Neutron Transport Calculations Research Articles

Neutron irradiation-induced shutdown dose rate estimation in EU DEMO divertor

The EU DEMO fusion reactor, which is part of the EUROfusion PPPT program and the successor to ITER, aims to facilitate the transition of fusion from the science laboratory to industrial use. Its key objective is net energy production. Its critical component, the divertor, manages power exhaust, ash, and helium removal. The key elements of the divertor include Plasma Facing Components (PFCs), shielding liners, reflector plates, divertor cassettes, and a vacuum vessel locking system. It is imperative that the shutdown dose rates are assessed to ensure workers' radiation protection during maintenance, plan the disposal of radioactive material, and ensure the overall safety of the plant. The shutdown dose rate tool employed in the present study is R2Smesh, which couples MCNP for radiation transport and FISPACT for neutron activation to calculate neutron-induced shutdown dose rates, utilizing an advanced, semi-heterogeneous EU DEMO divertor model, presenting a challenging task in neutron transport calculations.

Nuclear analysis for the test cell lithium system interface cell during operation and shutdown

This paper presents the shielding analyses, which will be provided for supporting the design of the Test Cell Lithium System Interface Cell (TLIC) and safety assessment. The study considers the radiation decay source from IFMIF-DONES operation with beam-on. Radiation shielding simulations have been performed for the safety concerns. Detailed simulation geometry was created from CAD drawing for the TLIC. Neutron transport calculation was performed for all TLIC components concerned. The particle flux, biological dose and absorbed dose maps are provided in the study. A series of neutron transport are performed using the MCNP Monte Carlo McDeLicious neutron source code coupled with FISPACT for inventory calculations for TLIC design.

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.

Improved Collision Probability Analysis of the Double-Heterogeneity Problem Based on Matrix Chord Length Correction

Dispersion fuel exhibits excellent safety performance and effectively reduces the risk of radioactive leakage, making it widely applied in high-temperature gas-cooled reactors (HTGRs) and other advanced nuclear reactors. The presence of stochastic media in dispersion fuel leads to the challenging double-heterogeneity problem in neutron transport calculations. Hébert proposed a collision probability analysis model for treating stochastic media, which has been implemented in the DRAGON5 code. As one important basis of derivation, it is assumed in the Hébert model that the neutron transmission probability is identical to the neutron escaping probability in matrix material. In this paper, it is figured out that the assumption is not rigorous for realistic stochastic media. Then, an improved approach based on the Hébert model is proposed to take into account the realistic chord length distribution as well as to ensure the conservation and reciprocity of collision probabilities. The proposed methodology has been implemented in the HTGR lattice physics code XPZ. By numerical analysis against Monte Carlo reference solutions, it is demonstrated that the improved Hébert model with chord length correction gives good accuracy for addressing realistic double-heterogeneity problems.

Neutronics analysis for conceptual design of target system based on a deuteron accelerator-driven fusion neutron source

A Breeding Blanket (BB), producing tritium and heat energy converted to electricity, is a critical component for the successful Fusion Demonstration Reactor (DEMO). A dedicated neutron source is required to validate the performance of the DEMO BB in a continuous long-term fusion-like environment. Therefore, a pre-conceptual design study has been carried out for the Integrated Breeding Test Facility (IBTF) to evaluate the DEMO BB performance. The IBTF is based on a 40 MeV deuteron accelerator-driven system with a maximum current of 10 mA. A solid Beryllium (Be) target with a 20 cm width and height is used to irradiate the tritium breeding unit (TBU).This study conducted a neutronics analysis of the Be target system of the IBTF. The produced neutron energy spectrum and yield were evaluated on a beam energy of 30 to 50 MeV. The analysis results show that the forward direction neutron yield with the 40 MeV deuteron is the highest at 4.92E + 15 n/s, and the neutron ratio of 10–20 MeV is also the highest. A Blistering Mitigation Layer (BML) was added to prevent the blistering effect caused by the deuteron beam within the Be target. A comparison was done for the performance evaluation of the BML candidates vanadium, palladium, tantalum, and niobium. There were no significant differences in the forward direction neutron yield for the BML options. Vanadium was the most beneficial based on the activation analysis results. Therefore, vanadium with a 0.3 mm thickness was added behind the Be target with a 5 mm thickness. In addition, neutronics analysis was conducted for the test cell shielding designs. Concrete 3.5 m thick was required to satisfy a dose of less than 100 uSv/h during the beam operation. When evaluating the dose rate during maintenance, a dose along the cooling pipes was observed due to the activation of the pipes. The neutron flux with the cooling pipes was reduced by using B4C in the maintenance cell shielding, the dose rate was below 100 uSv/h in the test cell.Deuteron and neutron transport calculations were carried out using MCNP6 with the TENDL2019 cross-section library. Activity analysis and gamma source production were performed using FISPACT-Ⅱ with the TENDL2017 cross-section library.

Investigation of discretization uncertainty in Monte Carlo neutron transport simulations of the Molten Salt Fast Reactor (MSFR)

In the present work, an assessment of the Neutronic Benchmark of the Molten Salt Fast Reactor (MSFR) was performed using mesh based Monte Carlo Neutron Transport (MCNT) calculations with numerical uncertainty quantification due to discretization in neutronic parameters. Calculations with Constructive Solid Geometry (CSG) models where made as a baseline for the developed mesh based models. The numerical uncertainty given by the mesh utilization is evaluated using an extended version of the Grid Convergence Index (GCI). The fuel salt reprocessing is evaluated regarding a constant reprocessing rate. The fuel salt inventory variation with time for the developed models (CSG and meshed) is presented. The differences caused by the discretization procedure are noticeable, which shows that mesh based MCNT require careful mesh sensitivity evaluation and further validation.

The deterministic neutron transport calculation for the HTR-PM by the three-dimensional method of characteristics code ARCHER

Due to the strong geometric adaptability, the Three-Dimensional (3-D) Method Of Characteristics (MOC) is a promising candidate for 3-D whole-core high-fidelity neutron transport calculations. However, the 3-D MOC can hardly be applied to large-scale full core problems on account of the huge computational costs in memory and time. In the past, the 3-D MOC was mainly used in traditional Light Water Reactor (LWR) calculations, but rarely used for more complex core calculations. For pebble-bed High Temperature gas-cooled Reactors (HTRs), most 3-D MOC codes are out of ability to construct complex pebble beds, let alone efficient acceleration methods. The 3-D MOC code ARCHER can efficiently simulate the large-scale pebble-bed HTRs through using the Linear Source Approximation (LSA), the Coarse Mesh Finite Difference (CMFD) and the hybrid MPI-OpenMP parallel. In this work, the two-level CMFD acceleration and efficient preconditioners on Krylov subspace linear solvers are implemented in the ARCHER code in order to achieve better performance. In addition, the practical HTR-PM criticality problem is calculated by ARCHER, which is the world’s first high-fidelity neutron transport solution of large-scale pebble-bed HTRs by deterministic numerical method. It also shows that the 3-D MOC has great application potential in other complex reactors.

Sensitivity of a control rod worth estimate to neutron detector position by time-dependent Monte Carlo simulations of the rod drop experiment

The control rod worth sensitivity to the neutron detector position in the rod drop experiment is studied by the time-dependent Monte Carlo (TDMC) neutron transport calculations for AGN-201K educational reactor and the Kyoto University Critical Assembly. The TDMC simulations of the rod drop experiments are conducted by the Seoul National University Monte Carlo (MC) code, McCARD, yielding time-dependent neutron densities at detector positions. The detector-position-dependent results of the total control rod worth calculated by the extrapolation, the integral counting, and the inverse methods are compared with the numerical reference using the MC eigenvalue calculations and the experimental results. From these comparisons, it is observed that the total control rod worth can be estimated with a considerable difference depending on the detector position through the rod drop experiment. The proposed TDMC simulation of the rod drop experiment can be applied for searching a better detector position or quantifying a bias for the control rod worth measurement.

A spatially auto-corrected reactimeter algorithm

Reactimeter algorithms enable real-time evaluation of the reactivity of a near-critical reactor from the signal of a neutron detector. They only depend on a few parameters defined by the inverse point kinetic equations, and which can be calculated by most neutron transport codes. However, the neutron population measured locally by a detector may not always lead to a good estimate of the reactivity. For example, this would be the case for an in-core detector placed just next to a moving control rod. In such special cases – or when measurement precision is an issue – costly simulations are needed to provide correction factors that account for variations in the spatial distribution of the neutron flux. This paper aims to provide an auto-corrected reactimeter algorithm (ACRA) in the special cases where rapid perturbations are applied to a core close to criticality. Such perturbations were successfully performed in the MINERVE reactor using a dedicated control rod to alternatively insert and withdraw a small sample of material under study. ACRA has been validated against 3D Monte Carlo neutron transport calculations using the signals of four in-core detectors located just next to the moving sample.

Neutron transport calculation for the BEAVRS core based on the LSTM neural network

With the rapid development of computer technology, artificial intelligence and big data technology have undergone a qualitative leap, permeating into various industries. In order to fully harness the role of artificial intelligence in the field of nuclear engineering, we propose to use the LSTM algorithm in deep learning to model the BEAVRS (Benchmark for Evaluation And Validation of Reactor Simulations) core first cycle loading. The BEAVRS core is simulated by DRAGON and DONJON, the training set and the test set are arranged in a sequential fashion according to the evolution of time, and the LSTM model is constructed by changing a number of hyperparameters. In addition to this, the training set and the test set are retained in a chronological order that is different from one another throughout the whole process. Additionally, there is a significant pattern that is followed when subsetting both the training set and the test set. This pattern applies to both sets. The steps in this design are very carefully arranged. The findings of the experiments suggest that the model can be altered by making use of the appropriate hyperparameters in such a way as to bring the maximum error of the effective multiplication factor keff prediction of the core within 2.5 pcm (10–5), and the average error within 0.5266 pcm, which validated the successful application of machine learning to transport equations.

Massive parametric study for prospective design space of a compact tokamak fusion reactor

Using a novel computational algorithm that integrates tokamak systems analysis with neutron transport calculations, the minimum major radius (R0) and resulting maximum magnetic field at the plasma center (BT) can be determined uniquely for a given plasma performance. Plasma performance was varied extensively using a supercomputer (KAIROS) and scanning over a wide range of physics, technology, and system parameters to derive the optimal design space for a compact tokamak fusion reactor. Given the design goals of fusion gain Q > 20.0, net electric power > 100 MW, neutron wall loading < 2.0 MW/m2, indicator of divertor power handling PSOL/R0 < 25 MW/m, direct capital cost < $4.0 billion, and steady-state operation, a prospective design space was determined depending on the levels of physics and technology. Advanced engineering features, such as maximum allowable magnetic field at the toroidal field coil (Bmax = 23 T), were implemented by adopting high-temperature superconducting magnet technology, using an advanced shield material such as tungsten carbide (WC), and a plug-bucked magnet support structure. It was found that by exceeding the energy confinement scaling laws of IPB98y2, a design space of R0 < 4.0 m could be accessed under the following conditions for a conventional tokamak: confinement enhancement factor H > 1.7, bootstrap current fraction fBS > 0.55, magnetic field at the magnetic axis BT > 4.0 T, fusion power Pfusion > 600 MW, and thermodynamic efficiency ηth > 0.33. For a spherical tokamak, these conditions were H > 1.3, fBS > 0.6, BT 〈 6.0 T, and Pfusion 〉 500 MW. Sensitivity studies on the energy confinement scaling laws showed that stricter conditions on the physics parameters were required with the ITPA20 scaling law, whereas the conditions were mitigated with the β-independent scaling law.

Neutron Importance Estimation via New Recursive Monte Carlo Method for Deep Penetration Neutron Transport

In Monte Carlo neutron transport calculations for local response or deep penetration problems, some estimation of an importance function is generally required in order to improve their efficiency. In this work, a new recursive Monte Carlo (RMC) method, which is partly based on the original RMC method, for estimating an importance function for local variance reduction (i.e., source-detector type) problems has been developed. The new RMC method is applied to two sample problems of varying degrees of neutron penetrations, namely, a one-dimensional iron slab problem and a three-dimensional concrete-air problem. Biased Monte Carlo calculations with variance reduction parameters based on the obtained importance functions by the new RMC method are performed to estimate detector responses in these problems. The obtained results are in agreement with those by the reference unbiased Monte Carlo calculations. Furthermore, the biased calculations offer an increase in efficiency on the order of 1 to 104 in terms of the figure of merit. The results also indicate that the efficiency increased as the neutron penetration became deeper.

Characterization of Fast Neutron Transmission Through an Iron Shield

In this paper we give an analysis of the neutron transmission through an iron sphere using Monte Carlo and transport theory methods based on ENDF/B-VII.1 general purpose library. The motivation for this investigation comes from a well-known deficiency in the iron inelastic data from the older library evaluation (ENDF/B-V), giving a concern for a fast neutron flux underestimation within the reactor pressure vessels. In order to benchmark the next-generation ENDF/B-VI iron data, the U.S. Nuclear Regulatory Commission and the former Czechoslovakian National Research Institute have jointly preformed several experiments in 1990s, addressing neutron leakage spectra obtained for a 252Cf fission source in a centre of an iron sphere. It was shown that the ENDF/B-VI iron cross section, containing several improvements over previous evaluations, will not entirely resolve the neutron spectrum discrepancies observed at high neutron energies. Since safety analyses of reactor pressure vessel embrittlement are often based on neutron transport calculations using specific multigroup cross section libraries, simulation of this benchmark was performed using a hybrid shielding methodology of ADVANTG3.0.3 and MCNP6.1.1b codes. Comparison of calculated and referenced dosimeter activation rates are presented for several "standard" nuclear reactions, often used in reactor pressure vessel dosimetry. For that purpose, the new IRDFF-II special library from the IAEA Nuclear Data Services was used as a reference source of dosimetry cross sections. The MCNP6.1.1b code was used for calculation of reaction rates, which were also compared with previous IRDFF-1.05 special library and general purpose ENDF/B-VII.1 library.

Activation Analyses of Disposal Options for Irradiated Be12Ti

The activity and disposal options for irradiated Be12Ti were assessed for the HCPB DEMO blankets making use of a code system that enables performing 3D activation calculations by linking the Monte Carlo transport code MCNP and the fusion inventory code FISPACT through an appropriate interface. The dedicated full-scale geometry MCNP model of the 11.25 degree HCPB DEMO torus was adapted to the requirements for the coupled 3D neutron transport and activation calculations. Special attention was paid to the use in the activation calculations of the commercial materials containing technological impurities. This has a crucial effect on the results and the impurities must be accounted for in any nuclear safety analyses. The short-term activity is formed by the radionuclides produced through the activation of Be and Ti nuclei and the long-term activity is formed by the products of the neutron irradiation taking place on the impurities. A prerequisite for the disposal or the recycling of the irradiated Be12Ti is its deep detritiation; otherwise, the very high-tritium activity would fully prevent any attempt for its treatment. The most preferable is the use of the Be12Ti with the composition including less material impurities, especially uranium. There could be the option to dispose the Be12Ti intermediate-level wastes in the French repository after 1 year of cooling, assuming the detailed control of the impurities that fulfil the French authority requirements. The USA near-ground repositories could be an alternative to the European sites. The recycling of the irradiated Be12Ti must first be elaborated and approved to ensure its treatment in a safe and efficient way. The remote handling technique must be developed for the re-fabrication of the Be12Ti blocks.

Goal-Oriented Mesh Adaptivity of Three-Dimensional Neutron Transport Calculation Using Weighted Difference Scheme and Dual-Weighted Residual Error Indicators

Maintaining a reasonable balance between computational accuracy and overhead is important for neutron transport simulations of engineering problems. This paper presents a goal-oriented mesh adaptive algorithm applied to the multigroup discrete ordinates equation for fixed source and criticality problems. The dual-weighted residual (DWR) approach estimates numerical solution errors and drives local mesh refinement for specific targets, such as detector response, integral flux, and multiplication factor. We employ a reconstruction method to evaluate the spatial residuals of the fluxes obtained by the weighted difference scheme. To improve the performance of adaptive algorithms, new estimation models are proposed for adjoint fluxes needed by the DWR theory, including a regional goal model for fixed source problems and an inconsistent fission source model for k-eigenvalue problems. Additionally, we analyze the impact of the truncation of flux reconstruction and isotropic approximation of adjoint fluxes on grid error indicators and adaptive calculations. Numerical results demonstrate that for the quantities of interest, our adaptive approach saves more than 70% of computational effort and run time when obtaining a level of high accuracy comparable to that of uniform fine grids.

Incorporation of anisotropic scattering into Fourier moment expanded axial DGFEM SN based 2D/1D coupling method

Fourier moment expanded axial DGFEM (Discontinuous Galerkin Finite Element Method) SN based 2D/1D coupling method is a promising variant for the pin-by-pin neutron transport calculation, due to its excellent computational efficiency and stability. In this study, the incorporation of anisotropic scattering based on spherical harmonic expansion is developed for the axial DGFEM SN based 2D/1D transport approach, to further capture the anisotropic scattering accurately for the heterogeneous fuel rod or strong absorber. Several well-known benchmarks are used to evaluate its computational performance. Numerical results shows that the implementation of anisotropic scattering can significantly improve the accuracy of 2D/1D coupling method. Moreover, compared with the traditional 1D SN based 2D/1D method, the newly developed method could achieve high computational efficiency and convergence rate, as well as a relatively low storage requirement.

Three-Dimensional Surrogate Model Based on Back-Propagation Neural Network for Key Neutronics Parameters Prediction in Molten Salt Reactor

The simulation and analysis of neutronics parameters in Molten Salt Reactors (MSRs) is fundamental for the design of the reactor core. However, high-fidelity neutron transport calculations of the MSR are time-consuming and require significant computational resources. Artificial neural networks (ANNs) have been used in various industries, and in recent years are increasingly introduced in the nuclear industry. Back-Propagation neural network (BPNN) is one type of ANN. A surrogate model based on BP neural network is developed to quickly predict two key neutronics parameters in reactor core: the effective multiplication factor (keff) and the three-dimensional channel-by-channel neutron flux distribution. The dataset samples are generated by modeling and simulating different operation states of the Molten Salt Reactor Experiment (MSRE) using the Monte Carlo code. Hyper-parameters optimization is performed to obtain the optimal surrogate model. The numerical results on the test dataset show good agreement between the surrogate model and the Monte Carlo code. Additionally, the surrogate model significantly reduces computation time compared to the Monte Carlo code and greatly enhances efficiency. The feasibility and advantages of the proposed surrogate model is demonstrated, which has important significance for real-time prediction and design optimization of the reactor core.

Parallel Communication Optimization Based on Graph Partition for Hexagonal Neutron Transport Simulation Using MOC Method

OpenMOC-HEX, a neutron transport calculation code with hexagonal modular ray tracing, has the capability of domain decomposition parallelism based on an MPI parallel programming model. In this paper, the optimization of inter-node communication was studied. Starting from the specific geometric arrangement of hexagonal reactors and the communication features of the Method of Characteristics, the computation and communication of all the hexagonal assemblies are mapped to a graph structure. Then, the METIS library is used for graph partitioning to minimize the inter-node communication under the premise of load balance on each node. Numerical results of an example hexagonal core with 1968 energy groups and 1027 assemblies demonstrate that the communication time is reduced by about 90%, and the MPI parallel efficiency is increased from 82.0% to 91.5%.

The improved odCMFD method based on the 2D/1D Fourier analysis

The coarse mesh finite difference (CMFD) method is widely used to accelerate neutron transport calculation. The Fourier analysis shows that approximately three times of 1D inner iteration can improve the convergence and efficiency in CMFD accelerated two-dimension/one-dimension (2D/1D) neutronic transport simulation. To further enhance the convergence and efficiency of the 2D/1D neutronic transport simulation, the improved odCMFD method is studied based on the 2D/1D Fourier analysis, and the scattering ratio correction term is implemented in the improved odCMFD method. The results of the VERA benchmark and the SPEPT whole-core problem indicate that the improved odCMFD method has better convergence than the traditional odCMFD method, which is of great significance to further improve the computational efficiency of the three-dimension (3D) full core transport calculation.

URANOS v1.0 – the Ultra Rapid Adaptable Neutron-Only Simulation for Environmental Research

Abstract. The understanding of neutron transport by Monte Carlo simulations led to major advancements towards precise interpretation of measurements. URANOS (Ultra Rapid Neutron-Only Simulation) is a free software package which has been developed in the last few years in cooperation with particle physics and environmental sciences, specifically for the purposes of cosmic-ray neutron sensing (CRNS). Its versatile user interface and input/output scheme tailored for CRNS applications offers hydrologists straightforward access to model individual scenarios and to directly perform advanced neutron transport calculations. The geometry can be modeled layer-wise, whereas in each layer a voxel geometry is extruded using a two-dimensional map from pixel images representing predefined materials and allowing for the construction of objects on the basis of pixel graphics without a three-dimensional editor. It furthermore features predefined cosmic-ray neutron spectra and detector configurations and also allows for a replication of important site characteristics of study areas – from a small pond to the catchment scale. The simulation thereby gives precise answers to questions like from which location do neutrons originate? How do they propagate to the sensor? What is the neutron's response to certain environmental changes? In recent years, URANOS has been successfully employed by a number of studies, for example, to calculate the cosmic-ray neutron footprint, signals in complex geometries like mobile applications on roads, urban environments and snow patterns.