Monte-Carlo Code TRIPOLI-4 Research Articles

Efficiency of variance-reduction techniques using TRIPOLI-4®: Application to equivalent dose rate calculations in a spent-fuel cask

This paper presents the comparison of different variance-reduction methods implemented in the Monte Carlo code TRIPOLI-4® in the case of a deep penetration problem. In this complex radiation transport situation, where the shielding is very thick to ensure protection, variance-reduction methods are necessary to obtain results with a good accuracy in a reasonable calculation time. The configuration investigated in this work is a spent-fuel transport cask. The various variance-reduction methods used here consist either of Importance Sampling with the Exponential Transform method, or of sophisticated population-control methods. These methods are detailed, then the results are presented and compared and the efficiency of these methods is investigated. While all methods implemented in TRIPOLI-4® are efficient versus analog simulations, the pre-calculation of importance maps with deterministic methods enables a faster convergence of the Monte Carlo simulations, especially when combined with the Exponential Transform.

Benchmarking of the SPERT-III E-core experiment with the Monte Carlo codes TRIPOLI-4®, TRIPOLI-5® and OpenMC

This paper presents a code-to-code verification of the SPERT-III reactor in its E-core configuration using the Monte Carlo codes TRIPOLI-4®, TRIPOLI-5® and OpenMC. A SPERT-III E-core model was originally developed for the Monte Carlo code TRIPOLI-4® and will be the baseline of our analysis The simulation results obtained for the main reactor physics parameters (neutron effective multiplication factor, rod worth, reactivity coefficients and kinetics parameters) with TRIPOLI-4®and OpenMC using different nuclear data libraries are compared and analyzed. Additional verifications are carried out with the next-generation Monte Carlo code TRIPOLI-5®, which is currently under development by CEA and IRSN (France). This paper summarizes a joint study that was conducted within an international research collaboration between CEA Paris-Saclay (France) and the Nuclear Research Center Negev (NRCN, Israel), and is a stepping stone towards future multi-physics simulations exploring the SPERT-III reactor power excursions, including thermal-hydraulics feedback.

Evaluation of the CNESTEN's TRIGA Mark II research reactor physical parameters with TRIPOLI-4® and MCNP

This paper focuses on the development of a new computational model of the CNESTEN's TRIGA Mark II research reactor using the 3D continuous energy Monte-Carlo code TRIPOLI-4 (T4). This new model was developed to assess neutronic simulations and determine quantities of interest such as kinetic parameters of the reactor, control rods worth, power peaking factors and neutron flux distributions. This model is also a key tool used to accurately design new experiments in the TRIGA reactor, to analyze these experiments and to carry out sensitivity and uncertainty studies. The geometry and materials data, as part of the MCNP reference model, were used to build the T4 model. In this regard, the differences between the two models are mainly due to mathematical approaches of both codes. Indeed, the study presented in this article is divided into two parts: the first part deals with the development and the validation of the T4 model. The results obtained with the T4 model were compared to the existing MCNP reference model and to the experimental results from the Final Safety Analysis Report (FSAR). Different core configurations were investigated via simulations to test the computational model reliability in predicting the physical parameters of the reactor. As a fairly good agreement among the results was deduced, it seems reasonable to assume that the T4 model can accurately reproduce the MCNP calculated values. The second part of this study is devoted to the sensitivity and uncertainty (S/U) studies that were carried out to quantify the nuclear data uncertainty in the multiplication factor keff. For that purpose, the T4 model was used to calculate the sensitivity profiles of the keff to the nuclear data. The integrated-sensitivities were compared to the results obtained from the previous works that were carried out with MCNP and SCALE-6.2 simulation tools and differences of less than 5% were obtained for most of these quantities except for the C-graphite sensitivities. Moreover, the nuclear data uncertainties in the keff were derived using the COMAC-V2.1 covariance matrices library and the calculated sensitivities. The results have shown that the total nuclear data uncertainty in the keff is around 585 pcm using the COMAC-V2.1. This study also demonstrates that the contribution of zirconium isotopes to the nuclear data uncertainty in the keff is not negligible and should be taken into account when performing S/U analysis.

Comparing dynamic and quasi-static methods for rod-drop transients with TRIPOLI-4®

Since dynamic reactivities measured on actual reactors are significantly impacted by delayed nuclear data and technological uncertainties, it is of major importance to validate at first the methodology of interpretation against state-of-the-art simulation. In this way, we set up a reference simulation of rod-drop transients with a subcritical core from 3 to 16 $ in the CABRI reactor using the dynamiafforganizationc capabilities of the Monte-Carlo code TRIPOLI-4®. With this tool, the fission-shape evolution and the reactivity are computed for each time step. These quantities are then compared to the output of static stochastic methods based on eigenvalue computations and the Modified Source Method (MSM) to validate the hypotheses of those methods. There is a reactivity discrepancy of 2 % between the MSM model and the dynamic simulation. The fission shape is predicted with a maximum of 2 % discrepancy by the MSM method. This is significantly lower than the direct comparison to the fundamental mode, which proves the interest of a constant-delayed source hypothesis for a quasi-static approach. The nature of the rod-drop (instant or ramp-like) does not influence the fission shape and reactivity values so much, confirming the validity of the prompt-drop hypothesis. The sensitivity of reactivity to kinetic parameters is limited. These results contribute to the identification of the validity domain of the MSM method. Hypotheses investigation and sensibility studies produced pave the way to even better experimental interpretations.

Atomic scale Monte-Carlo simulations of neutron diffraction experiments on stoichiometric uranium dioxide up to 1664 K

The neutron transport in nuclear fuels depends on the crystalline structure of materials when neutron energies lie below a few eV. For that purpose, the theoretical formalism that describes the neutron elastic and inelastic scatterings by crystals has been implemented in the CINEL processing tool in order to provide temperature-dependent neutron cross sections usable by the Monte-Carlo code TRIPOLI4®. The performances of the Monte-Carlo calculations are illustrated with the analysis of neutron powder diffraction data on UO2 measured up to 1664 K with the D4 and D20 diffractometers of the Institute Laue–Langevin (Grenoble, France). The comparison of the experimental and simulated pair distribution functions confirms the unusual decrease of the U–O atomic distances with increasing temperature when an ideal fluorite structure (Fm3̄m space group) with harmonic atomic vibrations is assumed over the full temperature range. The flexibility of the CINEL code allowed to explore disorder or anharmonic oxygen vibrations in the Fm3̄m space group by using either a four-site model with a relaxation term or a structure factor equation with a non-zero anharmonic third-cumulant coefficient. As none of these models succeeded to improve the agreement with the experiments, recent works that propose other local crystalline symmetries for UO2 at elevated temperatures were investigated with the CINEL code. The case of the Pa3̄ symmetry is briefly discussed in this paper.

Comparison of variance-reduction techniques for gamma dose rate determination

Three-dimensional computer simulation and virtual reality technology enable the visualization of dose encountered by workers during dismantling operations by using simplified real-time dose computation tools. Such tools generally use a macroscopic approach for gamma dose rate calculation, namely the point kernel integration method with build-up factors. This simplified physical model enhances calculation performance but presents also some restrictions. In contrast, stochastic Monte Carlo methods enable a precise estimation of gamma dose rate, but computing time is prohibitive for real-time dose applications. To speed up the simulation, Monte Carlo codes can be used in combination with variance-reduction techniques, which have to be used very cautiously to stay within their limits of validity. This paper presents a comparison between two variance-reduction techniques implemented in the Monte Carlo code TRIPOLI-4 $$\circledR $$ , the exponential transform and the adaptive multilevel splitting, testing their efficiency in dismantling-like configurations.Both methods behave better in deep penetration problems but require a good amount of user experience in the creation of the importance map. This study shows the need to develop a new type of algorithm capable to tackle configurations where the lack of collisions can limit the efficiency of the current VRT.

ANALYSIS AND COMPARISON OF APOLLO3® AND TRIPOLI-4® NEUTRON NOISE SOLVERS

Neutron noise analysis addresses the description of small time-dependent flux fluctuations in reactor cores, induced by small global or local perturbations of the macroscopic cross sections due to density fluctuations of the coolant, to vibrations of fuel elements, control rods, or structural materials. The general noise equations are obtained by assuming small perturbations around a steady-state neutron flux and by subsequently taking the Fourier transform in the frequency domain. Recently, new neutron noise solvers have been implemented in diffusion and transport theory in APOLLO3®, the multi-purpose deterministic transport code developed at CEA, and a new stochastic solver has been implemented for the neutron noise analysis in the frequency domain in the Monte Carlo code TRIPOLI-4®, also developed at CEA. In this paper, we compare the two solvers for the case of fuel pin oscillations in a simplified UOX fuel assembly, in view of proposing the examined configurations as a benchmark for neutron noise calculations.

PISTIL, a reactivity modulation device to probe the transfer function of the nuclear reactor CROCUS

The present article summarizes the development and testing of a reactivity modulation device developed by the French Atomic and Alternative Energies Commission (CEA). It was installed in the CROCUS reactor of the Swiss Federal Institute of Technology in Lausanne (EPFL). Experimental tests were performed in the framework of a collaboration between CEA and EPFL. The so-called PISTIL device aims at measuring the nuclear reactor transfer function in the frequency range of interest between 1 mHz and 200 Hz, in order to probe the in-core kinetic behavior of prompt and delayed neutrons. The reactivity modulation is obtained from the rotation of cadmium foils. The design of the system was driven with the objective of installing PISTIL at the center of the CROCUS reactor. Neutronic simulations with TRIPOLI-4 Monte Carlo code were performed to select the suitable design parameters and meet the safety requirements of the reactor operation. The total reactivity worth of the device, as estimated by TRIPOLI-4 Monte Carlo calculation, was approximately 0.16 $ and the maximum amplitude of the reactivity modulation was about 0.013 $. In-core reactivity calibration was then performed and were consistent as compared to TRIPOLI-4 estimations.

Numerical and experimental characterization of the reaction rates in the core of the CNESTEN’s TRIGA Mark II research reactor

Education, training and isotopes production are the most important uses of the Moroccan 2 MW TRIGA Mark II reactor situated at the National Center for Energy Sciences and Nuclear Techniques (CNESTEN, Morocco). To develop new R&D projects in research reactors, the particular and advanced knowledge of neutron and photon flux distribution, within and around the reactor core, is crucial. In order to precisely preparing the experiments in the CNESTEN’s TRIGA reactor, a detailed model was developed using the 3D continuous energy Monte Carlo code TRIPOLI-4 and the continuous energy cross-section data from the JEFF3.1.1 nuclear data library. This new model was used to carry out preliminary neutron and photon calculations to estimate flux levels in the irradiation channels as well as to calculate kinetic parameters of the reactor, core excess reactivity, integral control rods worth and power peaking factors. As a first step of the validation of the model, the obtained results were compared with the experimental ones available in the Final Safety Analysis Report (FSAR) of the TRIGA reactor. A study is being carried out at the end of which the results will be published as an evaluated benchmark. Furthermore, this work aims at experimentally characterize the reaction rates in various irradiation channels inside and outside the reactor core. The measurements are carried out using the neutron activation technique. To set up the experimental design for the activation experiments a series of preliminary calculations were performed using the TRIPOLI-4 model to calculate the expected gamma flux/intensity levels of various materials after irradiations in different positions in the irradiation facilities. Different activation foils with known characteristics are then irradiated and the activity of several isotopes is measured with the Gamma Spectrometry Method. The measured relative reaction rates are then compared with the calculated ones evaluated through the new TRIPOLI-4 reactor model. Fairly good agreement was found, which indicates that the new computational model is accurate enough to reproduce experiments.

Two examples of recent advances in sensitivity calculations

This article reviews two recently established methods to compute sensitivities of some core parameters to basic nuclear data. First, perturbation theory offers an efficient way to compute sensitivities to nuclear parameters in continuous energy transport simulations: making use of the Iterated Fission Probability method, and by coupling the Monte Carlo code TRIPOLI-4® to the nuclear evaluation code CONRAD, we were able to compute the sensitivity of core reactivity to nuclear parameters for simple ICSBEP benchmarks. Second, using a multipoint description of a nuclear system and deterministic transport calculations the sensitivity of the state eigenvector of the system to multigroup nuclear data is computed using simple and fast partial importance calculations.

TOWARDS THE VALIDATION OF NOISE EXPERIMENTS IN THE CROCUS REACTOR USING THE TRIPOLI-4 MONTE CARLO CODE IN ANALOG MODE

Intrinsic neutron noise experiments offer a non-invasive manner to measure the prompt decay constant or reactivity of fissile systems. Using the fluctuations in the density of fission chains, one can infer the kinetics parameters via correlation analysis such as the Rossi-alpha method. The models allowing for the interpretation of these measurements typically rely on the assumption of the system behaving according to point kinetics. When dealing with systems where point kinetics fail to predict the true time correlation – such as heterogeneous or large cores – the direct simulation of fission chains using Monte Carlo methods appears as the only reliable candidate to provide reference predictions for the correlation functions. Monte Carlo methods using explicit fission model libraries are thus being examined as tools for prediction in noise analysis. In this work we illustrate the developments and simulation results of the analog transport capabilities of the TRIPOLI-4 Monte Carlo code coupled with the LLNL fission library FREYA, as applied to a set of neutron noise experiments carried out in the CROCUS zero-power reactor with emphasis on the identification of spatial effects. To validate the general capability of the code to predict noise correlations, we examine time distributions of the whole core fission and explicit detection reactions. We present the methodology to achieve a good agreement between experiments and simulations. We reproduced experimental results for relative α, within typical biases, and conclude on the general feasibility of the analog method. We further explore a decoupled core model and analyze it using the noise method. The results indicate an effective method to treat decoupled systems.

Interpretation of the JANUS Phase 7 shielding experiment with TRIPOLI-4® and quantification of uncertainties due to nuclear data

The JANUS Phase 7 shielding experiment performed in the NESTOR experimental reactor in 1991 studied deep fast neutron propagation in mild steel, boron carbide and sodium. Several steel plates, followed by boxes containing boron carbide and sodium were used as neutron shielding next to a fission plate. Gold, manganese, rhodium and sulphur detectors were positioned at several depths in order to measure the neutron flux at different energies. This experiment is interpreted using the Monte-Carlo code TRIPOLI-4® and different nuclear data for iron 56 and sodium. C/E results exhibit discrepancies generally smaller than 10% for the gold detector, while larger discrepancies are obtained for the sulphur detector. In order to understand the obtained biases, sensitivity calculations were performed to compute the uncertainties on the detector responses due to nuclear data. We show that the propagated uncertainties may explain a large part of the observed discrepancies.

Modeling the consequences of fuel assembly bowing on PWR core neutronics using a Monte-Carlo code

The effect of assemblies bowing in PWR nuclear reactors onto core neutronics is an observed phenomenon still poorly understood which can lead to Power Ratio Tilt. Studies of the consequences of rod/assembly bowing involve many different fields addressed by nuclear power plant, such as neutronics, thermohydraulics, mechanics… in a complex combination of multi-physical interactions. For the neutronic part, the modeling of bowed assemblies in Monte Carlo codes must allow to correctly describe the shape of fuel rods. In this article, two discrete ways to model bowed geometries are tested: the first one consists in a stacking of vertical small cylinders following the shape of the fuel rod by small shifts between neighboring cylinders; the second one, newly introduced in the present research, consists in a sequence of rotated cylindrical segments arranged to as to follow the shape of the fuel rod more closely. Both models are used to reproduce two specific bowing patterns, namely C-shape and S-shape, for which a reference modeling involving an analytical toroidal volume cut by planes is available for use with CEA’s Monte Carlo code Tripoli-4®. Results of comparisons between both models and analytical reference show that, even if the segment modeling requires a specific effort to handle implementation constraints, it appears preferable compared to stacking modeling. It provides accuracy with fewer discrete entities and is therefore computationally affordable and it is far more robust when increasing bowing deflection. This approach is thus only considered ready for its application to any kind of bowing patterns.

Trends on Major Actinides from an Integral Data Assimilation

Nuclear data evaluations on major actinides can be improved by integral data assimilation. Appropriate integral measurements with reliable experimental techniques have been selected such as ICSBEP, IRPhE and MASURCA critical masses, PROFIL irradiation experiments and the FCAIX experimental programme (critical masses and spectral indices). Highly reliable analyses are possible with the use of as-built geometries calculated with the TRIPOLI4 Monte Carlo code. The C/E values have been used in an integral data assimilation solving the Bayes equation. The trends on the JEFF3.1.1235U capture cross section are quite consistent with recent differential measurements. Assimilation results suggest up to a 2.5% decrease for238U capture from 3 keV to 60 keV, and a 4-5% decrease for238U inelastic in the plateau region. For this energy range, uncertainties are respectively reduced from 3-4 to 1-2% and from 6-9% to 2-2.5% for 238U capture and238U inelastic. Results on239Pu fission cross sections are included in posterior uncertainties. The increase trends on239Pu capture cross-section is of around 3% in the [2 keV-100 keV] energy range. For240Pu capture cross section, the increase is of around 4% in the [3 keV-100 keV] energy range and goes in the same direction as a recent evaluation.

Correlated Production and Analog Transport of Fission Neutrons and Photons Using Fission Models FREYA, FIFRELIN, and the Monte Carlo Code TRIPOLI-4

Fission modeling in general-purpose Monte Carlo transport codes often relies on average nuclear data provided by the international evaluation libraries. As such, only average fission multiplicities are available and correlations between fission neutrons and photons are missing. Whereas uncorrelated fission physics is usually sufficient for standard reactor core and radiation shielding calculations, correlated fission secondaries are required for specialized nuclear instrumentation and detector modeling. For coincidence counting detector optimization for instance, the precise simulation of fission neutrons and photons that remain correlated in time from birth to detection is essential. New developments were recently integrated into the Monte Carlo transport code TRIPOLI-4 to model fission physics more precisely, the purpose being to access event-by-event fission events from two different fission models: Fission Reaction Event Yield Algorithm (FREYA) and Fission Fragment Evaporation Leading to an Investigation of Nuclear Data (FIFRELIN). TRIPOLI-4 simulations can now be performed, either by connecting via an application programming interface to the Lawrence Livermore National Laboratory fission library including FREYA, or by reading the external fission event data files produced by FIFRELIN beforehand. These new capabilities enable us to easily compare results from the Monte Carlo transport calculations using the two fission models in a nuclear instrumentation application. In the first part of this paper, the broad underlying principles of the two fission models are recalled. We then present the experimental measurements of neutron angular correlations for 252Cf(sf) and 240Pu(sf). The correlations were measured for several neutron kinetic energy thresholds. In the latter part of this paper, simulation results are compared with the experimental data. Spontaneous fissions in 252Cf and 240Pu are modeled by FREYA or FIFRELIN. Emitted neutrons and photons are subsequently transported to an array of scintillators by TRIPOLI-4 in the analog mode to preserve their correlations. Angular correlations between fission neutrons obtained independently from these TRIPOLI-4 simulations, using either FREYA or FIFRELIN, are compared with the experimental results. For 240Pu(sf), the measured correlations were used to tune one of the FREYA model parameters. Similarly, different sets of parameters have been tested in FIFRELIN to try to improve the agreement with the experimental data.

Advances in the Treatment of the Electromagnetic Cascade in the TRIPOLI-4 Monte Carlo Code

TRIPOLI-4 is a Monte Carlo particle transport code developed at CEA Saclay (France) that is employed in the domains of nuclear reactor physics, criticality safety, shielding/radiation protection, and nuclear instrumentation. The goal of this paper is to report on current developments, validation, and verification made in TRIPOLI-4 in the treatment of electron/positron/photon transport. The new capabilities and improvements concern refinements to the electron transport algorithm, the introduction of a charge-deposition score, the new thick-target bremsstrahlung option, the upgrade of the bremsstrahlung model, and the improvement of electron angular straggling at low energy. The importance of each of the developments mentioned above is illustrated by comparisons with calculations performed with other codes and with experimental data.

New perturbation and sensitivity capabilities in Tripoli-4®

Estimating the changes in a nuclear system due to perturbations in the input nuclear data by separate Monte Carlo calculations might be extremely cumbersome for reactor applications. The Iterated Fission Probability (IFP) method has recently paved the way for the application of first-order standard perturbation theory in continuous-energy Monte Carlo codes. In this work, we detail the reactivity perturbation and k-eigenvalue sensitivity analysis capabilities of the Monte Carlo code Tripoli-4®. Simulation results obtained by using the newly implemented IFP algorithm of Tripoli-4® are compared to findings coming from other Monte Carlo methods (such as the differential operator and the correlated sampling) and codes (such as MCNP6 and KENO). For this purpose, we select some benchmark configurations (Godiva, Stacy, Jezebel, Flattop and a fuel lattice) and we test some of the most common perturbation and sensitivity methods currently available in production codes. Their respective advantages and drawbacks are analyzed, and possible future improvements are suggested. Our main finding is that Tripoli-4® produces very similar results to MCNP6 when the same techniques are used. Uncertainty propagation based on the obtained sensitivity profiles and on the COMAC nuclear data covariance matrices is finally discussed.

Neutron multiplication in random media: Reactivity and kinetics parameters

Eigenvalue problems for neutron transport in random geometries are key for many applications, ranging from reactor design to criticality safety. In this work we examine the behaviour of the reactivity and of the kinetics parameters (the effective delayed neutron fraction and the effective neutron generation time) for three-dimensional UOX and MOX assembly configurations where a portion of the fuel pins has been randomly fragmented by using various mixing statistics. For this purpose, we have selected stochastic tessellations of the Poisson, Voronoi and Box type, which provide convenient models for the random partitioning of space, and we have generated an ensemble of assembly realizations; for each geometry realization, criticality calculations have been performed by using the Monte Carlo code Tripoli-4®, developed at CEA. We have then examined the evolution of the ensemble-averaged observables of interest as a function of the average chord length of the random geometries, which is roughly proportional to the correlation length of the fuel fragmentation. The methodology proposed in this work is fairly general and could be applied, e.g., to the assessment of re-criticality probability following severe accidents.

Generalized Iterated Fission Probability for Monte Carlo eigenvalue calculations

The so-called Iterated Fission Probability (IFP) method has provided a major breakthrough for the calculation of the adjoint flux and more generally of adjoint-weighted scores in Monte Carlo eigenvalue calculations. So far, IFP has been exclusively devoted to the analysis of the standard k-eigenvalue equation, by resorting to a formal identification between the adjoint fundamental eigenmode φk† and the neutron importance Ik. In this work, we extend the IFP method to the α-eigenvalue equation, enabling the calculation of the adjoint fundamental eigenmode φα† and the associated adjoint-weighted scores, including kinetics parameters. Such generalized IFP method is first verified in a simple two-group infinite medium transport problem, which admits analytical solutions. Then, α-adjoint-weighted kinetics parameters are computed for a few reactor configurations by resorting to the Monte Carlo code Tripoli-4®, and compared to the k-adjoint-weighted kinetics parameters obtained by the standard IFP. The algorithms that we have developed might be of interest in the interpretation of reactivity measurements, in the context of reactor period calculations by Monte Carlo simulation.

Evaluation of [formula omitted] measurements from BERENICE programme with Tripoli4® and uncertainty qualification

The effective delayed neutron fraction (βeff) is an important characteristic of nuclear reactors since it affects transients significantly. It is therefore important to characterise it correctly. The use of best-estimate codes and data together with an evaluation of the uncertainties is required not only for their use in safety studies but also to assess reactivity effects which are being measured relative to the effective delayed neutron fraction (βeff) in $.The use of the Iterated Fission Probability method in the Monte Carlo code Tripoli4® confirms results obtained with deterministic codes such as ERANOS for calculating βeff. The asset of Tripoli4® is the possibility to get a better representation of experimental cores. Its use for evaluating the calculated parts of the “experimental” βeff of the BERENICE experimental programme has led to significant improvements of the C/E ratios, especially the R2 experimental core.This work is in support of the ASTRID project which developed the concept of a Sodium cooled Fast Reactor (SFR). In order to get a reduced uncertainty it is recommended to repeat the βeff measurement within the future GENESIS experimental programme in the refurbished zero power reactor (ZPR) MASURCA with an improved noise measurement technique.The nuclear data uncertainty propagation has led to a 2.8% uncertainty for U-Pu core and 2.6% for enriched uranium cores (with JEFF-3.2) with main contributors being the delayed neutron fission yield and the fission cross section of U238.