Total Monte Carlo Research Articles

Evaluating Embedded Monte Carlo vs. Total Monte Carlo for Nuclear Data Uncertainty Quantification

The purpose of this paper is to compare a new method called Embedded Monte Carlo (EMC) to the well-known Total Monte Carlo (TMC) method for nuclear data uncertainty propagation. Indeed, the TMC methodology is based on the use of a large number of random samples of nuclear data libraries and performing separate Monte Carlo calculations for each random sample. Then, the computation of nuclear data uncertainty is based on the difference between the total uncertainty and the statistical uncertainty of each Monte Carlo simulation. This method can either be applied to MC and deterministic codes where there are no statistical uncertainties. The goal of EMC is to compute statistical uncertainty for each random sample by utilizing historical statistics instead of the batch statistics employed in TMC. Consequently, one large Monte Carlo simulation can be conducted where each batch represents a new random sample, thereby embedding the propagation of uncertainties within a single calculation and reducing computational expenses. This approach allows for the calculation of nuclear data uncertainty using history statistics in fixed source and eigenvalue calculations. This paper demonstrates the capability of this new method using OpenMC. The analysis will be performed on a Godiva sphere benchmark by propagating the uncertainty on two input parameters: the average neutron multiplicity v and 235U density.

Using Total Monte Carlo with hybrid calculation methods for constructing the covariance matrix of a neutron spectrum: Applications in spectrum adjustment

A new calculation scheme has been developed to improve the quality of covariance matrices of a-priori neutron spectra. A high quality covariance matrix is essential for guiding the adjustment of the a-priori calculated neutron spectrum to experimental dosimetry measurements in a physically realistic way. This new calculation scheme incorporates state-of-the-art hybrid deterministic/Monte Carlo methods and does not rely on prior knowledge of correlations between the different energy groups. The ADVANTG code was used to generate weight-windows for the full MCNP reactor model of the High Flux Reactor (HFR) in Petten, the Netherlands. This then allowed Total Monte Carlo (TMC) calculations to be performed with very low statistical uncertainties. A detailed demonstration of applying these covariance matrices to spectrum adjustment is also provided by utilising an algorithm adopted from the STAY’SL program. We have used the example of the HELIOS irradiation experiment performed at the HFR to demonstrate the approach here, but the flexibility of the method means it may be applied universally to neutron spectra calculated anywhere.

Statistical Analysis of Tritium Breeding Ratio Deviations in the DEMO Due to Nuclear Data Uncertainties

For the stable and self-sufficient functioning of the DEMO fusion reactor, one of the most important parameters that must be demonstrated is the Tritium Breeding Ratio (TBR). The reliable assessment of the TBR with safety margins is a matter of fusion reactor viability. The uncertainty of the TBR in the neutronic simulations includes many different aspects such as the uncertainty due to the simplification of the geometry models used, the uncertainty of the reactor layout and the uncertainty introduced due to neutronic calculations. The last one can be reduced by applying high fidelity Monte Carlo simulations for TBR estimations. Nevertheless, these calculations have inherent statistical errors controlled by the number of neutron histories, straightforward for a quantity such as that of TBR underlying errors due to nuclear data uncertainties. In fact, every evaluated nuclear data file involved in the MCNP calculations can be replaced with the set of the random data files representing the particular deviation of the nuclear model parameters, each of them being correct and valid for applications. To account for the uncertainty of the nuclear model parameters introduced in the evaluated data file, a total Monte Carlo (TMC) method can be used to analyze the uncertainty of TBR owing to the nuclear data used for calculations. To this end, two 3D fully heterogeneous geometry models of the helium cooled pebble bed (HCPB) and water cooled lithium lead (WCLL) European DEMOs were utilized for the calculations of the TBR. The TMC calculations were performed, making use of the TENDL-2017 nuclear data library random files with high enough statistics providing a well-resolved Gaussian distribution of the TBR value. The assessment was done for the estimation of the TBR uncertainty due to the nuclear data for entire material compositions and for separate materials: structural, breeder and neutron multipliers. The overall TBR uncertainty for the nuclear data was estimated to be 3~4% for the HCPB and WCLL DEMOs, respectively.

Nuclear data assimilation, scientific basis and current status

The use of Data Assimilation methodologies, known also as a data adjustment, liaises the results of theoretical and experimental studies improving an accuracy of simulation models and giving a confidence to designers and regulation bodies. From the mathematical point of view, it approaches an optimized fit to experimental data revealing unknown causes by known consequences that would be crucial for data calibration and validation. Data assimilation adds value in a ND evaluation process, adjusting nuclear data to particular application providing so-called optimized design-oriented library, calibrating nuclear data involving IEs since all theories and differential experiments provide the only relative values, and providing an evidence-based background for validation of Nuclear data libraries substantiating the UQ process. Similarly, it valorizes experimental data and the experiments, as such involving them in a scientific turnover extracting essential information inherently contained in legacy and newly set up experiments, and prioritizing dedicated basic experimental programs. Given that a number of popular algorithms, including deterministic like Generalized Linear Least Square methodology and stochastic ones like Backward and Hierarchic or Total Monte-Carlo, Hierarchic Monte-Carlo, etc., being different in terms of particular numerical formalism are, though, commonly grounded on the Bayesian theoretical basis. They demonstrated sufficient maturity, providing optimized design-oriented data libraries or evidence-based backgrounds for a science-driven validation of general-purpose libraries in a wide range of practical applications.

Estimation of uncertainty in transmutation rates of LLFPs in a fast reactor transmutation system via an estimation of the cross-section covariances

ABSTRACT A new concept of transmutation system for six long-lived fission products (LLFPs: 79Se, 93Zr, 99Tc, 107Pd, 129I, and 135Cs) consisting of three small-size fast reactor cores was proposed. In order to establish a method to estimate the effects of cross-section uncertainties on the transmutation rates of the LLFPs, cross section covariances for the six LLFPs were estimated using a T6 system which includes resonance and statistical models via propagation of model uncertainties, and the uncertainties of transmutation rates and support factors of the six LLFPs in the three fast reactors were estimated based on a Total Monte Carlo (TMC) method. It was made clear that some of the transmutation rates of these LLFPs have large uncertainties indicating that the accuracy of cross sections for them is not enough, and hence the strategy for efficient transmutation may have to be reconstructed. It is concluded that the T6 system and the TMC method used in this study are quite effective not only to estimate the uncertainties of cross sections but also to assess the effect of error propagation throughout the series of calculations conducting in this study.

Assessment of neutron kerma coefficients and its calculation methodologies using recent basic ENDF-6 libraries

The generation of heat due to interaction of neutrons with matter is an important aspect in the designing of nuclear reactors. The estimation of neutron heating depends profoundly on the evaluated nuclear reaction parameters. Hence, within the purview of radiation damage of materials, it is necessary to investigate the effects of improvements in nuclear databases on the neutron heating rates under various neutron spectra. There are two well established methods to quantify the neutron kerma coefficients in matter: energy balance method and direct method. The well established code like NJOY21 gives the energy balance neutron kerma. In this study, the importance and performance of the direct method has been investigated, as the recent general purpose basic evaluated nuclear data files provide more complete database. Though both the methods predict closely the reported measured values of neutron kerma coefficients for structural elements, significant differences are observed between these two methods at higher energies where contributions from charged particle emitting reactions become important. The direct method is found to be more meaningful as it always ensures positive kerma coefficients and helps to separately identify the contributions from light charged particles and recoil nucleus. The neutron spectrum dependence of neutron kerma from both the methods are also investigated. Further, the nuclear data uncertainties in neutron heating are quantified by the Total Monte Carlo (TMC) methodology using the random ENDF-6 files in TENDL-2015 and the results show that the nuclear data uncertainties are in the range of 9–29%.

Uncertainty quantification and sensitivity studies on Thorium-fueled reactors

This paper shows how Total Monte Carlo (TMC) method and Perturbation Theory (PT) can be applied to quantify uncertainty due to nuclear data on reactor static calculations of integral parameters such as keff and βeff. This work focuses on thorium fueled reactors and it aims to rank different cross sections uncertainty regarding criticality calculations. The consistency of the two methods are first studied. The cross sections set used for the TMC method is computed to build adequate correlation matrices. Those matrices are then multiplied by the sensitivity coefficients obtained thanks to the PT to obtain global uncertainties that are compared to the ones calculated by the TMC method. Results in good agreement allow us to use correlation matrix from the state of the art nuclear data library (JEFF 3-3) that provide insight of uncertainty on keff and βeff for thorium fueled Pressurized Water Reactors. Finally, maximum uncertainties on cross sections are estimated to reach a target uncertainty on integral parameters. It is shown that a strong reduction of the current uncertainty is needed and consequently, new measurements and evaluations have to be performed.

An estimation of neutron-induced production of gases with propagation of uncertainties in nuclear data for structural materials of fission and fusion reactors

An accurate estimation of production of gases due to interactions of neutron in structural materials of nuclear systems is an important aspect within the purview of studies of primary radiation damage. Towards this objective, the indigenous code CRaD, which computes neutron primary radiation damage due to displacements of atoms, has been added with the capability to compute gas production for applications in Indian fast reactors. It includes the computation of gas production cross sections by using standard ENDF-6 procedure, estimation of gases in structural materials due to different types of neutron spectra and propagation of nuclear data uncertainties by Total Monte Carlo (TMC) methodology. A comparison of gas production cross sections from CRaD and NJOY (NJOY-2016.31 and NJOY21) is made and a few discrepancies noted with the processing of charged particle production cross sections using the above versions of NJOY are briefly outlined. A simple linear transmutation methodology is adapted in CRaD to estimate the concentrations of gases and validated with the published theoretical data which were obtained using a similar methodology. The study shows that the representation of charged particle data in different ENDF-6 files is not unique and spectrum-averaged gas production cross sections show large variations. The effect of spread in the activation cross sections from different libraries on the two-step processes of gas production in Nickel under different spectra is also discussed. Detailed TMC-based statistical analyses of gas production in Fe are performed and the mean, standard deviation, skewness and channel-wise and isotope-wise correlation coefficients are quantified. The uncertainties in the production of gases in Fe are estimated to be in the range of 16–56%, with the larger uncertainties being observed in the productions of tritium and helium-3 gases. The gas production parameters have shown non-Gaussian distributions.

Propagation of uncertainties in basic nuclear reaction data to uncertainties in the parameters of primary radiation damage by neutrons

The primary radiation damage formation in materials subjected to neutron radiation is very sensitive to the energy spectra of primary knock-on atoms (PKAs) and their collision cascade in the crystal lattice. The estimated values of the primary radiation damage metrics, such as displacements per atom (dpa) cross sections, integrated dpa, PKA spectrum and spectrum averaged PKA energy are uncertain because of uncertainties present in both the basic nuclear reaction data and the displacement damage model parameters. The Total Monte Carlo (TMC) methodology, which uses the random evaluated nuclear data files for nuclides, is well recognized to propagate the uncertainties in basic nuclear data to the derived quantities in nuclear reactor physics. The uncertainties in the above mentioned primary radiation damage parameters are obtained in this study by propagating the uncertainties in basic evaluated nuclear data, following the TMC methodology. The knowledge of uncertainties in the spectrum averaged PKA energies also enables us to ascertain the uncertainties in the production of vacancies through self-ion simulations using SRIM-2013 code. The present study is an outcome of our systematic approach towards establishing the procedure. This includes pre-processing a large number of TENDL nuclear data random files using NJOY-2016, developing an indigenous code CRaD for handling these point and multigroup data libraries and computing primary radiation damage metrics and their associated uncertainties including energy-energy and nuclear reaction channel-channel correlation matrices. The uncertainties in dpa cross sections and PKA spectra due to uncertainties in basic nuclear data are found to be comparatively larger than the uncertainties in respective integrated parameters; viz. dpa and average PKA energy. This study also confirms the non-Gaussian distributions of derived primary radiation damage parameters.

Efficient use of Monte Carlo: the fast correlation coefficient

Random sampling methods are used for nuclear data (ND) uncertainty propagation, often in combination with the use of Monte Carlo codes (e.g., MCNP). One example is the Total Monte Carlo (TMC) method. The standard way to visualize and interpret ND covariances is by the use of the Pearson correlation coefficient, [see formula in PDF] where x or y can be any parameter dependent on ND. The spread in the output, σ, has both an ND component, σND, and a statistical component, σstat. The contribution from σstat decreases the value of ρ, and hence it underestimates the impact of the correlation. One way to address this is to minimize σstat by using longer simulation run-times. Alternatively, as proposed here, a so-called fast correlation coefficient is used, [see formula in PDF] In many cases, cov(xstat; ystat) can be assumed to be zero. The paper explores three examples, a synthetic data study, correlations in the NRG High Flux Reactor spectrum, and the correlations between integral criticality experiments. It is concluded that the use of ρ underestimates the correlation. The impact of the use of ρfast is quantified, and the implication of the results is discussed.

Propagation of neutron-reaction uncertainties through multi-physics models of novel LWR's

The novel design of the renewable boiling water reactor (RBWR) allows a breeding ratio greater than unity and thus, it aims at providing for a self-sustained fuel cycle. The neutron reactions that compose the different microscopic cross-sections and angular distributions are uncertain, so when they are employed in the determination of the spatial distribution of the neutron flux in a nuclear reactor, a methodology should be employed to account for these associated uncertainties. In this work, the Total Monte Carlo (TMC) method is used to propagate the different neutron-reactions (as well as angular distributions) covariances that are part of the TENDL-2014 nuclear data (ND) library. The main objective is to propagate them through coupled neutronic and thermal-hydraulic models in order to assess the uncertainty of important safety parameters related to multi-physics, such as peak cladding temperature along the axial direction of an RBWR fuel assembly. The objective of this study is to quantify the impact that ND covariances of important nuclides such as U-235, U-238, Pu-239 and the thermal scattering of hydrogen in H2O have in the deterministic safety analysis of novel nuclear reactors designs.

XGPT: Extending Monte Carlo Generalized Perturbation Theory capabilities to continuous-energy sensitivity functions

The XGPT method extends the Generalized Perturbation Theory capabilities of Monte Carlo codes to continuous-energy sensitivity functions. In this work, this method is proposed as a new approach to nuclear data uncertainty propagation. XGPT overcomes some of the limitations of legacy perturbation-based approaches. In particular, it allows the nuclear data uncertainty propagation to be performed adopting continuous energy covariance matrices, instead of discretized (multi-group) data. The XGPT capabilities are demonstrated in three simple fast criticality benchmarks for 239Pu and 208Pb cross section uncertainties. The new method is also applied in selected cases to estimate higher moments of the keff distribution, starting from TENDL random evaluations. The XGPT estimates, when compared against reference Total Monte Carlo (TMC) results, show a good agreement and a significant reduction in computational requirements with respect to the TMC approach. Finally, the capabilities for uncertainty propagation involving adjoint-weighted response functions are demonstrated.

Selecting benchmarks for reactor simulations: An application to a lead fast reactor

For several decades reactor design has been supported by computer codes for the investigation of reactor behavior under both steady state and transient conditions. The use of computer codes to simulate reactor behavior enables the investigation of various safety scenarios saving time and cost. There has been an increase in the development of in-house (local) codes by various research groups in recent times for preliminary design of specific or targeted nuclear reactor applications. These codes must be validated and calibrated against experimental benchmark data with their evolution and improvements. Given the large number of benchmarks available, selecting these benchmarks for reactor calculations and validation of simulation codes for specific or target applications can be rather tedious and difficult. In the past, the traditional approach based on expert judgement using information provided in various handbooks, has been used for the selection of these benchmarks. This approach has been criticized because it introduces a user bias into the selection process. This paper presents a method for selecting these benchmarks for reactor calculations for specific reactor applications based on the Total Monte Carlo (TMC) method. First, nuclear model parameters are randomly sampled within a given probability distribution and a large set of random nuclear data files are produced using the TALYS code system. These files are processed and used to analyze a target reactor system and a set of criticality benchmarks. Similarity between the target reactor system and one or several benchmarks is quantified using a similarity index. The method has been applied to the European Lead Cooled Reactor (ELECTRA) and a set of plutonium and lead sensitive criticality benchmarks using the effective multiplication factor (keff). From the study, strong similarity were observed in the keff between ELECTRA and some plutonium and lead sensitive criticality benchmarks. Also, for validation purposes, simulation results for a list of selected criticality benchmarks simulated with the MCNPX and SERPENT codes using different nuclear data libraries have been compared with experimentally measured benchmark keff values.

Workshop 5 – Cross Section, Nuclear Data, and Uncertainties

The Cross Section, Nuclear Data, and Uncertainties Workshop met with 30 participants. There was a lively discussion that covered several different topics. Some of the topics had resonance with topics brought up in other workshop at this symposium. One major issue was how to assign an a priori uncertainty to the trial spectrum used in spectrum adjustment techniques, or, more specifically, the need for a more rigorous and automated coupling of uncertainties into the radiation transport codes that are used to generate the a priori (trial) spectrum that is used in neutron spectrum adjustment approaches. Approaches based on discrete ordinate transport provide a means of generating sensitivity coefficients for specific variations, but fall short of the required task. While some Monte Carlo-based radiation transport codes permit the user to vary the cross sections for specific reactions or to vary material densities, a more universal and automated variation of all relevant inputs to the radiation transport code is required. One approach mentioned was a Total Monte Carlo (TMC) approach provided by a coupling into radiation transport codes of the recently generated statistical sample of random ENDF nuclear data evaluations produced by the TALYS code and incorporated into the TENDL library (for some isotopes). This would provide a set of self-consistent nuclear data files that can be sampled in a transport calculation. This variation of nuclear data would need to be coupled with a variation in material composition, density, and spatial dimensions. Another discussion topic was the need for the community to revisit the consistency of current approaches to spectrum unfolds/adjustment, i.e. a new round of the older REAL-84 and REAL-88 exercises to assess our status. While the dosimetry community has made great strides with the IRDFF library in establishing an international community consensus for dosimetry cross sections and associated nuclear data, the differences within the community in the treatment of the uncertainty in the trial spectrum and the availability of new spectrum adjustment techniques, such as Maximum Entropy codes like MAXED and the use of genetic algorithms, warrant a revisit of these international exercises to assess the current consistency (within stated uncertainty bonds) of approaches within the community to the characterization of neutron spectra and towards expressing the uncertainty in integral metrics based on these spectrum uncertainties. Since the IAEA/NDS has done such a good job in coordinating an international consensus in dosimetry cross sections and nuclear data, and since they coordinated the older REAL-8X exercises, we look to them to coordinate a new international assessment of our consistency in treating spectrum adjustments and characterizing the resulting uncertainties.

Fission Activities of the Nuclear Reactions Group in Uppsala

This paper highlights some of the main activities related to fission of the nuclear reactions group at Uppsala University. The group is involved for instance in fission yield experiments at the IGISOL facility, cross-section measurements at the NFS facility, as well as fission dynamics studies at the IRMM JRC-EC. Moreover, work is ongoing on the Total Monte Carlo (TMC) methodology and on including the GEF fission code into the TALYS nuclear reaction code. Selected results from these projects are discussed.

Experiments and Theoretical Data for Studying the Impact of Fission Yield Uncertainties on the Nuclear Fuel Cycle with TALYS/GEF and the Total Monte Carlo Method

We describe the research program of the nuclear reactions research group at Uppsala University concerning experimental and theoretical efforts to quantify and reduce nuclear data uncertainties relevant for the nuclear fuel cycle. We briefly describe the Total Monte Carlo (TMC) methodology and how it can be used to study fuel cycle and accident scenarios, and summarize our relevant experimental activities. Input from the latter is to be used to guide the nuclear models and constrain parameter space for TMC.The TMC method relies on the availability of good nuclear models. For this we use the TALYS code which is currently being extended to include the GEF model for the fission channel. We present results from TALYS-1.6 using different versions of GEF with both default and randomized input parameters and compare calculations with experimental data for 234U(n,f) in the fast energy range. These preliminary studies reveal some systematic differences between experimental data and calculations but give overall good and promising results.

Uncertainty and correlation analysis of lead nuclear data on reactor parameters for the European Lead Cooled Training Reactor

The Total Monte Carlo (TMC) method was used in this study to assess the impact of 204,206,207,208Pb nuclear data uncertainties on reactor safety parameters for the ELECTRA reactor. Relatively large uncertainties were observed in the keff and the coolant void worth (CVW) for all isotopes except for 204Pb with significant contribution coming from 208Pb nuclear data; the dominant effect came from uncertainties in the resonance parameters; however, elastic scattering cross section and the angular distributions also had significant impact. It was also observed that the keff distribution for 206,207,208Pb deviates from a Gaussian distribution with tails in the high keff region. An uncertainty of 0.9% on the keff and 3.3% for the CVW due to lead nuclear data were obtained. As part of the work, cross section-reactor parameter correlations were also studied using a Monte Carlo sensitivity method. Strong correlations were observed between the keff and (n,el) cross section for all the lead isotopes. The correlation between the (n,inl) and the keff was also found to be significant.

Efficient Use of Monte Carlo: Uncertainty Propagation

A new and faster Total Monte Carlo (TMC) method for the propagation of nuclear data uncertainties in Monte Carlo nuclear simulations is presented (the fast TMC method). It addresses the main drawback of the original TMC method, namely, the necessary large time multiplication factor compared to a single calculation. With this new method, Monte Carlo simulations can now be accompanied with an uncertainty propagation (other than statistical), with small additional calculation time. The fast TMC method is presented and compared with the TMC and fast GRS methods for criticality and shielding benchmarks and burnup calculations. Finally, to demonstrate the efficiency of the method, uncertainties due to uncertainties in 235,238U, 239Pu, and thermal scattering nuclear data, for the local deposited power in 12.7 million cells, are calculated for a full-size reactor core.

Comparison of Two Approaches for Nuclear Data Uncertainty Propagation in MCNPX for Selected Fast Spectrum Critical Benchmarks

Nuclear data uncertainty propagation based on stochastic sampling (SS) is becoming more attractive while leveraging modern computer power. Two variants of the SS approach are compared in this paper. The Total Monte Carlo (TMC) method by the Nuclear Research and Consultancy Group (NRG) generates perturbed ENDF-6-formatted nuclear data by varying nuclear reaction model parameters. At Paul Scherrer Institute (PSI) the Nuclear data Uncertainty Stochastic Sampling (NUSS) system generates perturbed ACE-formatted nuclear data files by applying multigroup nuclear data covariances onto pointwise ACE-formatted nuclear data. Uncertainties of 239Pu and 235U from ENDF/B-VII.1, ZZ-SCALE6/COVA-44G and TENDL covariance libraries are considered in NUSS and propagated in MCNPX calculations for well-studied Jezebel and Godiva fast spectrum critical benchmarks. The corresponding uncertainty results obtained by TMC are compared with NUSS results and the deterministic Sensitivity/Uncertainty method of TSUNAMI-3D from SCALE6 package is also applied to serve as a separate verification. The discrepancies in the propagated 239Pu and 235U uncertainties due to method and covariance differences are discussed.

Quantification of Uncertainties due to 235,238U, 239,240,241Pu and Fission Products Nuclear Data Uncertainties for a PWR Fuel Assembly

Uncertainty analysis on reactivity and discharged inventory for a typical PWR fuel element as a result of uncertainties in 235,238U, 239,240,241Pu, and fission products nuclear data was performed. The Total Monte-Carlo (TMC) method was applied using the deterministic transport code DRAGON. The nuclear data used in this study is from the JEFF-3.1 evaluations, with the exception of the nuclear data files for U, Pu and fission products isotopes, which are taken from the nuclear data library TENDL-2012. Results show that the calculated total uncertainty in keff (as result of uncertainties in nuclear data of the considered isotopes) is virtually independent on fuel burnp and amounts to 700 pcm. The uncertainties in inventory of the discharged fuel is dependent on the element considered and lies in the range 1–15% for most fission products, and is below 5% for the most important actinides.