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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Space to Air High-Altitude Region Adjoint Neutron Transport

Neutrons from an atmospheric nuclear explosion can be detected by sensors in orbit. Current tools for characterizing the neutron energy spectrum assume a known source and use forward transport to recreate the detector response. In realistic scenarios the true source is unknown, making this an inefficient, iterative approach. In contrast, the adjoint approach directly solves for the source spectrum, enabling source reconstruction. The time–energy fluence at the satellite and adjoint transport equation allow a Monte Carlo method to characterize the neutron source’s energy spectrum directly in a new model: the Space to High-Altitude Region Adjoint (SAHARA) model. A new adjoint source event estimator was developed in SAHARA to find feasible solutions to the neutron transport problem given the constraints of the adjoint environment. This work explores SAHARA’s development and performance for mono-energetic and continuous neutron energy sources. In general, the identified spectra were shifted towards energies approximately 5% lower than the true source spectra, but SAHARA was able to capture the correct spectral shapes. Continuous energy sources, including real-world sources Fat Man and Little Boy, resulted in identifiable spectra that could have been produced by the same distribution as the true sources as demonstrated by two-dimensional (2D) Kolmogorov–Smirnov tests.

LaMere, Zachary W.↗
DOE OSTI2016

Analytic Solution for Time-Dependent Neutron Transport with Delayed Neutrons via Singular Eigenfunction Expansion

An important way to verify the proper functioning of a computer code, and its underlying numerical schemes, is by comparing numerical results generated with the code to an analytic solution. To this end, we present an analytic solution for time-dependent neutron transport with delayed neutrons, which can be used to verify computer codes for modeling reactor kinetics phenomena. To develop our analytic solution, we use the singular eigenfunction expansion method. Ganapol et al. have also developed a solution to this problem, but by using the multiple collision technique. Our approach has certain advantages with respect to this previous work, in particular that it yields a closed form (i.e., in terms of an integral rather than an infinite series) explicit expression for the angular flux (i.e., instead of just the scalar flux or the angular flux at a single spatial point). In addition, Su and Olson have presented an analytic solution for a very similar problem: non-equilibrium radiative transfer. Their approach involves a Laplace transform, which they invert by showing there are no singularities in the right complex plane of the Laplace transform parameter and then simply choosing the Bromwich contour as the imaginary axis. To extend this previous work to our case, we would further need to exclude supercritical problems in order to use the same contour. The resulting analytic solution would then be of limited interest. In contrast, our analytic solution is completely general with respect to sub, delayed super, or prompt supercriticality. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Stability and accuracy of 3D neutron transport simulations using the 2D/1D method in MPACT

A consistent “2D/1D” neutron transport method is derived from the 3D Boltzmann transport equation, to calculate fuel-pin-resolved neutron fluxes for realistic full-core Pressurized Water Reactor (PWR) problems. The 2D/1D method employs the Method of Characteristics to discretize the radial variables and a lower order transport solution to discretize the axial variable. This paper describes the theory of the 2D/1D method and its implementation in the MPACT code, which has become the whole-core deterministic neutron transport solver for the Consortium for Advanced Simulations of Light Water Reactors (CASL) core simulator VERA-CS. Several applications have been performed on both leadership-class and industry-class computing clusters. Results are presented for whole-core solutions of the Watts Bar Nuclear Power Station Unit 1 and compared to both continuous-energy Monte Carlo results and plant data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Resolving Neutron Transport with the CoGNAC Neutron Scattering Program at LANSCE [Poster]

Neutron Scattering Defines Neutron Transport. Elastic (n,n) and inelastic (n,n'γ) reactions dictate the neutronic energy flow. Each scattering reaction changes neutron direction $\vartheta$ and energy E. Scattering cross sections and angular distributions are essential for neutron transport. Uncertainties on scattering evaluations and measurements dominate total uncertainties. New, high-precision neutron scattering measurements and evaluations are needed from light elements to actinides

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Characterizing Fluence as a Function of Areal Density for 1 and 14 MeV Neutrons Transported Through Air

Computing neutron dosimetry involves transporting neutrons [n] from a source to a sink, determining the neutron heating within the sink and multiplying the neutron heating by a quality factor to compute the dose equivalent. The space and energy dependent neutron fluence is a measure of the amount of neutrons crossing a particular surface area, about a particular energy and is given in units of [n/cm{sup 2}]. Microscopic cross sections are given in units of area and vary by isotope and reaction type as a function of energy. The product of the atom density of a particular atom in a specie and the microscopic cross section of a particular reaction results in the macroscopic cross section of a particular reaction, given in units of per length [1/cm] as a function of energy. Summing the macroscopic cross sections of all isotopes, and all collisions resulting in heating, within a volume, results in a total collision heating macroscopic cross section for that volume. The product of the energy and spatial dependent collision heating macroscopic cross section and the energy and spatial dependent fluence, within an energy group, results in a collision heating reaction density for that particular reaction in that energy group. Weighting each energy group's collision heating reactions, with the corresponding energy dependent particle damage per collision heating event (usually biological damage), and then integrating over energy and volume results in the delivered dose. Therefore understanding dose delivery involves examining the spatial and energy (and time) dependent fluence behavior. Because of the coupled energy and space dependence of the heating weighting and macroscopic cross sections, the fluence is not so easily separable in energy and space; however, the energy integrated fluence can be used as a first order approximation of the relative magnitude of reactions as a function of space. Here we examine the first part in the dosimetry calculation process, transporting neutrons from source to sink, as applied to neutron transport in air, examining characteristics of the fluence. Presented here is analysis regarding the nature of the fluence peak between 10 g/cm{sup 2} and 100 g/cm{sup 2} for a typical air transport calculation. Due to the high concentration of nitrogen and oxygen isotopes of these elements, these isotopes tend to dominate the transport. From the analysis presented here, the fluence peak is the result of scatter back and forth across the peak regime, and (n,2n) has a minimal (<4%) contribution. Further evidence of minimal (n,2n) impact in the 10-100 g/cm{sup 2} span includes the 1 MeV fluence peak being so much larger than the 14 MeV peak; where 1 MeV is not above the (n,2n) threshold. Also presented here is the usefulness of using tally tagging with cell flagging to further dissect the nature of the fluence. These technologies allow us to understand the originating volume that makes a contribution to a scoring regime. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

A time-dependent neutron transport method of characteristics formulation with time derivative propagation

A new time-dependent Method of Characteristics (MOC) formulation for nuclear reactor kinetics was developed utilizing angular flux time-derivative propagation. This method avoids the requirement of storing the angular flux at previous points in time to represent a discretized time derivative; instead, an equation for the angular flux time derivative along 1D spatial characteristics is derived and solved concurrently with the 1D transport characteristic equation. This approach allows the angular flux time derivative to be recast principally in terms of the neutron source time derivatives, which are approximated to high-order accuracy using the backward differentiation formula (BDF). This approach, called Source Derivative Propagation (SDP), drastically reduces the memory requirements of time-dependent MOC relative to methods that require storing the angular flux. An SDP method was developed for 2D and 3D applications and implemented in the computer code DeCART in 2D. DeCART was used to model two reactor transient benchmarks: a modified TWIGL problem and a C5G7 transient. The SDP method accurately and efficiently replicated the solution of the conventional time-dependent MOC method using two orders of magnitude less memory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Assessment of the Lagrange Discrete Ordinates Equations for Three-Dimensional Neutron Transport

The Lagrange Discrete Ordinates (LDO) equations, developed by Ahrens as an alternative to the traditional discrete ordinates formulation, have been implemented in Denovo, a threedimensional radiation transport code developed by Oak Ridge National Laboratory. The LDO equations retain the formal structure of the classical discrete ordinates equations but treat particle scattering in a different way. Solutions of the LDO equations have an interpolatory structure such that the angular flux can be naturally evaluated at directions other than the discrete ordinates used in arriving at the solutions, and the ordinates themselves may be chosen in a strategic way for the problem under consideration. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. In this paper we present scalar flux solutions of the LDO equations for a small number of test cases of interest and compare the results against flux solutions generated using standard quadrature types. The LDO equations’ flux solutions were found to be comparable to those resultant from the standard quadrature types in value; results from the LDO equations were also found to be commensurate with those of standard quadrature types when comparing the flux solutions in the context of the experimental benchmark test case examined.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Structures of the fractional spaces generated by the difference neutron transport operator

The initial boundary value problem for the neutron transport equation is considered. The first, second and third order of accuracy difference schemes for the approximate solution of this problem are presented. Highly accurate difference schemes for neutron transport equation based on Padé approximation are constructed. In applications, stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained.The positivity of the neutron transport operator in Slobodeckij spaces is proved. Numerical techniques are developed and algorithms are tested on an example in MATLAB.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

The Lattice Boltzmann Method applied to neutron transport

In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data reduction in deterministic neutron transport calculations using machine learning

Neutron cross section matrices for fission and scattering data are required for each material, temperature, and enrichment level to calculate the neutron transport equation accurately. Here, this information can be a limiting factor when using the multigroup discrete ordinates (S N ) method when the number of energy groups is large. Machine Learning (ML) can be used to replace the need for the cross section matrices by reproducing the function that maps the scalar flux to the scattering and fission sources. Through the use of autoencoders and Deep Jointly-Informed Neural Networks (DJINN), the data storage requirements are reduced by 94% of the original data for a 618 group problem. This is accomplished while preserving the scalar flux, maintaining generality, and decreasing wall clock times.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Rayleigh Quotient Iteration in 3D, Deterministic Neutron Transport

Today's "grand challenge" neutron transport problems require 3-D meshes with billions of cells, hundreds of energy groups, and accurate quadratures and scattering expansions. Leadership-class computers provide platforms on which high-fidelity fluxes can be calculated. However, appropriate methods are needed that can use these machines effectively. Such methods must be able to use hundreds of thousands of cores and have good convergence properties. Rayleigh quotient iteration (RQI) is an eigenvalue solver that has been added to the Sn code Denovo to address convergence. Rayleigh quotient iteration is an optimal shifted inverse iteration method that should converge in fewer iterations than the more common power method and other shifted inverse iteration methods for many problems of interest. Denovo's RQI uses a new multigroup Krylov solver for the fixed source solutions inside every iteration that allows parallelization in energy in addition to space and angle. This Krylov solver has been shown to scale successfully to 200,000 cores: for example one test problem scaled from 69,120 cores to 190,080 cores with 98% efficiency. This paper shows that RQI works for some small problems. However, the Krylov method upon which it relies does not always converge because RQI creates ill-conditioned systems. This result leads to the conclusion that preconditioning is needed to allow this method to be applicable to a wider variety of problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗