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DOE OSTI2025

The accuracy of multi-group models for nonlocal electron transport in magnetized plasmas

In the extreme conditions of inertial confinement fusion experiments, heat flow plays a vital role, but local diffusive models frequently break down and overestimate the heat flow. The situation becomes more complicated again in the significant magnetic fields generated during laser–plasma interactions or in magnetized fusion schemes. Accurate non-local and magnetized heat flow computations can be carried out using Vlasov–Fokker–Planck (VFP) simulations, but these are computationally expensive. There is, therefore, significant interest in using faster multi-group models to accurately calculate the non-local heat flow in magnetized plasmas. We benchmark two such multi-group models for calculating the heat flow, M1 and hybrid-AWBS-BGK, against diffusive models and full VFP simulations, before applying the models to realistic example test cases, both magnetized and unmagnetized. We find that the multi-group models generally perform very well for moderate non-localities up to kλmfp∼0.01, but the computational cost increases dramatically. hybrid-AWBS-BGK performs more effectively than M1 at high non-localities, up to kλmfp∼1, due to its adaptive solver and robust P1 closure, but tends to fail in very strong magnetic fields. Both codes are much faster than VFP simulations but are still slow in steep temperature gradients.

Arran, C. (ORCID:0000000286448118)↗

DOE OSTI2024

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↗

DOE OSTI2025

E-scooter safety: How attitudinal factors influence risky behavior among shared e-scooter riders

In recent years, e-scooter usage for short-distance trips has grown rapidly. This surge in e-scooter use, combined with the high exposure of e-scooter riders to accident risk, has sparked concerns regarding e-scooter safety. Despite some studies focusing on e-scooter safety, little is known about how attitudinal factors lead e-scooter riders to engage in risky riding behaviors. In this paper, we developed a survey-based empirical model to identify the attitudinal factors influencing engagement in risky behaviors among e-scooter users. We used survey data collected from 420 shared e-scooter users in Chicago in 2022. The survey showed that 47.7% of respondents had experienced at least one collision or fall-off while riding e-scooters. We employed the Partial Least Squares Structural Equation Model (PLS-SEM) to examine the relationships between latent attitudinal factors and risky behavior engagement. Moreover, we conducted Permutation Multi-group Analysis (PMGA) to assess the moderating effect of socio-demographic factors within the estimated model. The findings suggest that riders’ unsafe riding attitude and riding confidence are the most influential factors shaping their risky behavior engagement. In addition, accident experience, infrastructure suitability, perceived enjoyment, traffic risk perception, and operational risk perception are among the other significant predictors. Among socio-demographic factors, gender, age, education, and car use frequency significantly influence riders’ engagement in risky behaviors. The results highlight the importance of infrastructure suitability and accident experience in analyzing e-scooter users’ riding behavior. The developed model advances our understanding of factors contributing to e-scooter riders’ risky behavior engagement. The findings offer valuable insights for policymakers and e-scooter vendors aiming to mitigate e-scooter users’ accident risk. Specifically, we recommend three safety countermeasures: (1) safety training programs to encourage a safer attitude, (2) practice-based initiatives to enhance riding confidence, and (3) infrastructure improvements, especially the expansion of bike lanes.

E-scooter↗

DOE OSTI2024

Simulations of radiatively cooled magnetic reconnection driven by pulsed power

Magnetic reconnection is an important process in astrophysical environments, as it reconfigures magnetic field topology and converts magnetic energy into thermal and kinetic energy. In extreme astrophysical systems, such as black hole coronae and pulsar magnetospheres, radiative cooling modifies the energy partition by radiating away internal energy, which can lead to the radiative collapse of the reconnection layer. In this paper, we perform two- and three-dimensional simulations to model the MARZ (Magnetic Reconnection on Z) experiments, which are designed to access cooling rates in the laboratory necessary to investigate reconnection in a previously unexplored radiatively cooled regime. These simulations are performed in GORGON, an Eulerian two-temperature resistive magnetohydrodynamic code, which models the experimental geometry comprising two exploding wire arrays driven by 20 MA of current on the Z machine (Sandia National Laboratories). Radiative losses are implemented using non-local thermodynamic equilibrium tables computed using the atomic code Spk, and we probe the effects of radiation transport by implementing both a local radiation loss model and P 1/3 multi-group radiation transport. The load produces highly collisional, super-Alfvénic (Alfvén Mach number M A ≈ 1.5), supersonic (Sonic Mach number M S ≈ 4–5) strongly driven plasma flows which generate an elongated reconnection layer (Aspect Ratio L/δ≈100 , Lundquist number S L ≈ 400). The reconnection layer undergoes radiative collapse when the radiative losses exceed the rates of ohmic and compressional heating (cooling rate/hydrodynamic transit rate = τ$^{–1}_{cool}$/τ$^{–1}_{H}$ ≈100); this generates a cold strongly compressed current sheet, leading to an accelerated reconnection rate, consistent with theoretical predictions. Lastly, the current sheet is also unstable to the plasmoid instability, but the magnetic islands are extinguished by strong radiative cooling before ejection from the layer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Gray two-moment neutrino transport: Comprehensive tests and improvements for supernova simulations

Aims. In this work we extended an energy-integrated neutrino transport method to facilitate efficient, yet precise, modeling of compact astrophysical objects. We particularly focus on core-collapse supernovae. Methods. We implemented a gray neutrino-transport framework from the literature into FLASH and performed a detailed evaluation of its accuracy in core-collapse supernova simulations. Based on comparisons with results from simulations using energy-dependent neutrino transport, we incorporated several improvements to the original scheme. Results. Our analysis shows that our gray neutrino transport method successfully reproduces key aspects from more complex energy-dependent transport across a variety of progenitors and equations of state. We find both qualitative and reasonable quantitative agreement with multi-group M1 transport simulations. However, the gray scheme tends to slightly favor shock revival. In terms of gravitational wave and neutrino signals, there is a good alignment with the energy-dependent transport, although we find 15–30% discrepancies in the average energy and luminosity of heavy-lepton neutrinos. Simulations using the gray transport are around four times faster than those using energy-dependent transport.

Astronomy & Astrophysics↗

DOE OSTI2023

A Primer on Nuclear "Recoil" Data

For many years the ENDF-6 format has existed to contain evaluated nuclear data. One primary driver for the format and the data is neutron transport calculations. Evaluated data can be processed by a code like NJOY into either continuous energy form (ACE format) for Monte Carlo codes like MCNP or into multi-group form (NDI tables) for deterministic codes like Partisn. The reaction cross sections are found in the MF 3 section of the ENDF-6 format. If the reaction produces one or more neutrons as outputs, then secondary neutron data must also be given in MF 4,5 or 6 sections of the format. Energy and angular distributions for the output neutrons must be given in one of several available formats. The most general formats are found in MF 6. MF 4 is for angular distributions, MF 5 is for Energy distributions, and MF 6 contains both. In recent years, more interest has developed in the other output particles (i.e., the “recoil” particles) from neutron induced reactions. This has been driven by interest in charged particle transport and in more specialized partial kermas. ( A separate total neutron kerma has been available for a long time.) Partial kermas are a breakdown of the Kinetic Energy Released into the MAterial by output particle or by neutron reaction. The sum of the partial kermas should be equal to the total kerma on a group-wise basis. The ENDF-6 format is general enough for these new data requirements. Ideally, evaluated data would exist for every output particle (including the secondary neutrons) from every neutron-induced reaction. In the MF 6 format section, data for multi-particle outputs may be entered using the LAW =1 option. This option explicitly allows energy and angular output distributions for each particle produced in the reaction. Such information should preserve the balance between partial kermas and the total kerma at the groupwise level as well as the individual particle averaged energies. For simpler 2-body reactions, LAW = 2 is available. This allows the evaluation to specify only enough data to specify the 2-body reaction fully. Such a simplification does not exist for 3 (or more) body breakups. A simplified form of LAW 2, i.e., LAW 3, also exists to generate approximate recoil output distributions in the absence of full data. However, evaluated data does not generally exist at this fine granularity for reactions involving more than 2 output particles ( e.g., the 3-body break-up reaction). When the multi-body detailed output distribution data is not available, LAW=6 may be employed in NJOY. LAW 6 produces approximate output distributions for all the particles produced in the reaction. Just like in the 2-body case, the smaller particles will generally carry off more energy. At any particular energy, the balance between the sum of the partial kermas and the total kerma will not necessarily be preserved. However, the average energy of each output particle from a reaction is preserved.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

A Tutorial for Generating Correlated Random Samples in the Context of Replica Cross Section Data Used in the Propagation of Uncertainty (Second Edition)

The following sample problem write-ups are designed as a tutorial for generating correlated random samples (e.g., replica multi-group cross section data) for use in propagation of uncertainty problems. These problems were set up and solved in MATLAB, but any programming environment with basic statistical functions can be used to generate similar results. Since linear sample problems were chosen, helpful comparisons to the “sandwich” rule propagation of uncertainty are available and were used.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A Family of Multi-Dimensional Thermal Radiative Transfer Test Problems

Many thermal radiative transfer (TRT) test problems have been introduced over the years. Here, we will combine the good features of several tests into one new problem. Our goals are to have a multi-dimensional, multi-group TRT problem that stresses the physics and numerics of codes in a realistic way, but the geometry and materials are idealized just enough to be simple to set up in any code. The proposed problem has no connection to any physical experiment; it is simply meant to have a combination of properties that stress the solvers with both the optically thick and thin limits. To achieve this, we are willing to give up any form of analytic solution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

VARI3D & PERSENT: Perturbation and Sensitivity Analysis (Revision 5)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Public Release of the MENDF80 and MT80 Nuclear Data Libraries for NDI

This document describes the MENDF80 and MT80 data libraries, which are multi-group neutron cross section libraries based on ENDF/B-VIII.0 for LANL’s Nuclear Data Interface (NDI). MENDF80 is a downscatter-only library, while MT80 is multi-temperature. Both libraries also have 30-group pre-collapsed versions, MENDF80 30 and MT80 30.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Generating An Advanced Cross-section Library For HTGR Pebble Bed Depletion Calculations Using Reduced-Order Model Generation Techniques

For code development, Advanced Reactor Technologies - Gas Cooled Reactors Program (ART-GCR) rely on a collaboration with the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, but the cross sections generation and the methodology definition is part of this program area goals. Based on previous studies in FY23, the size of microscopic cross section libraries increases rapidly with the number of tabulations, requiring significant amount of memory and drastically slowing down the Griffin calculations when evaluating cross sections via the multivariate linear interpolation approach. Rising to these challenges, this work investigates constructing Reduced-order Models (ROMs) for the multi-group microscopic cross sections to accelerate the cross section evaluation in Griffin. A database of multigroup cross sections is first collected considering all possible parameters that a designer could change for optimization. Down-selection of the ROM techniques afterward shows Deep Neural Network (DNN) as the best candidate when jointly consider memory efficiency, predictive accuracy, computational cost, scalability, flexibility and ease of implementation of the algorithms in comparison to the multidimensional interpolation. This work develops a specific interface that enables the cross section predictions using pre-trained DNN models into Griffin leveraging the existing ROM capabilities. DNNs have been trained for all isotopes for use in Griffin. Preliminary Griffin testing shows that DNNs exhibit exceptional predictive accuracy and the use of DNNs provides orders of magnitude improvement in memory efficiency compared to conventional interpolation techniques. With such ROM techniques, it holds great promise to further increase the fidelity of the Pebble Bed Reactor (PBR) simulation by increasing the number of tabulations/state variables during cross section evaluation, while maintaining the computational cost affordable in Griffin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

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↗

DOE OSTI2024

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↗