Neutron Transport Research Articles

Высокоточная схема для уравнения переноса в задаче нейтронной защиты

The paper considers the problems of calculating the stationary transport of high-energy neutrons from an external source in a hollow metal structure. The spatial grid for calculation consists of tetrahedra, which allows to model complicated geometric shapes of objects. The calculated area is highly heterogeneous, since it consists of metal parts with strong absorption and scattering and practically non-absorbing internal parts. A scheme based on a minimal stencil, within a single tetrahedron for the calculation. The scheme has a high approximation order and is based on characteristic approaches. For a smooth solution and a constant absorption coefficient in each cell, the scheme has a third order of convergence. The cells are traversed using the graph topological sorting algorithm. A new version of the parallelization of the calculation for the OpenMP standard has been proposed. For discretization by an angular variable, a cubature formula of the direct product type over two angles with an algebraic order of accuracy of nine is used. The angular grid is constructed in such a way as to correctly calculate the moments for narrowly directed beams of external radiation. The standard 26-group approximation of the BNAB library is used for energy sampling. A decrease in the neutron flux inside the structure is shown for groups with an energy above 1 MeV. Graphs of the angular distribution inside the structure are given.

Results of the reactor dosimetry experiments performed for verification of the neutron transport calculations at the Hungarian Paks Nuclear Power Plant

The operational lifespan of all four units at the Hungarian Paks Nuclear Power Plant (NPP) has been extended by 20 years beyond the original 30-year term. This extension has been implemented gradually, in one- to two-year increments, since 2013. The Hungarian Atomic Energy Authority, responsible for granting approval for these life extensions, has prescribed the continuous and rigorous monitoring of the reactor pressure vessel (RPV) throughout the plant’s extended service life. Among the key requirements is the validation of the neutron transport calculations, with specific attention to the large Lead Factor (LF), which reaches around 12 at the reactor core’s center. To meet these regulatory requirements, neutron transport calculations and reactor dosimetry measurements using neutron activation detectors (neutron monitors) have been conducted both inside and outside the RPV. Inside measurements were taken in the RPV surveillance channel, while outside measurements were conducted in the cavity adjacent to the outer wall of the RPV. These efforts aim to determine the key parameters of the neutron irradiation and validation is achieved if the experimental results agree with the neutron transport calculations at both the surveillance position and the RPV's outer wall (in the cavity), ensuring that the calculations are also valid for the inner wall of the RPV. This paper presents the validation of experimental data used to confirm the accuracy of the neutron transport calculations. The results of irradiations conducted over one- and four-year periods are compared and analyzed to demonstrate the authenticity of the experimental data for validation of the calculation results.

Study on the Particle Sorting Performance for Reactor Monte Carlo Neutron Transport on Apple Unified Memory GPUs

In simulation of nuclear reactor physics using the Monte Carlo neutron transport method on GPUs, the sorting of particles plays a significant role in performance of calculation. Traditionally, CPUs and GPUs are separated devices connected at low data transfer rate and high data transfer latency. Emerging computing chips tend to integrate CPUs and GPUs. One example is the Apple silicon chips with unified memory. Such unified memory chips have opened doors for new strategies of collaboration between CPUs and GPUs for Monte Carlo neutron transport. Sorting particles on CPU and transport on GPU is an example of such new strategy, which has been suffering the high CPU-GPU data transfer latency on the traditional devices with separated CPU and GPU. The finding is that for the Apple M2 max and M3 max chip, sorting on CPU leads to better performance per power than sorting on GPU for the ExaSMR whole core benchmark problems and the HTR-10 high temperature gas reactor fuel pebble problem. The partially sorted particle order has been identified to contribute to the higher performance with CPU sort than GPU. The in-house code using both CPU and GPU achieves 7.6 times (M3 max) power efficiency that of OpenMC on CPU for ExaSMR whole core benchmark with depleted fuel, and 130 times (M3 max) for HTR-10 fuel pebble benchmark with depleted fuel.

Acceleration of an improved linear scheme for the neutron transport

This paper presents an accelerated version of an improved linear method of characteristics scheme that preserves first order spatial moments of the flux. This scheme has slow convergence rate and this is why an acceleration method has been investigated. This acceleration is obtained by using the double PN (DPN) method described in previous studies and used in other codes developed by the APOLLO3® team. While the improved linear MoC has a high memory cost and is difficult to implement, the DPN acceleration is shown to save a significant amount of time on a benchmark problem, even at the zeroth order treated in this paper.

A quantified approach to assessing the effectiveness of nuclear reactor pressure vessel neutron fluence monitoring programs

This paper presents a quantitative approach to characterize the effectiveness of neutron fluence monitoring programs using adjoint neutron transport calculations. The results of adjoint calculations are useful for this purpose because the adjoint solution is the expected contribution from one region of phase space to a response of interest, i.e., the importance of that region of phase space to the response. Thus, by identifying a response of interest (for this work, the fast (E > 1.0 MeV) neutron fluence rate at the peak fluence rate location in the reactor pressure vessel (RPV)), one can identify the fuel regions most important to that response. Once identified, the ability of various surveillance programs to adequately monitor the most-important fuel region(s) can be assessed. The approach described is applied to a three-loop Westinghouse pressurized water reactor to compare the effectiveness of surveillance-capsule neutron dosimetry versus ex-vessel neutron dosimetry to monitor the fuel assemblies that contribute to the peak fast (E > 1.0 MeV) neutron fluence rate in the RPV.

TRIPOLI-4® calculations of neutron multiplicity counting rates of 3He array detectors and verification tests of an automatic MCNP-to-TRIPOLI conversion tool for recent ICSBEP subcritical experiments

TRIPOLI-4® is a general-purpose Monte Carlo radiation transport code developed at CEA Paris-Saclay center. It uses continuousenergy nuclear data to simulate neutron transport for diverse nuclear engineering fields. Neutron multiplication calculations of subcritical systems are important for application areas including criticality safety, reactor ex-core monitoring, and non-proliferation of nuclear materials. Subcritical experiments were performed by the LANL teams to improve subcritical simulation capabilities of MCNP code and to validate 3He based array detectors. Three of these experimental series based on Ni, W, and Cu reflected Pu spheres and related MCNP calculations were published on 2020 ICSBEP handbook. New automation conversion tool of MCNP geometries to TRIPOLI-4® ones has been available. In this study, the traditional manual modelling of above Pu-W and Pu-Cu cases (17 configurations including Cu and polyethylene reflectors) was first prepared. The MCNP/TRIPOLI-4® converted ones were secondly set for Pu-Cu cases. Finally the singles counting rate R1 (cts/s) in a single NPOD detector for Pu-W cases and in two NoMAD detectors for Pu-Cu cases were calculated. Generally, a good agreement of R1 was obtained between the TRIPOLI-4® calculations and the ICSBEP reported results. When using the polyethylene reflector layers in some Pu-Cu experiments, a difference of 5 to 16 % for R1 was observed between TRIPOLI-4 (Converted) results and the ICSBEP measured ones.

Numerical qualification of the GSP3(0) theory using the analytic function expansion nodal method

The simplified P3 (SP3) method is an important way to implement the pin-by-pin neutron transport calculation of the core. This method has the high accuracy but costs twice the computing time of the diffusion method. Recently, the Generalized SPN (GSPN) theory has been developed, and the ad hoc SPN theory is resolved through rigorous theoretical derivation. GSP3(0) theory is the 3rd order and the 0th layer of GSPN theory. Compared with GSP3(0) theory, the SP3 theory with Marshak boundary condition is regarded as the traditional SP3 theory. The equations of the two theories are the same while the interface and the boundary conditions are different. Based on the GSP3(0) theory and the traditional SP3 theory, transport calculation codes have been developed using the analytical function expansion nodal (AFEN) method. The numerical results show that both of the two SP3 theories are more accurate than the diffusion theory, and the GSP3(0) theory can further improve the accuracy of the pin power calculation compared to the traditional SP3 theory.

Cross section modeling using Monte Carlo tally derivatives for transient multiphysics prediction

Monte Carlo neutron transport is often seen as the standard for accurate neutronics simulation of nuclear reactors in steady-state. However, the time dependent equation includes time derivatives of flux and delayed neutron precursors which are difficult to model and tally. In this work, a high-order/low-order approach is adopted that uses the omega method to approximate the time derivatives as frequencies. While this scheme has been previously applied to prescribed transients, thermal feedback is now incorporated to provide a fully self-propagating Monte Carlo transient multiphysics solver which can be applied to transients of several seconds long. Such multiphysics problems are less straight-forward than prescribed transients that can be forced to be axially symmetric or otherwise artificially constrained. This work leverages tally derivatives, which are a Monte Carlo perturbation technique that can identify how a tally will change with respect to a small change in the system, to successfully predict thermal feedback and greatly improve accuracy in an axially non-symmetric, flow-initiated transient. Results show good agreement with a reference solution where very fine outer time steps are used for Monte Carlo calculations.

On the effect of the core boundary power distribution on the radiation situation in reactor components

The assessment of the neutron flux distribution in nuclear power plant components, like reactor internals and the pressure vessel, is one of the most important parts of their residual lifetime evaluation process because the irradiation damage of these components is strongly dependent on it. The fast neutron fluences in power reactors are generally determined using calculations and verified by measurements. Discrepancies between them sometimes occur, which can be caused by be the inaccuracies in the power distribution used in neutron transport calculations. This paper quantifies the effect of uncertainty in power density on the neutron fluences behind the reactor pressure vessel (RPV). An increase in power density was experimentally simulated by implementing a higher uranium enrichment of certain selected pins. The experiment was also simulated using the MCNP code with the ENDF/B-VII.1 library. Both the experimental and calculational data show a significant local increase in neutron flux. Even behind the RPV, the increase is as high as 25%, while the local power increase in the perturbed pins is about 70–80%, which is approximately equal to the 2 σ power density uncertainties. A good agreement between measurement and calculation was found.

Improved determination of fast neutron fluence onto the WWER pressure vessel metal surveillance specimens

The special methodology for the determination of the neutron fluences onto the surveillance specimens of the WWER-1000 reactor pressure vessel metal has developed by INR NASU specialists and is successfully applied. The methodology is based on the Monte-Carlo code that is used for neutron transport calculations to the locations of the surveillance specimens. The methodology improvement is described. The fundamentals of the technique of the calculation-experimental determination of the fast neutron fluences onto surveillance specimens and their errors are presented. It is shown a dosimetry experiment in a particular reactor is needed to obtain experimental data about irradiation conditions in the locations of the surveillance specimens.

Positivity-preserving linear discontinuous scheme for solving neutron transport equation in heterogeneous slabs

Positivity-preserving linear discontinuous scheme for solving neutron transport equation in heterogeneous slabs

Upgrading the neutronic version of the PSI cycle check-up methodology for full core PWR Monte Carlo simulations

Full core Monte Carlo (MC) simulations are of high interest and can be used to study the beginning of live conditions of reactors. However, current hardware limitations make it difficult to perform such studies for other cycles, as the whole irradiation history of the fuel assemblies (FAs) loaded must be considered on a time scale of several years using MC depletion capabilities. Therefore, at PSI, a cycle check-up methodology (CHUP) is currently being developed to address this challenge. By extracting operating conditions and isotopic compositions from validated reference deterministic core-follow models (using CASMO5/SIMULATE5), MC neutron transport models are generated for selected operating points. These models can then be used to estimate quantities beyond the capabilities of deterministic solvers. This article presents the verification performed on a hot zero power (HZP) operating condition of a Swiss PWR using the newly updated CHUP methodology. This update consists of extracting information generated automatically from reference core models, minimising as much human intervention as possible. The performance of the method was first evaluated against the reference deterministic lattice code. Then, the memory requirements of the full core simulation were studied under different approximations. Finally, verification was performed against the nodal reference scheme.

Efficient sweep kernels on shared-memory architectures for the discrete ordinates neutron transport equation on Cartesian and hexagonal geometries

This paper describes the implementation of DONUT, a small multi-group SN-DG transport solver that aims at providing efficient and portable sweep kernels on shared-memory architectures for Cartesian and hexagonal geometries. DONUT heavily relies on the Kokkos C++ library for portability and genericity. First encouraging performance results are presented for multicore CPU architectures.

Optimization of multi-group energy structures for solving the neutron transport equation

We develop a framework to determine an optimal broad group structure of the energy variable when solving the neutron transport equation, starting from a fine structure. This broad group structure is required to perform the energy condensation method, where the fine group cross sections are collapsed into the broad group cross sections. In this optimization work, we study the objective function based on the error of the reaction rates and the k-effective as well. Moreover, together with the automatic coarse energy (ACE) algorithm proposed in [1] and the particle swarm optimization (PSO) usually applied to optimize the broad group structure, we introduce the Leave Group Out (LGO) and Add Group In (AGI) approaches. Numerical results for the core calculation are investigated to illustrate the performance of the proposed algorithms.

An efficient calculation method for particle transport problems based on neural network

Monte Carlo (MC) method is a powerful tool for solving particle transport problems. However, it is extremely time-consuming to obtain results that meet the specified statistical error requirements, especially for large-scale refined models. This paper focuses on improving the computational efficiency of neutron transport simulations. Specifically, this study presents a novel method of efficiently calculating neutron fixed source problems, which has many applications. This type of particle transport problem aims at obtaining a fixed target tally corresponding to different source distributions for fixed geometry and material. First, an efficient simulation is achieved by treating the source distribution as the input to a neural network, with the estimated target tally as the output. This neural network is trained with data from MC simulations of diverse source distributions, ensuring its reusability. Second, since the data acquisition is time consuming, the importance principle of MC method is utilized to efficiently generate training data. This method has been tested on several benchmark models. The relative errors resulting from neural networks are less than 5% and the times needed to obtain these results are negligible compared with those for original Monte Carlo simulations. In conclusion, in this work we propose a method to train neural networks, with MC simulation results containing importance data and we also use this network to accelerate the computation of neutron fixed source problems.

Optimal Monte Carlo particle splitting for neutron transport equation

Global tallying problem is hard to be solved efficiently when using Monte carlo method to simulate neutron transport equation, especially for sys- tem with big scale and/or strong imbalanced characteristics. Among numerous global variance reduction methods, particle splitting is an easy-to-implement method, but the efficiency is hard to be satisfying for practical problems. The essential challenge lies in the fact there are too many parameters to be opti- mized. In this paper, a systematic approach for setting all splitting parameters is proposed based on maximization of some global efficiency indicator. Results of two models show this approach can increase the global efficiency indicator up to two orders of magnitude while keeping the results unbiased.

Discrepancy across various OpenMC versions due to thermal neutron scattering law

The performance of neutron transport calculations is heavily reliant on the fidelity of nuclear data. The Free Gas Model (FGM) is no longer applicable at low neutron energy range due to nucleus binding effects, necessitating the implementation of the Thermal Scattering Law (TSL). The present study systematically reports the unexpected discrepancies in keff calculations with TSL across different versions of OpenMC, an open-source Monte Carlo code developed by MIT. Based on four representative benchmark series (HMT-026, HMT-027, BEAVRS, and TRIGA fuel rod), the analysis reveals that updates in OpenMC v0.13.0 significantly contribute to these discrepancies, sometimes up to ~1000 pcm. After further review, a modification in the source code for coherent elastic scattering (suggestion #1949) may affect the sampling of the cosine of the coherent scattering angle. Additionally, recompilation of OpenMC v13.2 using the older segment code aligns reactivity calculations closely with version 0.12.2 and thus confirms the above conclusion. Nevertheless, both the developers and we are still uncertain whether this update is correct until now. A systematic examination of the source code is necessary in the near future. Another direct conclusion from the present study is the importance of including diverse benchmarks for code verification and validation.

Measurement of prompt neutron capture gamma coming from iron and chlorine

Prompt gamma radiation mostly comes from neutron reactions, thus naturally accompanying neutron transport. Therefore, it is an important part of the gamma field in nuclear installations, which accompanies neutrons leaking from the system. This also implies that good knowledge of the prompt gamma description of iron is essential in reactor dosimetry, especially as part of gamma heating and related issues. As the prompt gamma has a discrete character, it can be efficiently used in nuclear forensics for the identification of various isotopes. Prompt gamma rays from neutron capture on iron and chlorine were measured using HPGe and stilbene detector. Iron (as FeSO4) and chlorine (as NaCl) were dissolved in water to maximize the thermalization process of 252Cf(s.f.) neutrons emitted from acentrally positioned neutron source in the solution tank. Not only iron and chlorine peaks were found in the HPGe spectra, but six sulfur peaks from ferrous sulphate were identified as well. The experiments were simulated with the MCNP6.2 code using the ENDF/B-VIII.0, JEFF-3.3 and JENDL-5 libraries. Peak comparisons using HPGe results were generally discrepant in all libraries. Astudy of prompt gammas from thermal neutron capture reveals significant differences between the libraries studied. The comparison of whole spectra using stilbene results shows discrepancies in the gamma production data for chlorine in all libraries. Calculations with FeSO4 give quite good results for JENDL-5 and ENDF/B-VIII.0 and discrepant results for JEFF-3.3.

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.