods was not achieved. We also derived and implemented the capability to compute sensitivities for multiplicity measurements into the SENSMG code, and this capability was used in a data assimilation application, but it was not used for solving inverse problems. With regard to (iii), developing benchmarks to demonstrate the importance of high-order sensitivity and uncertainty analysis, the most significant accomplishment of this project were two test problems that showed how important second-order sensitivities are.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS1970

FASTER 3: A generalized-geometry Monte Carlo computer program for the transport of neutrons and gamma rays. Volume 1: Summary report

The theory used in FASTER-III, a Monte Carlo computer program for the transport of neutrons and gamma rays in complex geometries, is outlined. The program includes the treatment of geometric regions bounded by quadratic and quadric surfaces with multiple radiation sources which have specified space, angle, and energy dependence. The program calculates, using importance sampling, the resulting number and energy fluxes at specified point, surface, and volume detectors. It can also calculate minimum weight shield configuration meeting a specified dose rate constraint. Results are presented for sample problems involving primary neutron, and primary and secondary photon, transport in a spherical reactor shield configuration.

Jordan, T. M.↗
DOE OSTI2021

Informing nuclear physics via machine learning methods with differential and integral experiments

Information from differential nuclear-physics experiments and theory is often too uncertain to accurately define nuclear-physics observables such as cross sections or energy spectra. Integral experimental data, representing the applications of these observables, are often more precise but depend simultaneously on too many of them to unambiguously identify issues in the observable with human expert analysis alone. Here, we explore how we can leverage physics knowledge gained from differential experimental data, nuclear theory, integral experiments, and neutron-transport calculations to better understand nuclear-physics observables in the context of the application area represented by integral experiments. We support this task with machine-learning methods to discern trends in a large amount of convoluted data. Differential and integral information was used in an analysis augmented by the random forest and the Shapley additive explanations metric. We chose as an application area one that is represented by criticality measurements and pulsed-sphere neutron-leakage spectra. We show one representative example ( 241 Pu fission observables) where the combination of differential and integral information allowed to resolve issues in data representing these observables. As a starting point, the machine learning (ML) algorithms highlighted several observables as leading potentially to bias in simulating integral experiments. Differential information, paired with sensitivity to integral quantities, allowed us then to pinpoint one specific observable ( 241 Pu fission cross section) as the main driver of bias. The comparison to integral experiments, on the other hand, allowed us to indicate a likely reliable experiment among several discrepant ones for this observables. In other cases (e.g., 239 Pu observables), we were not able to resolve the confounding introduced by integral experiments but instead highlighted the need for targeted new experiments and theory developments to better constrain the nuclear-physics space for the application area represented by integral experiments. We were able to combine information from differential experimental data, nuclear-physics theory, integral experiments, and neutron-transport simulations of the latter experiments with the help of the random forest algorithm and expert judgment. This combination of knowledge allows to improve our description of nuclear-physics observables as applied to a particular application area.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Setup and verification of a SCALE/KENO platform for generic FHR benchmark calculations

The work presented in this article is preliminary to downstream analysis of a generic fluoride salt-cooled high-temperature reactor (gFHR) core performed by the University of Tennessee in collaboration with Kairos Power (KP). A Monte Carlo transport model of the publicly available gFHR equilibrium core is developed in SCALE/KENO with multigroup energy treatment. Several output quantities of interest are used to verify the simulations against a benchmark model developed by KP using the continuous energy Monte Carlo code Serpent 2. Good agreement is seen in flux and fission rate profiles with a maximum relative difference of 1.4% and 2.8% respectively. Furthermore, an effective multiplication factor bias of 44 pcm was observed between the two simulations. The fuel temperature reactivity coefficient calculated with SCALE is within uncertainty to the reference model. This verification acts as a publicly reproducible benchmark for the gFHR in SCALE/KENO. A simplified depletion model is also presented where a single fuel pebble is depleted to discharge burnup through the equilibrium core while the equilibrium core is assumed to be invariant. This method produces results that intercept the equilibrium core concentrations in every case, however, an interesting artifact of this particular depletion model is uncovered. The phenomenon is shown to be a fundamental feature of the differential rate equations and inspires questions about how this system behaves when the time evolution of the equilibrium core is considered. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Validating first-principles phonon lifetimes via inelastic neutron scattering

Phonon lifetimes are a key component of quasiparticle theories of transport; yet first-principles lifetimes are rarely directly compared with inelastic neutron scattering (INS) results. Existing comparisons show discrepancies even at temperatures where perturbation theory is expected to be reliable. In this paper, we demonstrate that the reciprocal space voxel (q voxel), which is the finite region in reciprocal space required in INS data analysis, must be explicitly accounted for within theory in order to draw a meaningful comparison. Here, we demonstrate accurate predictions of peak widths of the scattering function when accounting for the q voxel in CaF 2 and ThO 2 . Passing this test implies high fidelity of the phonon interactions and the approximations used to compute the Green's function, serving as a critical benchmark of theory and indicating that other material properties should be accurately predicted, which we demonstrate for thermal conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Single pair of Weyl nodes in the spin-canted structure of EuCd 2 As 2

We report time reversal symmetry breaking Weyl semimetals are unique among Weyl materials in allowing the minimal number of Weyl points, thus offering the clearest signatures of the associated physics. Here we present neutron diffraction, density-functional theory, and transport measurement results which indicate that EuCd 2 As 2 , under ambient field, strain, and pressure, is such a material with a single pair of Weyl points. Our work reveals a magnetic structure (magnetic space group C2'/m') with Eu moments pointing along the [210] direction in plane and canted ~ 30° out of plane. Density functional theory calculations using this structure show that the observed canting drastically alters the relevant electronic bands, relative to the in-plane order, leading to a single set of well-defined Weyl points. Furthermore, we find the canting angle can tune the distance of the Weyl points above the Fermi level, with the smallest distance at low canting angles. Finally, transport measurements of the anomalous Hall effect and longitudinal magnetoresistance exhibit properties indicative of a chiral anomaly, thus supporting the neutron scattering and DFT results suggesting EuCd 2 As 2 is close to the ideal situation of the Weyl hydrogen atom.

36 MATERIALS SCIENCE↗
NASA NTRS1975

Modulation and diffusion theory of cosmic rays

Papers given on the modulation of galactic cosmic rays by the solar wind at the 14th International Cosmic Ray Conference are reviewed. Some of the topics treated in this review are Pioneer and Helios radial gradient measurement, heliolatitude effects in modulation models, diffusion (scattering) theory - including pitch angle diffusion diagrams - solar flare particle transport theory and cosmic ray fluctuations at neutron monitor energies.

Forman, M. A.↗
DOE OSTI2022

Investigations about iso-geometric analysis for self-shielding calculations with the subgroup method

The implementation of a self-shielding method for a neutron transport calculation code based on the iso-geometric analysis (IGA) method that can resolve the multi-group neutron transport equation for arbitrary spatial domain, is presented. The self-shielding model based on the subgroup theory is adopted because the subgroup method can be used to perform calculations for any arbitrary geometrical domain which is the main purpose of our IGA code. Some basic theory of the subgroup method is given. A self-shielding calculation based on the PWR fuel pin composed of MOX fuel is presented and compared with a Monte Carlo calculation. The result is that the combination of SN transport theory, IGA and the subgroup method gives correctly shielded cross sections. Validation of the combination of the IGA method and SN neutron transport for subgroup calculations in two steps are presented: the first step is to ascertain the correctness of the IGA solutions compared to a known analytical solution in diffusion theory; the second step is a validation of the IGA solutions compared to a reference calculation in SN transport theory. The relation between the settings for the IGA solver and the accuracy of the results are elucidated. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Electronic and magnetic properties of hole-doped topological kagome Fe 1−𝑥 ⁢Mn 𝑥 ⁢Sn thin films

We have investigated the electronic and magnetic structures of topological kagome Fe 1−𝑥 ⁢Mn 𝑥 ⁢Sn (0 ≤ 𝑥 ≤ 0.3) thin films via neutron diffraction, electronic transport measurements, and ab initio density functional theory (DFT) to understand the interplay between hole doping, magnetism, and the electronic structures. Temperature-dependent neutron diffraction measurements on parent FeSn reveal the Néel temperature to be 𝑇 N ∼ 355 K and the underlying A-type antiferromagnetic ordering is associated with a wave vector 𝒒 = (001/2). Upon Mn doping to 𝑥 = 0.15, 𝑇 N decreases slightly while the magnetic ordering vector remains the same. Resistivity measurements show metallic characteristics and in-plane anisotropy down to 10 K for all the investigated samples. The effects of hole doping are mapped in terms of electronic ground state calculations via DFT which show that the Dirac point is moved closer to the Fermi level (𝐸 F ) and the flat bands get pushed away from 𝐸 F upon hole doping. However, a comparison between hole-doped Fe 1−𝑥⁢ Mn 𝑥⁢ Sn and electron-doped Fe 1−𝑥 ⁢Co 𝑥 ⁢Sn indicates that the Néel temperature does not scale with the position of 𝐸 F relative to the flat band. Furthermore, our results establish the antiferromagnetic state of FeSn and Fe 1−𝑥 ⁢Mn 𝑥⁢ Sn films at room temperature, laying the groundwork for future studies of magnetism in kagome heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Room temperature sodium diffusion in sodium iron phosphate investigated with neutron scattering

Sodium iron phosphate, Na x FePO 4 , is currently one of the most promising cathode materials for sodium ion batteries. Here we employ a systematic approach using three neutron scattering techniques to investigate temperature dependent properties with a focus on the charge transfer processes. Two distinct Na + diffusive motions are observed with quasielastic neutron scattering, including room temperature motion. These processes correspond to rapid double jumps through extrinsic vacancy sites of ∼6 Å along with the more fundamental nearest neighbor jumps of 3.1 Å. Experimental observations of room temperature ionic diffusion are highly desirable, as the diffusion pathways are naturally well suited for efficient transport. Inelastic neutron scattering was used to probe the vibrational density of states that assist in the ionic and electronic (polaronic) transport processes, which are further supported with density functional theory. Neutron diffraction examines the disordering of the sodium sublattice upon transition to the solid-solution phase, which is believed to enhance the overall kinetics during sodium insertion/extraction. Finally, 57 Fe Mössbauer spectroscopy measurements probes polaron hopping and the local structural evolution that modifies the electron density surrounding the redox active iron sites. This study sheds light on the temperature induced atomic scale dynamics that occur in olivine Na x FePO 4 .

Novak, Eric [Swarthmore College, Swarthmore, PA (U↗
DOE OSTI2022

A quick introduction to linear transport phenomena

The goal of this report is to provide an introductory-level overview of the linear Boltzmann equation in the context of neutron transport. After deriving the transport equation, we discuss some of its basic applications in reactor theory. Finally, we review several simplifying approximations of the linearized Boltzmann equation that are essential to solving it in many applications. Although the context of neutron transport is called upon to add concreteness to our discussion, many of the concepts and approximations that we discuss remain relevant in other many other phenomena.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗