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DOE OSTI2022

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Measurement of the 28 Si ⁢(𝑛,𝑛′⁢𝛾) cross section with 𝑛, 𝛾, and correlated 𝑛−𝛾 angular distributions

Silicon has become an unavoidable element in the circuitry central to everyday life. In turn, the interactions of silicon isotopes with neutrons for nuclear physics applications, among other motivations, have become increasingly important to understand. The dominant isotope of silicon, 28 Si, is thus of primary interest for enhanced understanding for neutron transport calculations and related investigations. Unfortunately, the existing measurement database for neutron scattering reactions on 28 Si is minimal, and nuclear data evaluations on this topic have not been updated for decades. This article details new measurements of the 28 Si ⁢(𝑛,𝑛′⁢𝛾) reaction utilizing multiple analysis methods available within the correlated gamma neutron array for scattering (CoGNAC). Specifically, high-precision near-threshold results and high-incident-energy results were obtained using the 𝛾-only and correlated 𝑛−𝛾 techniques. First-ever measurements of the correlated 𝑛−𝛾 angular distribution for particles emitted following population of the first excited state in 28 Si were obtained as well, which provide unique insight into theoretical descriptions of the inelastic neutron scattering reaction mechanism itself and detailed guidance for nuclear reaction models. The results agree well with literature data where they exist, and substantially expand on the current database for neutron reactions on 28 Si .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

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 ↗

DOE OSTI2024

Three-Dimensional Full-Core BEAVRS Using OpenMOC with Transport Equivalence

Using an optimized implementation of the three-dimensional (3D) method of characteristics for neutron transport, along with a novel equivalence method for transport calculations that was designed to correct self-shielding errors from neglecting the angular dependence of resonant group absorption, a 3D full-core light water reactor hybrid stochastic-deterministic eigenvalue calculation was achieved. This paper presents the optimizations developed and compares the transport solutions obtained. For the statepoint, run times near 10 000 CPU hours are achieved—improving on previous works by an order of magnitude—with near 1% error on pin fission to 238 U capture ratios and a few dozen pcms on the eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

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↗

DOE OSTI2021

Exploring Gamma-Ray and Neutron Spectroscopy Missions to Mars Caves [Slides]

In this work, we investigate the sensitivity of active neutron detector systems in Mars caves using MCNP6 to model neutron transport in different cave geometries, compositions, and detectors to determine if active neutron measurements can be used to identify the hydration of cave walls vs floor vs ceilings, and to perform a concept study for potential future Mars cave missions in search of hydration and habitable regions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Uncertainty Analysis for a Criticality Benchmark [Slides]

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

High-fidelity Pebble Bed Reactor Depletion Based on Pebble Tracking Transport in Griffin

The pebble tracking transport (PTT) method is a high-fidelity, heterogeneous deterministic transport technique for pebble bed reactor analysis. It discretizes the broad-group neutron transport equation in space and angle with the discontinuous finite element and the discrete ordinates method, and utilizes various solving techniques, including mesh sweeping and diffusion acceleration, to provide pebble- wise reaction rates. This work presents the extension of the PTT method to enable fuel depletion capability in the Griffin code. We discuss the implementation details of the PTT-based high-fidelity depletion where isotope inventory of all individual pebbles is tracked through pre-determined pebble flow paths in the core. The implementation is verified with a generic pebble bed reactor model. Some preliminary equilibrium core results are included. Future works are also discussed.

97 - MATHEMATICS AND COMPUTING↗

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 OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint, and the sensitivity of $k$ ∞ to perturbations in the multigroup nuclear data of a single species isotropic elastic scattering material. In the appendix, we present the multigroup nuclear data for U-235 and U-238 along with the corresponding k-eigenvalue, flux, adjoint, and sensitivity profiles, which include the sensitivity of $k$ ∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

This work presents a general set of equations that can be used to rapidly generate new benchmarks to verify nuclear data sensitivity calculations. The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint flux, and the sensitivity of k∞ to perturbations in the multigroup nuclear data of a single species, isotropic and elastic scattering, material. The multigroup nuclear data for U-235 and U-238 is presented along with their corresponding k-eigenvalues, forward flux, adjoint flux, and sensitivity profiles, which include the sensitivity of k∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group-wise fission neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

COG User's Manual: A Multiparticle Monte Carlo Transport Code (Sixth Edition)

COG is a high-resolution code for the Monte Carlo simulation of coupled particle transport in arbitrary 3-D geometry. COG will transport neutrons, protons, deuterons, alpha particles with energies up to hundreds of GeV, and photons with energy ranges limited by the available cross section sets and physics models. Electrons can be transported via the EGS5 electron transport kernel, electrons can also be transported. The COG code is a significant upgrade from earlier Monte Carlo transport codes and has been written specifically to make it more versatile, accurate, and easy to use. COG has provisions for calculating deep penetration (shielding) problems, criticality problems, and neutron activation problems while retains all of the standard capabilities found in other Monte Carlo transport codes. COG uses high-resolution pointwise cross-section databases and makes no compromises in the transport physics, so that the results of a COG run are limited only by the accuracy of the databases used. COG runs primarily on Linux Operating System workstations with MPICH software installed – currently, Red Hat 7 & 8, Windows 10 (Windows Subsystem for Linux –WSL), Ubuntu 16, 18 & 20, OpenSUSE Leap 15.2, Fedora 32, Apple Power Mac with Intel CPU (with MacPorts installed) workstations, and LLNL LC supercomputer CTS-1 cluster with TOSS 3 are supported.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Driving mode analysis—How uncertain functional inputs propagate to an output

Abstract Driving mode analysis elucidates how correlated features of uncertain functional inputs jointly propagate to produce uncertainty in the output of a computation. Uncertain input functions are decomposed into three terms: the mean functions, a zero‐mean driving mode, and zero‐mean residual. The random driving mode varies along a single direction, having fixed functional shape and random scale. It is uncorrelated with the residual, and under linear error propagation, it produces an output variance equal to that of the full input uncertainty. Finally, the driving mode best represents how input uncertainties propagate to the output because it minimizes expected squared Mahalanobis distance amongst competitors. These characteristics recommend interpretation of the driving mode as the single‐degree‐of‐freedom component of input uncertainty that drives output uncertainty. We derive the functional driving mode, show its superiority to other seemingly sensible definitions, and demonstrate the utility of driving mode analysis in an application. The application is the simulation of neutron transport in criticality experiments. The uncertain input functions are nuclear data that describe how Pu reacts to bombardment by neutrons. Visualization of the driving mode helps scientists understand what aspects of correlated functional uncertainty have effects that either reinforce or cancel one another in propagating to the output of the simulation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

AR reactor neutronics multi-code validation*

The affordable, robust, compact (ARC) reactor is a tokamak fusion reactor concept currently under development by Commonwealth Fusion Systems and Massachusetts Institute of Technology. There are three important neutronics considerations for the operation of the ARC reactor: (1) breeding of enough tritium in the blanket to sustain the D–T reaction in the plasma; (2) ensuring low fluence on the superconducting toroidal field coils; and (3) assessing neutron volumetric heating in structural components. Here, this work aims to perform a validation of the neutronics analysis approach by code-to-code comparison. State-of-the-art software stacks are employed for the neutronics analysis of the ARC reactor, and a computer-aided design (CAD) model is used directly for Monte Carlo (MC) neutron transport calculations. Three software stacks, Attila-MCNP, OpenMC-DAGMC, and Shift-DAGMC, are used to perform neutronic analyses of a 90° sector CAD model of the ARC reactor. In conclusion, results show that the flux tallies calculated by the three software stacks are very close. Also, the volumetric heating and tritium breeding values have less than 0.6% relative difference between codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

SERPENT 2 and TRIPOLI-4 neutronics benchmarking of the Jules Horowitz reactor

Jules Horowitz Reactor (JHR) is a future center for nuclear material testing in Europe, currently under construction at CEA Cadarache in southern France. It has been modelled extensively with CEA's HORUS3D/N neutron calculation package, that includes a Monte-Carlo neutron transport code TRIPOLI-4. In order to support the future computational analyses on the reactor core physics, VTT's Monte Carlo neutronics code SERPENT 2 has been used to create an alternative model of the JHR, taking advantage of the pre-existing Constructive Solid Geometry (CSG) structures on which the TRIPOLI-4 model was built. This work describes a benchmark, in which two JHR core configurations were analyzed using both of these models. The first configuration is a fresh fuel core at the beginning of life, in which aluminum based dummy-devices are installed in the reactor test positions. The second configuration represents the end-of-cycle equilibrium core with a heterogeneous burnup distribution, in which CALIPSO devices containing cladding material samples are installed at the in-core experimental positions, while the reflector positions are occupied by DEN-REP devices containing UO{sub 2} fuel. Neutron flux spectra and heat deposition are the parameters of interest in this study, due to their high importance in creating the desired experimental irradiation environment. The impact of delayed gamma energy deposition will be studied in detail, since the two models account for it with different methods. This work aims to establish a SERPENT 2 model of JHR, understanding its differences and agreements with TRIPOLI-4, and discussing its potential future applications. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Shutdown dose rate analysis with the Shift Monte Carlo radiation transport code and modular verification workflow

Calculation of the shutdown dose rate is crucial for safe fusion reactor operations. The Rigorous-two-step (R2S) method is a method that requires connected neutron transport, activation, and gamma transport. Shift has integrated variance reduction with a deterministic solver Denovo, supports multiple geometry formats, and is scalable. These features make it an attractive transport solver choice for an R2S workflow. An R2S workflow for the Shift Monte Carlo code is developed and compared to the existing Oak Ridge National Laboratory Shutdown Dose Rate Code Suite (ORCS) workflow. Also, a Python framework for integrating two R2S workflows is developed to mix and match each step in the R2S workflow for improved collaboration and verification experience. In this study, results show that the Shift-Denovo R2S workflow and the ORCS workflow calculate the shutdown dose rate of the ITER Shutdown Dose Rate benchmark problem with an average relative error of 2.285%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

COG11.3 Abstract

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Secondary-Source Core Reload Modeling with VERA

The CASL reactor simulation package VERA has been adapted to provide high-fidelity simulation capabilities for modeling source range detector response during subcritical reactor configurations. New features include the activation and shuffling of secondary-source assemblies, use of burned fuel neutron emission data from the ORIGEN depletion solver to the MPACT deterministic neutron transport solver, allowance of user-defined sources in MPACT based on material composition, ability to solve the subcritical source-driven system with neutron multiplication using the MPACT diffusion solver, and transfer of the calculated fission source from MPACT to the continuous-energy Monte Carlo solver Shift for final detector response evaluation using the CADIS methodology for variance reduction. These new capabilities were benchmarked against Watts Bar Unit 1 plant operating data for the first few fuel loading steps and were found to demonstrate excellent agreement with the measured data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗