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The divergence of the Chicago Pile 1 (CP-1) on December 2nd, 1942, marks the birth of the nuclear age. Built under the West Stands of the Stagg Field in Chicago in slightly over two weeks, CP-1 was the first man-made nuclear reactor, conceived as a proof-of-principle physics experiment to demonstrate the feasibility of a self-sustained neutron chain reaction. The fuel consisted in a mixture of uranium oxide and metal uranium, with lumps of several sizes and shapes stacked within bricks of graphite used as moderator to form a cubic lattice. After only three months of operation, CP-1 was dismantled due to safety reasons and rebuilt at the Argonne Site in twenty-one days, under the name of Chicago Pile 2 (CP-2): the new pile had a longer life, contributing vastly to research on material science and nuclear reactor theory, and was finally decommissioned in 1954. Prompted by the eightieth anniversary of the Chicago Pile(s), in this talk we celebrate these astonishing scientific artifacts by building fully detailed three-dimensional digital twins of CP-1 and CP-2 using TRIPOLI-4®, the Monte Carlo code developed at CEA. Technological data for the models have been retrieved from published and unpublished documents of the Manhattan Project. We compare the simulation results to the available experimental measurements, encompassing the reactivity of the piles, the control rod worth, the kinetics parameters and several reactivity coefficients. For each, we examine the associated uncertainties due to missing or incomplete technological data as well as the bias due to nuclear data libraries.

In the context of computing 3D volumetric scores for nuclear applications, combiningMonte Carlo methods andHigh Performance Computing is key to achieve precise, computationally tractable simulations andmeet the industrial deadlines. The next-event “split exponential track-length estimator” (seTLE) is typically adapted to the estimation of a tally in a mesh. We take advantage of the computing capabilities of Graphics Processing Unit (GPU) to mitigate the CPU-intensive tasks involved in the application of the seTLE: the estimation of cross section, the sampling of many out-going pseudo-particles at collision, the ray tracing across the geometry and the accumulation of scores in volumes. We discuss the performance improvements brought by porting each of these steps to GPU. We discuss the influence of the many parameters involved, and select a working point providing the best trade-off between the acceleration factor and the GPU utilization. We show on two examples thatwe obtain an acceleration factor of 8.56 on average over the entire map for the shielding application (up to 50 behind the concrete shield), and of 6.30 on average for the criticality application (up to 16 in the burnable poison tubes), compared to standard TLE on CPU.

In this work we present the verification of the unresolved resonance range treatment implementation in the Monte Carlo code TRIPOLI-5®, which relies on probability tables. For this purpose, we perform extensive code-to-code comparisons with respect to TRIPOLI-4® and OpenMC using two probability tables models (PURR and CALENDF), on a set of benchmark configurations. These tests allow on one hand verifying TRIPOLI-5® and on the other hand analyzing a number of discrepancies related both to the use of different probability tables models and more generally to the handling of nuclear data in the Monte Carlo codes.

This work presents an investigation of cross section library effects with the new TRIPOLI-5 Monte Carlo code, a joint project between CEA, IRSN and EDF in France. Cross section library effects on the absorption rate and the flux spectrum were highlighted for natural elements subjected to a thermal neutron flux. The numerical benchmark that is presented here is a sphere with a radius of 30 cm filled with 10−2 atoms·(barn·cm)−1 of a single element according to its natural isotopic abundances. For the thermal flux case, a smaller sphere with a radius of 1 cm is placed at the center of the main sphere to obtain a thermal-like flux from a pointwise Maxwellian source using a mixture of hydrogen and boron-10. A total of 12 cross sections libraries have been compared.

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.

Valjean is an open-source framework for workflow scheduling, post-processing and data analysis in verification and validation of neutronics codes. It provides native support for reading TRIPOLI-4® and APOLLO3® output files, but can be easily extended to other codes. We present here the structure of the Valjean package, together with a few typical usage examples.

Population-control methods are key to non-stationary Monte Carlo simulations of multiplying systems: they prevent either the unbounded growth or the disappearance of neutrons, occurring respectively in supercritical and subcritical conditions; furthermore, they contribute to an efficient allocation of computational resources by addressing the unbalance between the neutron and the precursor populations. In this paper, we present two alternative populationcontrol algorithms: the legacy implementation in TRIPOLI-4®, the Monte Carlo code developed at CEA, and an improved version that is currently under investigation, based on the use of a simplified point-kinetics solver. We assess the performance of these methods through the simulation of a $2.2 step reactivity insertion in a fast system (Flattop-Pu), leading to an increase of the neutron population by a factor 200, which is benchmarked against point kinetics. We show that the new implementation not only suppresses the slight bias that was present in the legacy method due to a stochastic normalization factor, but also outperforms the previous algorithm in terms of variance reduction and improvement of the figure of merit.

The neutron noise δφ describes the small variations of the neutron flux around the stationary state φ0, and is typically due to vibrations or oscillations of the core components, induced by fluid-structure interactions and other generally unwanted phenomena. Knowledge of δφ is useful for core monitoring: for this purpose, in recent years several new computational methods have been proposed in order to solve the neutron noise equations with state-of-theart deterministic or Monte Carlo solvers. In this paper we present a preliminary investigation of the convergence properties of Monte Carlo methods for neutron noise analysis, in view of improving their reliability. We carry out our investigation on an infinite-medium benchmark configuration: despite the introduced simplifications, our findings suggest some universal features that represent a stepping stone towards a broader theoretical framework.

Zero-variance Monte Carlo games are ideal sampling strategies that provide the theoretical foundations upon which very successful variancereduction schemes are built. In this work, we explore the robustness of zerovariance games and assess in particular the impact of two common simplifications used in production Monte Carlo codes. First, using a discretized adjoint function to bias the kernels that define the stochastic process. Second, replacing the exact sampling of the flight kernel by approximate sampling strategies that are more amenable to be implemented in production Monte Carlo codes. The resulting effects on the variance and on the Figure of Merit (FoM) will be probed in the framework of a benchmark configuration based on the singlespeed two-direction transport model.

The energy spectrum of prompt gamma-rays from 235U thermal fission is reproduced by a fission reaction model FIFRELIN to identify the origin of spectral features. This spectrum is characterized by a bump at 4-4.5 MeV, a shoulder at around 8 MeV, and a tail above 10 MeV, which are attributed to 132Sn and 133Sb, fission fragments with mass from 130 to 134, and those with mass from 99 to 104, charge from 40 to 42, and spin from 12 ℏto 16 ℏ, respectively. Among prompt gamma-rays, high-energy part is important to get insight into scission, because the quanta are emitted by highly excited fission fragments, which still keep the memory of the scission configuration. Our analysis suggests that coincidence detection of high energy gamma-rays and their source fission fragments identifying their isotopic species, spin and excitation energy with particular focus on those with mass number less than 104 will be useful to make conclusions about the origin of high energy gamma-rays.

In this work, we present the first dynamic calculations performed with the Monte Carlo neutron transport code TRIPOLI-4R with thermal-hydraulics feedback. For this purpose, the Monte Carlo code was extended for multi-physics capabilities and coupled to the thermal-hydraulics subchannel code SUBCHANFLOW. As a test case for the verification of transient simulation capabilities, a 3x3-assembly mini-core benchmark based on the TMI-1 reactor is considered with a pin-by-pin description. Two reactivity excursion scenarios initiated by control-rod movement are simulated starting from a critical state and compared to analogous simulations performed using the Serpent 2 Monte-Carlo code. The time evolution of the neutron power, fuel temperature, coolant temperature and coolant density are analysed to assess the multi-physics capabilities of TRIPOLI-4. The stabilizing e_ects of thermal-hydraulics on the neutron power appear to be well taken into account. The computational requirements for massively parallel calculations are also discussed.

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.

The solution of the time-dependent transport problem for neutrons and precursors in a nuclear reactor is hard to treat in a naive Monte-Carlo framework because of the largely different time scales associated to the prompt-fission chains and to the decay of precursors. The increasing computer power and the development of variance-reduction techniques specific for reactor kinetics have recently unlocked the possibility to calculate reference solutions to the time-dependent transport problem. However, the application of time-dependent Monte Carlo to large systems (i.e., a full reactor core) is still stifled by the enormous computational requirements. In this paper, we formulate the construction of an optimal Monte-Carlo strategy (in the sense that it results in a zero-variance estimator) for a specific observable in time-dependent transport, in analogy with the existing schemes for stationary problems. As far as we are aware, zero-variance Monte-Carlo schemes for neutron-precursor kinetics have never been proposed before. We verify our construction with numerical calculations for a benchmark transport problem.

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 electron/positron/photon sector. 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 above is illustrated by comparisons with calculations performed with other codes and with experimental data.

In the present work the Monte Carlo calculations of nucleon-induced fission on actinides and pre-actinides from 100 MeV to 1 GeV, described in a recent paper of ours [1], are extended up to an incident energy of 8 GeV. The calculated (p,f) cross sections are compared with the few experimental data available in the literature. The same model parameters are used to predict (n,f) cross sections in the same energy range. Possible shortcomings of decay models at high incident energies are discussed.

After fission or fusion reactor shutdown the activated structure emits decay photons. For maintenance operations the radiation dose map must be established in the reactor building. Several calculation schemes have been developed to calculate the shutdown dose rate. These schemes are widely developed in fusion application and more precisely for the ITER tokamak. This paper presents the rigorous-two-steps scheme implemented at CEA. It is based on the TRIPOLI-4® Monte Carlo code and the inventory code MENDEL. The ITER shutdown dose rate benchmark has been carried out, results are in a good agreement with the other participant.

The capability to simulate the transport of charged and/or high-energy hadrons (especially protons) is indispensable for a number of applications. This includes, among others, simulation studies concerned with radiation protection and decommissioning around accelerators and high-intensity laser facilities, as well as beam characterisation in spallation neutron sources. In the context of Monte-Carlo particle transport codes, solving these problems often requires the use of advanced variance-reduction techniques. TRIPOLI-4® is a reference Monte-Carlo particle transport code for the simulation of low-energy (≲ 20 MeV) neutrons and photons and offers a wide range of sophisticated variance-reduction schemes; however, it cannot be applied to the problems mentioned above because it lacks the capability to transport charged, high-energy hadrons. This limitation can be circumvented by coupling TRIPOLI-4r with the Geant4 particle-transport toolkit. We present here the first results of this coupling.

We use particle-transport simulations to show that secondary pions play a crucial role for the development of the hadronic cascade and therefore for the production of neutrons and photons from a thick spallation target. Considering the spallation target of the n_TOF Facility at CERN, we see that photon and neutron yields are relatively insensitive to large changes of the average pion multiplicity in the individual spallation reactions. We characterize this robustness as a peculiar property of hadronic cascades in thick targets.

TRIPOLI-4® is a 3D continuous-energy Monte-Carlo particle transport code developed by CEA (SERMA) and devoted to shielding, reactor physics, criticality-safety and nuclear instrumentation. In this paper, we present the recent developments in the TRIPOLI-4® for shielding and radiation protection applications. Some of these additional features are already available in the TRIPOLI-4® version 10 released in December 2015. Other features are in development.

The predictive power of the last version INCL4.6 of the Liège Intranuclear Cascade model for spallation is reviewed. The good results obtained both at low and high energy extend the domain of validity of the model and allow the description of spallation reactions, except the coherent processes, by a unique model from a few MeV to a few GeV incident energy.

We use the tools of hybrid intranuclear-cascade/nuclear-de-excitation models to evaluate the sensitivity of several physical observables to the inclusion of a multifragmentation stage in the deexcitation chain and assess the need for a multifragmentation model in the quantitative description of p + 56 Fe and p + 136 Xe reactions at 1-GeV incident energy. We seek clear signatures of multifragmentation by comparing different state-of-the-art de-excitation models coupled with intranuclear-cascade models and by focusing on discriminating observables such as correlations and fragment longitudinal-velocity distributions. None of the considered observables can be unambiguously interpreted as a multifragmentation footprint. The experimental data are best described as originating from sequential binary decays. However, no de-excitation model can reproduce the experimental longitudinal-volocity distributions from 1-GeV p + 136 Xe.

The de-excitation of compound nuclei has been successfully described for several decades by means of statistical models. However, such models involve a large number of free parameters and ingredients that are often underconstrained by experimental data. We show how the degeneracy of the model ingredients can be partially lifted by studying different entrance channels for de-excitation, which populate different regions of the parameter space of the compound nucleus. Fusion reactions, in particular, play an important role in this strategy because they fix three out of four of the compound-nucleus parameters (mass, charge and total excitation energy). The present work focuses on fission and intermediate-mass-fragment emission cross sections. We prove how equivalent parameter sets for fusion-fission reactions can be resolved using another entrance channel, namely spallation reactions. Intermediate-mass-fragment emission can be constrained in a similar way. An interpretation of the best-fit IMF barriers in terms of the Wigner energies of the nascent fragments is discussed.