Monte Carlo Transport Simulations Research Articles

Upsampling Monte Carlo Reactor Simulation Tallies in Depleted Sodium-Cooled Fast Reactor Assemblies Using a Convolutional Neural Network

The computational demand of neutron Monte Carlo transport simulations can increase rapidly with the spatial and energy resolution of tallied physical quantities. Convolutional neural networks have been used to increase the resolution of Monte Carlo simulations of light water reactor assemblies while preserving accuracy with negligible additional computational cost. Here, we show that a convolutional neural network can also be used to upsample tally results from Monte Carlo simulations of sodium-cooled fast reactor assemblies, thereby extending the applicability beyond thermal systems. The convolutional neural network model is trained using neutron flux tallies from 300 procedurally generated nuclear reactor assemblies simulated using OpenMC. Validation and test datasets included 16 simulations of procedurally generated assemblies, and a realistic simulation of a European sodium-cooled fast reactor assembly was included in the test dataset. We show the residuals between the high-resolution flux tallies predicted by the neural network and high-resolution Monte Carlo tallies on relative and absolute bases. The network can upsample tallies from simulations of fast reactor assemblies with diverse and heterogeneous materials and geometries by a factor of two in each spatial and energy dimension. The network’s predictions are within the statistical uncertainty of the Monte Carlo tallies in almost all cases. This includes test assemblies for which burnup values and geometric parameters were well outside the ranges of those in assemblies used to train the network.

A unified theory of the self-similar supersonic Marshak wave problem

We present a systematic study of the similarity solutions for the Marshak wave problem in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power law temperature dependent opacity and energy density. The properties of the solutions in both linear and nonlinear conduction regimes are studied as a function of the temporal drive, opacity, and energy density exponents. We show that there exists a range of the temporal exponent for which the total energy in the system decreases, and the solution has a local maxima. For nonlinear conduction, we specify the conditions on the opacity and energy density exponents under which the heat front is linear or even flat and does possess its common sharp characteristic; this characteristic is independent of the drive exponent. We specify the values of the temporal exponents for which analytical solutions exist and employ the Hammer–Rosen perturbation theory to obtain highly accurate approximate solutions, which are parameterized using only two numerically fitted quantities. The solutions are used to construct a set of benchmarks for supersonic LTE radiative heat transfer, including some with unusual and interesting properties such as local maxima and non-sharp fronts. The solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which highlights their usefulness as a verification test problem for radiative transfer simulations.

Self-similar solutions for the non-equilibrium nonlinear supersonic Marshak wave problem

Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gray, non-equilibrium diffusion approximation in the supersonic regime. These solutions constitute an extension of existing non-equilibrium supersonic Marshak wave solutions, which are linear to the nonlinear regime that prevails in realistic high energy density systems. The generalized solutions assume a material model with power law temperature dependent opacities, a material energy density that is proportional to the radiation energy density, and a surface radiation temperature drive that obeys a temporal power law. The solutions are analyzed in detail, and it is shown that they take various qualitatively different forms according to the values of the opacity exponents. The solutions are used to construct a set of standardized benchmarks for supersonic non-equilibrium radiative heat transfer, which are nontrivial but straightforward to implement. These solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which demonstrates the usefulness of these solutions as a code verification test problem.

131I dose coefficients for a reference population using age-specific models

Age-specific dose coefficients are required to assess internal exposure to the general public. This study utilizes reference age-specific biokinetic models of iodine to estimate the total number of nuclear disintegrations ã(r S,τ) occurring in source regions (r S) during the commitment time (τ). Age-specific S values are estimated for 35 target regions due to 131I present in 22 r S using data from 10 paediatric reference computational phantoms (representing five ages for both sexes) published recently by the International Commission of Radiation Protection (ICRP). Monte Carlo transport simulations are performed in FLUKA code. The estimated ã(r S,τ) and S values are then used to compute the committed tissue equivalent dose HT(τ) for 27 radiosensitive tissues and dose coefficients e(τ) for all five ages due to inhalation and ingestion of 131I. The derived ã(r S,τ) values in the thyroid source are observed to increase with age due to the increased retention of iodine in the thyroid. S values are found to decrease with age, mainly due to an increase in target masses. Generally, HT(τ) values are observed to decrease with age, indicating the predominant behaviour of S values over ã(r S,τ). On average, ingestion dose coefficients are 63% higher than for inhalation in all ages. The maximum contribution to dose coefficients is from the thyroid, accounting for 96% in the case of newborns and 98%–99% for all other ages. Furthermore, the estimated e(τ) values for the reference population are observed to be lower than previously published reference values from the ICRP. The estimated S, HT(τ) and e(τ) values can be used to improve estimations of internal doses to organs/whole body for members of the public in cases of 131I exposure. The estimated dose coefficients can also be interpolated for other ages to accurately evaluate the doses received by the general public during 131I therapy or during a radiological emergency.

Simulation of cosmic rays inside an aircraft: spectral perturbation and dose reduction due to aircraft structures and contents.

In this study, an intricate combinatorial geometry model of a Boeing 777-300ER aircraft was constructed for Monte Carlo transport simulations. The aircraft-induced perturbations of the energy spectra and effective doses of secondary cosmic rays at a typical civil aviation altitude (10km) were investigated on a component-by-component basis, which included neutrons, protons, photons, electrons, positrons, muons and charged pions. Two geomagnetic cutoff rigidities (1.35 and 15.53 GV) and two solar modulation parameters (430 and 1360 MV) were considered in the aforementioned simulations. The characteristics of various cosmic-ray components at six locations along the fuselage were assessed and compared with those of an unperturbed radiation field in the atmosphere. Aircraft structures and contents reduced the effective doses of personnel inside the aircraft to varying degrees, up to an ~32% reduction in the middle section of the passenger cabin. On average, the dose reduction was ~12-16% depending on geomagnetic and solar conditions. Quantifying the aircraft's self-shielding effects can further improve the estimation accuracy of aircrew and passengers' exposure to cosmic radiation. Information regarding the perturbed energy spectra of cosmic rays may be useful for designing onboard experiments or analyzing onboard measurement data.

Development and Application of Particle Transport Monte Carlo Simulation Modeling Toolkit

In particle transport Monte Carlo simulation, the manual modeling method is not suitable for complex geometric models. A Monte Carlo Simulation Modeling Toolkit (pyMCMT) is developed based on Python language. The toolkit can generate input card in several classical format such as MCNP and GDML format automatically. In this paper, two typical applications are presented based on the pyMCMT toolkit: 1, constructing a multilayer circular geometric model in complex density distribution by pyMCMT toolkit in order to satisfy the requirement of building large-space fine model with the influence of blast wave. A two-dimensional adaptive model is built for non-uniform atmospheric induced by blast wave. The number of the cells in this model is reduced vastly with the same model resolution; 2, producing the optimized weight window parameter using the mesh-based weight window variance reduction combined with density iteration method which is realized to solve the high statistical fluctuation and low counting efficiency problem in deep penetration process. The successful application of pyMCMT shows that pyMCMT is a modularized, parameterized, customizable and easy-to-debug toolkit for particle transport Monte Carlo simulation modeling, which can improve the modeling efficiency tremendously.

Phonon Sampling Method for Inelastic Thermal Neutron Scattering Events

Accurate representation of thermal neutron scattering in Monte Carlo transport simulations requires that the molecular vibrations of the target material be accounted for. Historically, this has been achieved by precomputing large multidimensional tables that are a function of temperature and the cosine of the scattering angle, as well as incoming and outgoing neutron energy. Most commonly used sampling techniques for thermal neutron scattering rely on large multidimensional tables, where higher resolution results in an increase in required memory and attempts to reduce memory can result in grid coarseness errors. An alternative sampling method is introduced here that is a significant departure from precomputed tables and instead relies on a more physical model of the scattering behavior. The phonon sampling method classifies neutron scattering events by the number of phonons excited/de-excited during the scattering collision. In doing so, energy exchange may be obtained via rejection sampling, and an analytical representation of the momentum exchange is obtained. This sampling method has been tested on graphite, yttrium hydride, and uranium nitride, and preliminary implementation of the phonon sampling method shows accurate results for angular and energy distributions, though resulting in up to a 40% slowdown in overall calculation time. This notable slowdown is countered, however, by a large reduction in storage (over 99% reduction compared to standard multidimensional tables).

Virtual Reality System for Monte Carlo Transport Simulation Codes Using Web Technology and Commodity Devices

A virtual reality (VR) system for Monte Carlo (MC) transport simulation codes, MCNP and Particle and Heavy Ion Transport Code System (PHITS), was developed. This system is aimed to provide a more reliable confirmation of the simulation geometry through an intuitive user interface. The VR system is implemented by extending the Geometry and CROSS Section VIEWer (Gxsview) code to run in a JavaScript environment, and it takes advantage of web technology and does not require dedicated hardware or geometry information supplied by computer-aided design software. Therefore, only WebXR-compatible head-mounted displays and browsers are required on the user side. In the VR space, visualization of the calculation geometry, cell selection, and cell grabbing operations is possible with a handheld controller. Further enhancements will be made in the future, such as performing shielding calculations with the cell changed by grabbing operations.

Nuclear data uncertainty propagation and implications for radioactive waste management of fusion steels

Predictions of material activity in commercial fusion conditions predominantly rely on computational methods, due to a lack of data on long-term effects of high-energy neutron irradiation on structural steels. Consequently, this could result in a bias due to uncertainties in nuclear data used. This work focused on modelling neutron activation of four structural steels in a fusion reactor environment after 20 years of operation. Eurofer, F82H and G91, were assessed as candidate in-vessel materials, whereas SS316L(N)-IG was solely modelled in the vacuum vessel. Activation calculations were performed using the inventory code FISPACT-II using inputs from Monte-Carlo transport simulations performed with OpenMC. The study employed a one-dimensional reactor model with a Helium-Cooled Pebble Bed (HCPB) tritium-breeding blanket design. With the XSUN-2022 code package, a nuclear data sensitivity and uncertainty analysis on production cross-sections of relevant radio-nuclides was carried out. Eurofer and F82H steels exhibited significantly higher resistance to neutron activation than G91 and SS316L(N)-IG. At 100 years after shutdown, none of the steels reached UK low-level waste (LLW) activity levels in the first wall. In the rear of the back-support structure (BSS) of the reactor blanket, all assessed steels reached LLW levels within approximately 30 to 45 years of reactor shutdown. It was found that the vacuum vessel (SS316L(N)-IG) would not be classifiable as LLW for several centuries. Dominant radio-nuclides for each material were identified with FISPACT-II to carry out the uncertainty analyses. The calculated uncertainties were too small to affect the waste disposal options for the first wall within 100 years, but the time-to-reach LLW for BSS and vacuum vessel steel could be uncertain by up to approximately 3 and 6 years, respectively.

Deuteron and alpha sub-libraries of JENDL-5

JENDL-5, the latest version of the Japanese evaluated nuclear data library, includes several sub-libraries to contribute to various applications. In this paper, we outline the evaluation and validation of the deuteron reaction sub-library developed mainly for the design of accelerator-based neutron sources and the alpha-particle reaction sub-library developed mainly for use in the back-end field. As for the deuteron sub-library, the data for 6,7Li, 9Be, and 12,13C from JENDL/DEU-2020 were partially modified and adopted. The data up to 200 MeV for 27Al, 63,65Cu, and 93Nb, which are important as accelerator structural materials, were newly evaluated based on the calculations with the DEURACS code. As for the alpha-particle sub-library, the data up to 15 MeV for 18 light nuclides from Li to Si isotopes were evaluated based on the calculations with the CCONE code, and then only the neutron production cross sections were replaced with the data of JENDL/AN-2005. Validation on neutron yield by Monte Carlo transport simulations was performed for both sub-libraries. As a result, it was confirmed that the simulations based on the sub-libraries showed good agreement with experimental data.

Accurate Nonlocal Impact Ionization Models for Conventional and Staircase Avalanche Photodiodes Derived by Full Band Monte Carlo Transport Simulations

We present a procedure to extract the nonlocal impact ionization coefficients in Avalanche Photodiodes (APDs) operating in the linear regime from Full Band Monte Carlo simulations. The Monte Carlo calculations have been calibrated on existing experimental data for GaAs p-i-n APDs with different thickness of the intrinsic region. Inspection of impact ionization generation rate in p-i-n and staircase GaAs APDs led us to identify the limitations of existing nonlocal-history dependent impact ionization models. The introduction of an energy dependent relaxation length for the computation of the effective fields significantly improves the model accuracy in predicting the gain and noise associated to conduction and valence band steps in staircase APDs without additional computational burden. This improved nonlocal-history dependent model is thus a powerful tool to design and optimize APDs with different architectures.

Measurement of 107-MeV proton-induced double-differential thick target neutron yields for Fe, Pb, and Bi using a fixed-field alternating gradient accelerator at Kyoto University

ABSTRACT Double-differential thick target neutron yields (TTNYs) for Fe, Pb, and Bi targets induced by 107-MeV protons were measured using the fixed-field alternating gradient accelerator at Kyoto University for the research and development of accelerator-driven systems (ADSs) and fundamental ADS reactor physics research at the Kyoto University Critical Assembly (KUCA). Note that TTNYs were obtained with the time-of-flight method using a neutron detector system comprising eight neutron detectors; each detector has a small EJ-301 liquid organic scintillator and photomultiplier tube. The TTNYs obtained were compared with calculation results using Monte Carlo-based spallation models (i.e. INCL4.6/GEM, Bertini/GEM, JQMD/GEM, and JQMD/SMM/GEM) and the evaluated high-energy nuclear data library, i.e. JENDL-4.0/HE, implemented in the particle and heavy ion transport code system (PHITS). All models, including JENDL-4.0/HE, failed to predict high-energy peaks at a detector angle of . Comparing the energy- and angle-integrated spallation neutron yields at energies of ≤20 MeV estimated using the measured TTNYs and the PHITS indicated that INCL4.6/GEM would be suitable for the Monte Carlo transport simulation of ADS reactor physics experiments at the KUCA.

Research on a Monte Carlo Simulation Method of Neutron Coded-Aperture Imaging

Pinhole imaging is an important test technique to obtain information on the spatial distribution of the radiation field in the target region and has been widely used in nuclear physics and inertial confinement fusion (ICF). Coded-aperture, able to maintain good resolution as well as enhancing signal strength, has become a more frequently used method than pinhole imaging in experimental studies. Thus, implementing Monte Carlo simulations of coded-aperture imaging will improve coded-aperture design, image reconstruction, and other related works. However, the current international mainstream Monte Carlo transport simulation programs do not possess the ability to directly simulate coded-aperture imaging. This paper develops a relatively complete coded-aperture imaging simulation function on the Neutron Photon Transport System code based on the next-event estimation method. With the application of Monte Carlo simulation techniques, such as variance reduction and rejection sampling, it is capable of simulating coded-aperture accurately, flexibly, and efficiently, including problems of multiple shapes and even irregular geometry. The results are consistent with combined pinhole imaging, and the computational efficiency has been improved significantly.

A deterministic method for the fast evaluation and optimisation of the 3D neutron wall load for generic stellarator configurations

The neutronic assessment of a fusion power plant design is usually a challenging and time-consuming task involving experts from several disciplines in order to assemble the geometry, source, as well as carry out computationally heavy Monte Carlo transport simulations. In order to overcome this challenge, we present in this work a deterministic method, which combines all these aspects in a single framework that can directly calculate a key neutronics performance indicator, the neutron wall load (NWL), at minimal computational cost for arbitrary stellarator configurations. As our method is based on simple vector and matrix manipulations, a speed on the order of a few CPU-seconds is achieved, which makes it suitable for optimisation frameworks. We demonstrate with a simple optimisation algorithm that it is possible to use our method to generate a first wall with reduced ‘heterogeneity’ in the NWL distribution.

Effect of the Series Resistance on the Current Response of a HgCdTe Avalanche Photodiode Under High-intensity Nanosecond Irradiation

We investigate the nonlinear signal current response of a Hg0.72Cd0.28Te avalanche photodiode (APD) irradiated by high-intensity, finite-duration laser pulses. At high irradiation levels and/or high gains, carrier-induced perturbations in the junction electric field and avalanche gain strongly influence the temporal behavior of the APD current. The total series resistance will play a major role here, and four values of the series resistance were used for mapping out the APD response. When striving for maximum achievable bandwidth, the internal junction capacitance and the internal series resistance set the ultimate limits for an APD. A signal analysis of these high-intensity nonlinear gain effects should therefore begin with an intrinsic APD, and proceed with adding appropriate external series resistances. A simultaneous modeling of the entire external circuit is then required. To this end, we have combined full-band Monte Carlo (MC) transport simulation in the active multiplication zone with conventional circuit modeling outside. We demonstrate how overshoot/undershoot and rapid oscillations in the signal current evolve in time as a function of the chosen external series resistances at two different high-intensity irradiation levels. Oscillations are shown to persist slightly beyond the duration of the laser pulse when operating the diode within the junction transit time-limited regime. The periodicity of the oscillations is related to the junction transit time and remains only weakly dependent on irradiation levels and external resistance values until we enter the resistance–capacitance (RC)-limited case. Here, a change occurs where oscillations are smoothed out as external series resistances are increased further.

Galactic Positrons from Thermonuclear Supernovae

Type Ia supernovae (SNe Ia) may originate from a wide variety of explosion scenarios and progenitor channels. They exhibit a factor of ≈10 difference in brightness and thus a differentiation in the mass of 56Ni → 56Co → 56Fe. We present a study on the fate of positrons within SNe Ia in order to evaluate their escape fractions and energy spectra. Our detailed Monte Carlo transport simulations for positrons and γ-rays include both β + decay of 56Co and pair production. We simulate a wide variety of explosion scenarios, including the explosion of white dwarfs (WDs) close to the Chandrasekhar mass (M Ch), He-triggered explosions of sub-M Ch WDs, and dynamical mergers of two WDs. For each model, we study the influence of the size and morphology of the progenitor magnetic field between 1 and 1013 G. Population synthesis based on the observed brightness distribution of SNe Ia was used to estimate the overall contributions to Galactic positrons due to escape from SNe Ia. We find that this is dominated by SNe Ia of normal brightness, where variations in the distribution of emitted positrons are small. We estimate a total SNe Ia contribution to Galactic positrons of <2% and, depending on the magnetic field morphology, <6–20% for M Ch and sub-M Ch, respectively.

Validation of realistic Monte Carlo plasma gamma-ray source on JET discharges

A novel modelling methodology has been developed for the creation of a realistic plasma gamma-ray source for Monte Carlo transport simulations in the tokamak JET. The methodology couples the TRANSP code for plasma transport calculations with the MCNP Monte Carlo particle transport code, thus connecting plasma physics with gamma-ray transport. This paper presents the validation of the developed source methodology by comparing calculated gamma-ray spectra with measurements performed at JET. The validation focuses on gamma-ray spectra measured by the tangential gamma-ray spectrometer during two JET three ion RF scenario discharges, performed in the JET 2019 deuterium experimental campaign. For validation the calculated plasma gamma-ray spectrum was combined with the neutron induced prompt gamma-ray background, originating in the vacuum vessel, and scaled to absolute values calculating the total number of plasma gamma-ray and neutron emitting reactions. The comparison between calculated and measured gamma-ray spectra shows good agreement with the shape of the calculated gamma-ray spectra matching that of measurements for both studied discharges. Moreover, the calculated absolute values of the gamma-ray spectra were of the same order of magnitude at the position of the gamma-ray detector located at the end of a long line-of-sight in a biological shield. The comparison has validated the developed plasma gamma-ray source methodology for MCNP photon transport calculations at JET. The validation provides a basis for the developed plasma gamma-ray source to be used as a support for the development of future tokamaks such as DEMO.

A perturbation-based hybrid methodology for control drum worth prediction applied to the HOLOS-Quad microreactor concept

Fast and accurate control system reactivity worth estimates are desirable in many applications. Unfortunately, the full core Monte Carlo transport simulations often used to estimate the reactivity worth of control drums are often too costly to run in the time scale needed for many applications, such as model predictive control, reactor design optimization, uncertainty quantification and sensitivity analysis. Therefore, this paper presents a general methodology for control drum worth estimation that is based on a hybrid model consisting of physics-based and statistics-based components. It was found that in the application of the methodology to the HOLOS-Quad Reactor Concept, errors as low as 50 pcm were achieved. Model accuracy was also analyzed as a function of training set size and it was found that the most accurate model required about 70 transport model evaluations to train with further reactivity estimates being calculated on the order of milliseconds.

Weibull-Fréchet random path length model for avalanche gain and noise in photodiodes

A four-parameter Weibull-Fréchet (WF) distribution function has been introduced in the random path length (RPL) model for nonlocal modelling of soft-threshold ionisation in semiconductors. The WF function has been demonstrated to be capable of reproducing the realistic probability distribution function (PDF) of electron and hole ionisation path lengths extracted from full band Monte Carlo (FBMC) transport simulations of bulk GaAs. The electron-initiated multiplication in GaAs avalanche photodiodes (APDs) calculated by the WF-RPL model is in excellent agreement with the results from FBMC. The predicted excess noise factor is closer to that of FBMC as compared to the hard threshold RPL model. The advantage of this improved RPL model as a tool for predicting the PDF of electron and hole ionisation path lengths in AlAs0.56Sb0.44 from the experimentally measured avalanche gain and noise has been analysed. The electron ionisation path length PDF of AlAs0.56Sb0.44 has a unique feature of two decay rates with a narrow full width at half maximum and a long tail. The extremely low hole ionisation coefficient in AlAs0.56Sb0.44 is found with a PDF of ionisation path length spanning over 50 µm at an electric field of 600 kVcm−1, supporting the very low hole feedback ionisation in AlAs0.56Sb0.44 APDs. The combination of the detailed and peaked electron’s ionisation path length PDF and of the broad hole’s ionisation path length PDF is responsible for the extremely low avalanche noise in the 1.55 µm thick AlAs0.56Sb0.44 APDs.

Geant4Reweight: a framework for evaluating and propagating hadronic interaction uncertainties in Geant4

Geant4Reweight is an open-source C++ framework that allows users to weight tracks produced by the Geant4 particle transport Monte Carlo simulation according to hadron interaction cross section variations and estimate uncertainties in Geant4 interaction models by comparing the simulation's hadron interaction cross section predictions to data. The ability to weight hadron transport as simulated by Geant4 is crucial to the propagation of systematic uncertainties related to secondary hadronic interactions in current and upcoming neutrino oscillation experiments, including MicroBooNE, NOvA, and DUNE, as well as hadron test beam experiments such as ProtoDUNE. We provide motivation for weighting hadron tracks in Geant4 in the context of systematic uncertainty propagation, a description of Geant4's transport simulation technique, and a description of our weighting technique and fitting framework in the momentum range 0–10 GeV/c, which is typical for the hadrons produced by neutrino interactions in these experiments.