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Results for “NEUTRON DIFFUSION EQUATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Investigation of neutron noise in a micro-scale, natural circulation molten salt fission battery system

The Molten Salt Reactor (MSR) concept is a rapidly evolving Generation IV design that has recently attracted favorable attention due to the potential for reducing waste generation, realizing passive safety features, and seizing on the opportunity for cost effective economics. A specific novel micro-MSR, natural circulation, battery design concept involves placing all primary components within a single reactor vessel containment without the need of primary forced pumping. This small modular, integral design presents potential cost savings while producing safety, reliable, and transportable carbon-free power for decades. This investigation evaluates the neutron noise induced by density and flow fluctuations in a natural circulation MSR battery concept being developed at the University of Idaho. This study finds numerical solutions to the one-dimensional, one-group, coupled diffusion equations for a bare, homogeneous core, and evaluates neutron flux and delayed neutron precursor concentration noise due to core flow and fuel salt density perturbation sources. Noise analysis shows both point kinetic and space-dependent behavior is present despite the small size, low-flow, closely-coupled nature of the natural circulation MSR concept. Analysis shows that the low flow of the convective system results in noise behavior typically representative of a larger forced-circulation MSR system. Finally, noise techniques may also be useful in MSR core diagnostics as a non-invasive, low-cost radiological option to traditional monitoring schemes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Griffin: A MOOSE-based reactor physics application for multiphysics simulation of advanced nuclear reactors

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor physics application for multiphysics simulations of advanced reactor designs jointly developed by Idaho National Laboratory and Argonne National Laboratory. This paper summarizes the motivation, significance, architecture, design, and features of Griffin. Griffin offers flexible and extensible features to address the challenges associated with advanced reactor designs. These features range from fundamental particle transport to specific reactor physics tasks. The features cover a wide range including on-the-fly and traditional two-step cross-section generation methods, steady-state and transient transport solvers suitable for both heterogeneous and homogeneous models, high-fidelity depletion where thousands of isotopes can be tracked and low-fidelity depletion characterized by burnup, etc. The most fundamental aspect that sets Griffin apart from other reactor analysis codes is that it is developed based on the MOOSE framework. A modular development approach is strongly enforced, with multiphysics being an essential element considered since the beginning of Griffin’s development. Griffin links various MOOSE physics modules and couples to other MOOSE-based applications and non-MOOSE-based applications for multiphyiscs simulations. Griffin includes three modules: ISOXML for preparing and managing multigroup cross sections, radiation transport for solving the neutron transport equation, and reactor analysis for user-oriented reactor physics analysis functionalities. Griffin uses various finite element methods for spatial discretization, multigroup approximation for energy discretization and discrete ordinates method, spherical harmonics expansion method, and diffusion approximation for streaming direction discretization to solve the neutron transport equation. Griffin’s flexibility is evidenced through Griffin’s various applications to fast reactor, high-temperature reactor, pebble bed reactor, molten salt reactor, and microreactor designs. Griffin development follows the software quality assurance procedure for MOOSE-based applications and with software requirements consistent with the ASME NQA-1 standard. Griffin has been adopted into the reactor analysis system for the U.S. NRC and is in use at U.S. companies, universities and national laboratories.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Magnetic field decay in isolated neutron stars

Three mechanisms that promote the loss of magnetic flux from an isolated neutron star - Ohmic decay, ambipolar diffusion, and Hall drift - are investigated. Equations of motions are solved for charged particles in the presence of a magnetic field and a fixed background of neutrons, while allowing for the creation and destruction of particles by weak interactions. Although these equations apply to normal neutrons and protons, the present interpretations of their solutions are extended to cover cases of neutron superfluidity and proton superconductivity. The equations are manipulated to prove that, in the presence of a magnetic force, the charged particles cannot be simultaneously in magnetostatic equilibrium and chemical equilibrium with the neutrons. The application of the results to real neutron stars is discussed.

Goldreich, Peter↗
DOE OSTI2022

Frequency-domain vs time-domain SP{sub N} equations to simulate neutron noise

Inside the reactor core mechanical vibrations of fuel assemblies can produce high fluctuations around a steady-state configuration, known as neutron noise. This effect can cause the triggering of power reduction measures. Classically, diffusion theory has been used to simulate this behavior. However, this equation has some limitations if the materials of the reactor have strong variations. In this work, we use the diffusive time-dependent simplified spherical harmonics equations that improve the previous results without the necessity of using high computational requirements. In particular, two types of analyses with these equations (SP{sub 3}) are made: a frequency-domain and a time-domain. A numerical neutron noise benchmark tests the methodology and compare both formulations. First, numerical results show a good agreement between the amplitudes and phases of the SP3 equations computed with the frequency-domain and time-domain. Therefore, as the frequency-domain computation only requires to solve a linear system, it is a recommendable option for neutron noise computations. Second, one can conclude that for this type of nuclear systems, where the assemblies are not homogenized, the SP{sub 3} approximation results improve considerably the accuracy of the diffusion theory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2008

Innermost Van Allen Radiation Belt for High Energy Protons at Saturn

The high energy proton radiation belts of Saturn are energetically dominated by the source from cosmic ray albedo neutron decay (CRAND), trapping of protons from beta decay of neutrons emitted from galactic cosmic ray nuclear interactions with the main rings. These belts were originally discovered in wide gaps between the A-ring, Janus/Epimetheus, Mimas, and Enceladus. The narrow F and G rings significant affected the CRAND protons but did not produce total depletion. Voyager 2 measurements subsequently revealed an outermost CRAND proton belt beyond Enceladus. Although the source rate is small, the trapping times limited by radial magnetospheric diffusion are very long, about ten years at peak measured flux inwards of the G ring, so large fluxes can accumulate unless otherwise limited in the trapping region by neutral gas, dust, and ring body interactions. One proposed final extension of the Cassini Orbiter mission would place perikrone in a 3000-km gap between the inner D ring and the upper atmosphere of Saturn. Experience with CRAND in the Earth's inner Van Allen proton belt suggests that a similar innermost belt might be found in this comparably wide region at Saturn. Radial dependence of magnetospheric diffusion, proximity to the ring neutron source, and northward magnetic offset of Saturn's magnetic equator from the ring plane could potentially produce peak fluxes several orders of magnitude higher than previously measured outside the main rings. Even brief passes through such an intense environment of highly penetrating protons would be a significant concern for spacecraft operations and science observations. Actual fluxes are limited by losses in Saturn's exospheric gas and in a dust environment likely comparable to that of the known CRAND proton belts. The first numerical model of this unexplored radiation belt is presented to determine limits on peak magnitude and radial profile of the proton flux distribution.

Cooper, John F.↗
DOE OSTI2022

Simulation of CEFR neutronic start-up tests with FENNECS

This paper presents simulation results of selected Neutronic Start-up Tests of the China Experimental Fast Reactor (CEFR) obtained by the neutronics code FENNECS that have been performed within the frame of the IAEA Coordinated Research Program I31032. The Finite Element Neutronics code FENNECS is developed at GRS and solves the few-group steady-state and transient diffusion equation using a Galerkin-based finite element approach. Its main purpose is the safety assessment of Small Modular Reactors and Micro Reactors with complex geometry (e.g., rotating control drums) which gain increased interest internationally. Serpent has been applied to create reference models of the CEFR and cross-section libraries in 10 energy groups for FENNECS. Using these libraries, the following experiments have been simulated with FENNECS: net criticality, control rod integral and differential worth, void reactivity effect, subassembly exchange reactivity effects and reaction rate distribution. The obtained satisfactory agreements with the measurements represent a valuable contribution to the validation of FENNECS. (author)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Benchmark calculations of infinite neutron matter with realistic two- and three-nucleon potentials

In this study, we present the equation of state of infinite neutron matter as obtained from highly realistic Hamiltonians that include nucleon-nucleon and three-nucleon coordinate-space potentials. We benchmark three independent many-body methods: Brueckner-Bethe-Goldstone (BBG), Fermi hypernetted chain/single-operator chain (FHNC/SOC), and auxiliary-field diffusion Monte Carlo (AFDMC). We find them to provide similar equations of state when the Argonne v 18 and the Argonne v' 6 nucleon-nucleon potentials are used in combination with the Urbana IX three-body force. Only at densities larger than about 1.5 the nuclear saturation density ( ρ 0 =0.16 fm ⁻3 ) the FHNC/SOC energies are appreciably lower than the other two approaches. The AFDMC calculations carried out with all of the Norfolk potentials fitted to reproduce the experimental trinucleon ground-state energies and nd doublet scattering length yield unphysically bound neutron matter, associated with the formation of neutron droplets. Including tritium β decay in the fitting procedure, as in the second family of Norfolk potentials, mitigates but does not completely resolve this problem. An excellent agreement between the BBG and AFDMC results is found for the subset of Norfolk interactions that do not make neutron-matter collapse, while the FHNC/SOC equations of state are moderately softer.

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↗
NASA NTRS1975

Possible theoretical explanations for occasional days of non-field-aligned diffusion at neutron monitor energies

It has been shown previously (Anath et al., 1973 and Kane, 1974) that 20 to 25% of days, the diffusion component of the cosmic-ray neutron diurnal anisotropy is directed more than 30 degrees away from the ecliptic projection of the interplanetary magnetic field averaged over the same 24 hours. A number of explanations for this deviation are discussed and it is concluded that transverse gradient drifts due to gradients perpendicular to the ecliptic are likely, that diurnal variations in the diffusion component of the neutron anisotropy may affect results from single stations and that the 24 hour mean interplanetary magnetic field may not be the field appropriate to the streaming equation at neutron monitor energies.

Forman, M. A.↗
NASA NTRS1985

The effect of the neutral sheet structure of the interplanetary magnetic field on cosmic ray distribution in space

Results of the numerical solution of the anistoropic diffusion equation are presented. The modulation depth of galactic cosmic rays is defined by the degree of curvature of the neutral current sheet in the heliosphere. The effect of the regular interplanetary magnetic field (IMF) on cosmic ray anisotropy in the period of solar activity minimum (in 1976) is analyzed by the data of the neutron super-monitors of the world network, and the heliolatitudinal gradient and cosmic ray diffusion coefficient are defined.

Alania, M. V.↗
DOE OSTI2023

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. In conclusion, our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Constraining Hamiltonians from chiral effective field theory with neutron-star data

Multi-messenger observations of neutron stars (NSs) and their mergers have placed strong constraints on the dense-matter equation of state (EOS). The EOS, in turn, depends on microscopic nuclear interactions that are described by nuclear Hamiltonians. These Hamiltonians are commonly derived within chiral effective field theory (EFT). Ideally, multi-messenger observations of NSs could be used to directly inform our understanding of EFT interactions, but such a direct inference necessitates millions of model evaluations. This is computationally prohibitive because each evaluation requires us to calculate the EOS from a Hamiltonian by solving the quantum many-body problem with methods such as auxiliary-field diffusion Monte Carlo (AFDMC), which provides very accurate and precise solutions but at a significant computational cost. Additionally, we need to solve the stellar structure equations for each EOS which further slows down each model evaluation by a few seconds. In this work, we combine emulators for AFDMC calculations of neutron matter, built using parametric matrix models, and for the stellar structure equations, built using multilayer perceptron neural networks, with the PyCBC data-analysis framework to enable a direct inference of coupling constants in an EFT Hamiltonian using multi-messenger observations of NSs. We find that astrophysical data can provide informative constraints on two-nucleon couplings despite the high densities probed in NS interiors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1959

A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

Schneider, Harold↗
NASA NTRS1959

Computer Program for Solving Nine-Group Diffusion Equations for Cylindrical Reactors

A method is presented for determining the critical size of a cylindrical reactor by a one-dimensional group-diffusion method extended to a two-dimensional solution by prescribing values of axial leakage based on assumed flux levels. The neutron energy spectrum is divided into nine groups, and the reactor into four concentric cylinders. A computing machine program for an IBM 650 computer with attachments and a method for using the program with nine, or less, groups and four, or less, regions are given.

Miser, James W.↗
DOE OSTI2021

Nuclear energy density functionals grounded in ab initio calculations

Here, we discuss the construction of a nuclear energy density functional (EDF) from ab initio computations and advocate the need for a methodical approach that is free from ad hoc assumptions. The equations of state (EoSs) of symmetric nuclear and pure neutron matter are computed using the chiral NNLO sat and the phenomenological AV4' + UIX c Hamiltonians as inputs to self-consistent Green's function (SCGF) and auxiliary field diffusion Monte Carlo (AFDMC) methods. We propose a convenient parametrization of the EoS as a function of the Fermi momentum and fit it on the SCGF and AFDMC calculations. We apply the ab initio based EDF to carry out an analysis of the binding energies and charge radii of different nuclei in the local density approximation. The NNLO sat -based EDF produces encouraging results, whereas the AV4' + UIX c -based one is farther from experiment. Possible explanations of these different behaviors are suggested, and the importance of gradient and spin-orbit terms is analyzed. Our paper paves the way for a practical and systematic way to merge ab initio nuclear theory and density functional theory, while shedding light on some critical aspects of this procedure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Neutron matter from local chiral effective field theory interactions at large cutoffs

Neutron matter is an important many-body system that provides valuable constraints for the equation of state (EOS) of neutron stars. Neutron-matter calculations employing chiral effective field theory (EFT) interactions have been extensively used for this purpose. Among the various many-body methods, quantum Monte Carlo (QMC) methods stand out due to their nonperturbative nature and the achievable precision. However, QMC methods require local interactions as input, which leads to the appearance of stronger regulator artifacts compared to nonlocal interactions. To circumvent this, we employ large-cutoff interactions derived within chiral EFT (400 MeV ≤ Λ 𝑐 ≤ 700MeV) for studies of pure neutron matter. These interactions have been adjusted to nucleon-nucleon scattering phase shifts, the triton binding energy, as well as the triton 𝛽-decay half-life. We find that regulator artifacts significantly decrease with increasing cutoff, leading to a significant reduction of uncertainties in the neutron-matter EOS. We discuss implications for the symmetry energy and demonstrate how our new calculations lead to a reduction in the theoretical uncertainty of predicted neutron-star radii by up to 30% for low-mass stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2010

The Evolution of Remnant Ice at the Lunar South Pole from Diviner Surface Temperature Results

The Diviner lunar radiometer instrument aboard the Lunar Reconnaissance Orbiter mission has revealed large areas of lunar polar terrain with surface temperatures well below 100K. At these temperatures, the sublimation rate of water ice is well below 1 mm per billion years. In contrast, the loss rate at 120K is more than 1 meter of ice in that time consequently volatiles delivered to the coldest locations can be trapped for over 1 Ga, but will be quickly lost from warmer locales. Here we investigate the loss or retention of a layer of ice-bearing regolith at the lunar south poe, assuming contemporary surface temperature conditions and no other loss processes. We use an analytic solution for the one-dimensional diffusion equation of water ice, assuming an isothermal regolith with pore space comparable to mean grain size, 75 micrometers. Only the top meter of soil is assumed to be ice-bearing. We can then calculate the history of ice content with time based on local temperature, and predict what the epithermal neutron output would be in the presence of such a concentration of hydrogen. We compare the present, observed distribution of hydrogen with what one would expect from the temperature-dependent loss or retention of ice for various times since emplacement.

Elphic, Richard C.↗