Neutron Transport Research Articles

Mitigating Spatial Error in the Iterative Quasi–Monte Carlo (iQMC) Method for Neutron Transport Simulations with Linear Discontinuous Source Tilting and Effective Scattering and Fission Rate Tallies

The iterative Quasi–Monte Carlo (iQMC) method is a recently proposed method for neutron transport simulations. iQMC can be viewed as a hybrid between deterministic iterative techniques, Monte Carlo simulation, and Quasi–Monte Carlo techniques. iQMC holds several algorithmic characteristics that make it desirable for high-performance computing environments, including an O ( N − 1 ) convergence scheme, a ray-tracing transport sweep, and a highly parallelizable nature similar to analog Monte Carlo. While there are many potential advantages of using iQMC, there are also inherent disadvantages, namely, the spatial discretization error introduced from the use of a mesh across the domain. This work introduces two significant modifications to iQMC to help reduce the spatial discretization error. The first is an effective source transport sweep, whereby the source strength is updated on the fly via an additional tally. This version of the transport sweep is essentially agnostic to the mesh, material, and geometry. The second is the addition of a history-based linear discontinuous source tilting method. Traditionally, iQMC utilizes a piecewise constant source in each cell of the mesh. However, through the proposed source tilting technique, iQMC can utilize a piecewise linear source in each cell and reduce spatial error without refining the mesh. Numerical results are presented from the two-dimensional (2-D) C5G7 and Takeda-1 k-eigenvalue benchmark problems. The results show that the history-based source tilting significantly reduces error in global tallies and the eigenvalue solution in both benchmarks. Through the effective source transport sweep and linear source tilting, iQMC was able to converge the eigenvalue from the 2-D C5G7 problem to less than 0.04% error on a uniform Cartesian mesh with only 204 × 204 cells.

Coupling between LOTUS and CTF with DYN3D within a multiscale and multiphysics software development

Coupling of nuclear codes can be performed at several scale levels and is necessary to improve their reliability and sustainability. Mainly, the coupling of nuclear codes that use nodal expansion neutronics with channel thermal hydraulics has been carried out at the fuel assembly level while, only recently, the coupling of nuclear codes that use advanced neutronics, thermal hydraulics, and thermo-mechanics has been carried out at either the fuel pin or materials level. Meanwhile, in the UK, a multiscale and multi-physics software development between NURESIM and CASL is being developed, which includes a coupling software environment that enables the coupling of nuclear codes at several scale levels. Full coupled reactor physics at either the fuel pin or materials level can be obtained by coupling the transport code LOTUS, the subchannel code CTF, and the nodal code DYN3D. In this journal article, a multi ways coupling between LOTUS and CTF at either the fuel pin or materials levels with DYN3D at the fuel assembly level is compared to a multi ways coupling between DYN3D and CTF at the fuel pin level with DYN3D at the fuel assembly level and a multi ways coupling between Open MC and CTF at the materials level with DYN3D at the fuel assembly level. These comparisons have been carried out to present the coupled reactor physics verifications at either the fuel pin or materials levels. These show that the multi ways coupling between LOTUS and CTF at either the fuel pin or materials levels with DYN3D at the fuel assembly level outperforms the multi ways coupling between DYN3D and CTF at the fuel pin level with DYN3D at the fuel assembly level due to the application in the former of full neutron transport. Also, these show that the multi ways coupling between LOTUS and CTF at the materials level with DYN3D at the fuel assembly level agrees with the multi ways coupling between Open MC and CTF at the materials level with DYN3D at the fuel assembly level due to the application in both of full neutron transport.

Energy Dissipation of Fast Electrons in Polymethylmethacrylate: Toward a Universal Curve for Electron-Beam Attenuation in Solids between ∼0 eV and Relativistic Energies.

Spectroscopy of correlated electron pairs was employed to investigate the energy dissipation process, as well as the transport and the emission of low-energy electrons on a polymethylmethacrylate surface, providing secondary electron spectra causally related to the energy loss of the primary. Two groups are identified in the cascade of slow electrons, corresponding to different stages in the energy dissipation process. The characteristic lengths for attenuation due to collective excitations and momentum relaxation are quantified for both groups and are found to be distinctly different: λ_{1}=(12±2) Å and λ_{2}=(62±11) Å. The results strongly contradict the commonly employed model of exponential attenuation with the electron inelastic mean free path as characteristic length, but they essentially agree with a theory used for decades in astrophysics and neutron transport, albeit with characteristic lengths expressed in units of angstroms rather than light-years.

VINUS: A neutron transport solver based on the variational nodal method for reactor core analysis

Compared to traditional transverse integration methods, the variational nodal method, with its unique advantages, is more suitable for high-fidelity calculations of reactor physics in reactors with complex geometries and finer detail descriptions. In this study, the basic theory of the variational nodal method was derived and the VINUS code is developed. The neutron solver based on this method is adaptable to various geometric models, and showcased the code's fundamental framework. On this basis, a set of self-designed macroscopic cross-section benchmarks, actual macroscopic cross-section benchmark VVER-440, and few-group microscopic cross-section benchmark RBEC-M for fast spectrum reactors were used to verify different functionalities of VINUS. The results were shown that VINUS code maintains good computational accuracy and convergence trends. For the VVER-440 benchmarks, the deviation of keff of VINUS from reference is less than 100 pcm, and the maximum power deviation is less than 4 %. For the RBEC-M, the deviation of keff is 125 pcm, and the maximum power deviation is less than 5 %. These outcomes collectively demonstrate the solver's potential for engineering applications in future advanced reactor designs.

A conservative first-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions

Deterministic transport codes play a fundamental role in the modeling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the Sn method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solves them using non-traditional techniques such as ray tracing. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low potential for optimization, as well as not being conservative. A new method has been developed that traces instead to a set of points on each of a zone's surfaces and computes the currents, before using these to obtain the flux. A comparison between these two ray tracing methods shows significant advantages to the new surface method, including inherent particle conservation, similar convergence rate and increased potential for optimization through ray sharing.

Numerical solution of a parameter estimation problem arising in Prompt-Gamma Neutron Activation Analysis

We study a parameter estimation problem which arises from measurements with QUANTOM, a measurement facility utilizing Prompt-Gamma Neutron Activation Analysis (PGNAA) to analyze elemental masses in 200-l nuclear waste drums. The presence of neutron flux measurements in QUANTOM offers additional information for elemental composition reconstruction, motivating an alternative to the standard iterative approach. Therefore, the measurement is modelled using approximate models for neutron and photon transport. We introduce a mathematical formulation for solving the resulting parameter estimation problem of QUANTOM measurements and employ an adjoint-based method to determine the elemental composition. Uniqueness of solutions in this context is studied, and the results offer novel insights for PGNAA applications.

Existence results for a nonlinear neutron transport equation with elastic and inelastic collision operators in L p -spaces

In this paper, we discuss the existence of solutions to a stationary neutron transport equation involving elastic and inelastic collision operators in L p - espaces ( 1 ≤ p < ∞ ) . For 1 < p < ∞ , we use the Krasnosel'slii fixed point theorem and the compactness which involved by the averaging result for neutron transport equation. For p = 1, our approach is different, it uses the measure of weak noncompactness of De Blasi, the concepts of Dunford–Pettis operators together with a recent version of Krasnosel'skii's fixed point theorem involving ws-compact and ww-compact operators and the weak compactness.

Optimizations of the Accelerated Axial Polynomial Method of Characteristics of the APOLLO3® Deterministic Neutron Transport Code

For some years now, the TDT (two- and three-dimensional transport) solver of the APOLLO3® deterministic neutron transport code has been able to perform lattice calculations on three-dimensional extruded and unstructured geometries. A polynomial expansion of the angular flux has been implemented to better describe the flux gradient axially to reduce the number of computational meshes required to reach a given accuracy. Then the polynomial approximation was extended to macroscopic cross sections to perform evolution calculations. Besides these transport schemes, synthetic acceleration has also been implemented, relying on double PN approximations of the angular flux on the boundaries of the spatial regions. The solver has already introduced several techniques to reduce the transport and memory footprint; for example, for the storage of the surfaces crossed by a trajectory or the classification of chords. In this paper, new optimizations are presented. One deals with how monomials of the polynomial basis are integrated along trajectories. Another one concerns the computation of the source term of the transmission equation in the case of polynomial cross sections. The last optimization exploits the fact that, along horizontal trajectories, the flux and the cross sections are constant to speed up the sweep algorithm. Calculations on 5 × 5 and 7 × 7 pressurized water reactor assemblies were performed to assess the gains of these recently developed strategies. The results show good improvements both in computing time and in memory footprint reductions.

Impact of fuel temperature on nuclear core design calculations

The operation of a nuclear power plant relies on precalculated nuclear design predictions based on core calculations of various reactor states. The fuel temperature is a crucial factor in determining the reactor fuel behavior, but assessing the temperature variation in a fuel pellet taking into account neutron transport is challenging. Detailed simulation of the temperature behavior within the fuel pellet can be obtained by coupling of Monte Carlo neutron transport codes with thermal-hydraulics solvers. However, this approach is not practical for standard nuclear design calculations, and computationally cheaper and faster methods must be used. In nuclear core simulators, a concept of a single "effective temperature" that yields the same neutron response as in the case of the actual temperature shape is mainly applied. This paper evaluates various fuel temperature models used in nuclear core simulation calculations, ultimately recommending a new effective temperature model that considers the burnup correction.

Monte Carlo / Dynamic Code (MC/DC): An accelerated Python package for fully transient neutron transport and rapid methods development

Monte Carlo / Dynamic Code (MC/DC): An accelerated Python package for fully transient neutron transport and rapid methods development

Vibrational enhancement of evolutionary monochromatic neutron transport

The monochromatic hyperbolic neutron density wave is conceived as a Rayleigh-like wave with mixed transverse and longitudinal components. It is proved for the first time that the absolute ratio of the longitudinal to transverse interfering components, varies, with increasing the frequency of this wave, from zero to 1. Such a limited variation is to be coined as vibrational enhancement of evolutionary one-speed neutron transport.

Study of MOX-fueled VVER-1000 pin cell using [formula omitted]-TRAC with ENDF/B-VIII.0 library

This paper compares the ENDF/B-VIII.0 library for the MOX-fueled VVER-1000 pin cell benchmark with ENDF/B-VII.0 library using the ν-TRAC code and demonstrates the modeling capability of the code. ν-TRAC is a MOC-based code for simulating neutron transport in fuel assembly lattices, with the ability to model cell heterogeneities. The material cross-section significantly impacts neutron transport calculations; therefore, a 172 multigroup cross-section library has been generated using the most recent version of ENDF/B-VIII.0 and the open-source NJOY-2016 code. This nuclear data file includes modifications to the cross-section of major actinides and other light nuclides. Five MOX fuel variants differing in fuel isotopic composition and five states differing in fuel temperature, the moderator, and poison in the moderator are investigated using the most recent library. The impact of new release on the infinite multiplication factor and reactivity change due to the different operating states is studied. Results of ν-TRAC code using multigroup data libraries based on ENDF/B-VIII.0 and ENDF/B-VII.0 are compared with corresponding results from SCALE/SAS2H, HELIOS, and MCU.

Modeling gamma detectors in OpenMC: Validation of a newly implemented pulse-height tally

Gamma spectroscopy measurements can be simulated using a pulse-height tally functionality of Monte Carlo particle transport codes. Such a functionality must account for the complete simulation history of a particle’s energy deposited in a particular volume. OpenMC, an open-source application for neutron and photon particle transport which is widely used in the nuclear engineering community, previously lacked adequate simulation capabilities for gamma spectroscopy. In this paper, we outline the implementation of the photon pulse-height tally for OpenMC. Additionally, we validate the new function by comparing results to analytical calculations, other software, and experimental data.

An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems

An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems

Numerical solutions for nonlinear mixed integro-differential equation and the neutron transport equation

In this work, I will discuss the solution of the new in a nonlinear integro-differential equation (NI-DE) form. The NI-DE is established from the nuclear transport equation, which is a linearized derivative of the equation developed by Boltzmann for the kinetic theory of gases. In this study, I will introduce the basic equations and boundary conditions for the formulation of the problem. Then, the NI-DE is established from the planar geometry problem of the neutron transport equation. In addition, I will prove the existence of a unique solution to the problem. In addition, I will use the numerical method to obtain a system of NI-DEs. Therefore, I will prove, under certain conditions, the existence of a unique solution to this system. Finally, I will present two different effective methods to solve the problem numerically, and I will discuss the results.

A re-activation model for 169Yb intensity modulated brachytherapy sources accounting for spatiotemporal isotopic composition.

Intensity modulated brachytherapy based on partially shielded intracavitary and interstitial applicators is possible with a cost-effective 169Yb production method. 169Yb is a traditionally expensive isotope suitable for this purpose, with an average γ-ray energy of 93keV. Re-activating a single 169Yb source multiple times in a nuclear reactor between clinical uses was shown to theoretically reduce cost by approximately 75% relative to conventional single-activation sources. With re-activation, substantial spatiotemporal variation in isotopic source composition is expected between activations via 168Yb burnup and 169Yb decay, resulting in time dependent neutron transmission, precursor usage, and reactor time needed per re-activation. To introduce a generalized model of radioactive source production that accounts for spatiotemporal variation in isotopic source composition to improve the efficiency estimate of the 169Yb production process, with and without re-activation. A time-dependent thermal neutron transport, isotope transmutation, and decay model was developed. Thermal neutron flux within partitioned sub-volumes of a cylindrical active source was calculated by raytracing through the spatiotemporal dependent isotopic composition throughout the source, accounting for thermal neutron attenuation along each ray. The model was benchmarked, generalized, and applied to a variety of active source dimensions with radii ranging from 0.4 to 1.0mm, lengths from 2.5 to 10.5mm, and volumes from 0.31 to 7.85 mm3, at thermal neutron fluxes from 1×1014to1×1015 n cm-2 s-1. The 168Yb-Yb2O3 density was 8.5g cm-3 with 82% 168Yb-enrichment. As an example, a reference re-activatable 169Yb active source (RRS) constructed of 82%-enriched 168Yb-Yb2O3 precursor was modeled, with 0.6mm diameter, 10.5mm length, 3 mm3 volume, 8.5g cm-3 density, and a thermal neutron activation flux of 4 × 1014 neutronscm-2s-1. The average clinical 169Yb activity for a 0.99 versus 0.31 mm3 source dropped from 20.1 to 7.5Ci for a 4×1014ncm-2s-1 activation flux and from 20.9 to 8.7Ci for a 1×1015ncm-2s-1 activation flux. For thermal neutron fluxes ≥2×1014ncm-2s-1, total precursor and reactor time per clinic-year were maximized at a source volume of 0.99 mm3 and reached a near minimum at 3mm3. When the spatiotemporal isotopic composition effect was accounted for, average thermal neutron transmission increased over RRS lifetime from 23.6% to 55.9%. A 28% reduction (42.5 days to 30.6 days) in the reactor time needed per clinic-year for the RRS is predicted relative to a model that does not account for spatiotemporal isotopic composition effects. Accounting for spatiotemporal isotopic composition effects within the RRS results in a 28% reduction in the reactor time per clinic-year relative to the case in which such changes are not accounted for. Smaller volume sources had a disadvantage in that average clinical 169Yb activity decreased substantially below 20Ci for source volumes under 1mm3. Increasing source volume above 3 mm3 adds little value in precursor and reactor time savings and has a geometric disadvantage.

Analysis of transport-activation internal coupling method implemented in Monte Carlo code cosRMC

When fusion nuclear reactor is in operation, neutron activation causes a large number of radioisotopes. Activation calculation is a very important step in both of reactor shielding calculation and radiation safety analysis. The capability of transport-activation coupling calculation was developed in Monte Carlo code cosRMC though the built-in burnup solver Depth. In the process of neutron transport, the one-group cross section of activation-related was calculated by internal coupling method and the manipulation and transfer of input file for energy spectrum to external activation code was no longer necessary, which is more efficient and flexible than traditional external coupling. A cuboid iron model is established, and the activation calculation is performed by cosRMC and ALARA respectively. In the constant energy spectrum mode, the relative error of 56Fe atomic density between two codes is 0.0019 %, which verified the accuracy of capability of activation internal coupling calculation in the cosRMC code. The relative errors of 57Fe and 58Fe atomic density are 17.97 % and 36.75 % between constant and variable energy spectrum. This showed that whether energy spectrum remains constant has a significant impact on the results. Moreover, the one-group reaction rate with continuous energy/ multi-group cross section were different, which is because the pre-generated multi-group cross section libraries are independent of the geometry and energy spectrum of the specific problem. The resonance shielding effect of the specific problem cannot be accurately considered when using the multi-group cross section, resulted in relative errors of 60 % for the one-group cross section of 56Fe(n,γ) reaction. cosRMC can directly use the continuous energy method to calculate the problem dependent one-group section, which will give more accurate results.

Simulation of Neutron Leakage Variations at Fuel Substitution in a Small Modular Reactor and Implications for Unattended Safeguards Monitoring

According to a recently proposed nuclear safeguards technique, monitoring the power-normalized, ex-core neutron detection rate over time could be used to detect undeclared changes to the fissile composition of a reactor core. In this study, Monte Carlo simulations have been used to verify some of the underlying assumptions of this technique and the possibilities of using it to detect undeclared fuel substitutions during the first 2-year cycle of a light water small modular reactor. Depletion calculations and neutron transport simulations were used to study the changes in the power-normalized neutron leakage rate J b / P core through the core barrel upon fuel substitutions and whether these changes are fully explained by changes in the core fissile composition. Several substitution scenarios have been studied, where partially depleted fuel assemblies were substituted with fresh fuel assemblies after 1 year of irradiation. The modeled substitution scenarios, which included substituting up to 4 out of 37 fuel assemblies in the core at a time, resulted in changes in J b / P core of up to 3.5% depending on which fuel assemblies were substituted. The results indicate that the ex-core neutron signatures are not only sensitive to core-averaged nuclide densities, fission cross sections, and neutron flux, but also the spatial distributions of these and other parameters throughout the core. Effects such as these could mean that monitoring the core fissile composition with the proposed technique might be more complex than previously suggested.

A cyclic-track decomposition method for 3D MOC neutron transport simulation

The method of characteristics (MOC) is a promising numerical technique for solving the neutron transport equation. This method has been parallelized to accommodate its high computing power and memory requirements. Angle decomposition is widely used by parallel MOC codes to distribute MOC tracks over CPU cores, but it may lead to load imbalance. Based on modular ray tracing, we present a cyclic-track decomposition method along with a load balancing strategy to address the limitations of angle decomposition for parallel MOC on 3D axially extruded geometries. It has been implemented as the top-level decomposition in the ANT-MOC code to demonstrate its effectiveness and to show its potential as an alternative to domain decomposition. We evaluated the cyclic-track decomposition method using a generalized performance model and some neutron transport benchmarks. Our evaluation showed that the cyclic-track decomposition method generated a more balanced load distribution than the angle decomposition method, and ANT-MOC with the new strategy for load balancing achieved a good performance of over 40% parallel efficiency as it scales from 10,240 to 98,304 cores on the ORISE supercomputer.

Development of Two-Step Method for Fast Chloride MSR Neutronics

This work presents neutronics models of a small and large fast-spectrum molten chloride-salt reactor. The models are similar to designs being pursued by industry, and they may serve as generic preconceptual and simplified neutronics models that provide information for decision making in licensing-related areas. The two models were created using Serpent, a Monte Carlo neutron transport code, and Moltres, a neutron diffusion core simulator tool. Specifically, this study focused on exploring the applicability of diffusion theory to fast molten salt reactor (MSR) models, the capabilities of an open-source, MSR-oriented simulation tool (Moltres), and optimal energy-group structures. The proposed two-step method involves group-constant generation with Serpent and a multigroup diffusion solution by Moltres. Three energy-group structures were applied. The accuracy of the solutions was determined through comparisons between the two-step and Monte Carlo flux and multiplication factor solutions. The findings indicated diffusion theory captures neutronics with minimal error for the large MSR and yielded best results with the 27-group structure. The 27-group structure yielded an average group flux error below 2% and keff agreement between diffusion and transport solutions within 30 pcm. The accuracy of the two-step method decreased for the very small (high-leakage) fast chloride MSR, but the neutronics were captured acceptably well with the 33-group structure. In addition to exploring the capabilities of Moltres, this work contributes to the sparse literature involving open-source models of fast-spectrum MSRs. Future work is noted as expanding the capabilities of the neutronics models to incorporate thermal hydraulics.