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Publication# Experimental and numerical study of stochastic branching noise in nuclear reactors

Abstract

Noise analysis applied to nuclear reactor physics is a powerful tool to investigate a reactor's kinetic parameters, and more generally underlying physical processes determining core behavior. The kinetic parameters are the coefficients of simplified time-dependent neutron population equations, the so-called point kinetics equations. Experimentally determined kinetic parameters aid to validate codes and to potentially evaluate nuclear data. This thesis focuses on improvements to the kinetic parameter and uncertainty quantification, the experimental techniques, and the direct simulation of noise experiments. In particular, the notion of spatial effects, i.e. effects that render point kinetics assumptions inaccurate for noise measurements, was investigated. This was achieved by drawing on experiments conducted in the zero power reactor CROCUS.

New detection instrumentation for noise experiments was developed for CROCUS, namely current mode amplifiers for neutron detectors to allow for higher detection efficiency and thus precision; and a scintillation-based gamma detection array, called LEAF, to enable the study of gamma noise. A set of reference neutron and gamma noise experiments were conducted to exemplify an improved method of parameter and uncertainty estimation based on bootstrapping. It lead to a full uncertainty budget showing a relative uncertainty of 3.6% and 1.3% on the prompt decay constant with neutron and gamma noise, respectively. Moreover, reporting of full distributions of kinetic parameters was shown to be required in order to provide an accurate representation of the experimental results. Gamma noise was shown to be superior in terms of precision by a factor of at least two compared to neutron noise when determining the prompt decay constant.

To study spatial effects and the spatial extent of the noise field of CROCUS, a set of experiments with varying detector locations, reactivity, and particle type were conducted. The neutron noise field study showed that measurements are limited to the immediate proximity of the core, and that CROCUS is reliably modeled as a point kinetic reactor for static configurations. Nonetheless, a systematic trend was shown when comparing to code predictions, pointing to a weak spatial effect biasing neutron noise measurements at a distance. The observable gamma noise field using high efficiency detectors was shown to extend beyond neutron noise limits, enabling ex-vessel measurements. The prompt decay constant was determined at about 0.9 meters to the core center with comparable accuracy to that of gamma in-core reference experiments using less-efficient detectors. Gamma correlations were be observed outside of the reactor cavity in front of an experimental channel, enabling a prompt decay constant determination at 7 meters to the core center.

To complement the experimental investigation and to study the underlying physics, a simulation methodology to estimate noise responses was developed. Specifically, the explicit simulation of noise experiments using analog Monte Carlo transport coupled to a fission model was studied. An established code with an existing fission library coupling, TRIPOLI-4, was used as reference. In addition, a newly developed coupling of a fission library to Serpent 2 allowed for code-to-code comparison. The full methodology, verification, and validation to the aforementioned CROCUS experiments is presented.

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Pavel Frajtag, Vincent Pierre Lamirand, Tom Mager, Oskari Ville Pakari, Andreas Pautz

We experimentally demonstrate the advantages of gamma detection for noise measurements to deter-mine the prompt neutron decay constant a of a nuclear reactor using the power spectral density (PSD) method, coupled to a new uncertainty estimation scheme based on bootstrapping. We compare the rel-ative precision of gamma noise measurements and neutron noise measurements performed in the CROCUS research reactor. The reference neutron noise experiment employs two large U-235 fission chambers, whereas the new gamma noise experiment is based on two CeBr3 scintillators. The results demonstrate that gamma noise is superior to neutron noise with respect to precision, giving an advantage with regards to measurement time to reach desired uncertainty levels: the uncertainty budget shows a relative uncertainty of 3.6% and 1.3% on the prompt neutron decay constant with neutron and gamma noise, respectively. Moreover, thanks to bootstrapping, the reporting of full distributions - rather than assuming Gaussian spreads - of kinetic parameters is shown to be relevant in order to provide an accurate rep-resentation of the experimental results in some cases. In addition, we notably discuss the lower level discrimination threshold and its effect on the gamma PSDs. Gamma ray cross PSDs exhibit a behaviour contrary to that of a standard neutron acquisition system, and we discuss the implications. Gamma noise could prove to be a cheaper, more precise, and more flexible method to determine reactor kinetics. (C) 2022 The Author(s). Published by Elsevier Ltd.

During the past ten years, different independent factors, such as the rapidly increasing worldwide demand in energy, societal concerns about greenhouse gas emissions, and the high and volatile prices for fossil fuels, have contributed to the renewed interest in nuclear technology. It is in this context that the Generation IV international forum (GIF) launched the initiative, in 2000, to collaborate on the research and development (R&D) efforts needed for the next generation, i.e. Generation IV, of nuclear reactors. These advanced systems will be ideally deployed beyond the year 2030, following the Generation III or III+ nuclear power plants, which are mainly based on light water technology and are currently entering deployment. A particular goal set for Generation IV systems is closure of the nuclear fuel cycle. Thus, apart from improvements in safety, they are expected to offer a better utilization of natural resources, as also a minimization of long-lived radioactive wastes. Among the systems selected by the GIF, the Gas-cooled Fast Reactor (GFR) is a highly innovative system with advanced fuel geometry and materials (fuel pellets of mixed uranium-plutonium carbide within a plate-type, honeycomb structure made of SiC). It is in the context of the large, 2400 MWth reference GFR design that the present doctoral research has been conducted, the principal aim having been to develop and qualify the control assembly (CA) pattern and corresponding CA implementation scheme for this system. The work has been carried out in three successive and complementary phases: (1) validation of the neutronics tools, (2) the CA pattern development and related static analysis, and (3) dynamic core behavior studies for hypothetical CA driven transients. The deterministic code system ERANOS and its associated nuclear data libraries for fast reactors were developed and validated for the previous generation of sodium-cooled reactors. The validation of ERANOS for GFR applications was, therefore, the first task to be realized in the present research. This has entailed a systematic reanalysis of the GFR-relevant, integral data generated at PSI during the GCFR-PROTEUS experimental program of the 1970's. Thus, during the first phase of the thesis, the reference PROTEUS test lattice from these experiments has been analyzed with ERANOS-2.0 and its associated, adjusted nuclear data library ERALIB1, in order to derive a reference computational scheme to be used later for the GFR analysis. Additionally, benchmark calculations were performed with the Monte Carlo code MCNPX, allowing one to both check the deterministic results and to analyze the sensitivity to different modern data libraries. It has been found that, for the main reaction rate ratios, the new analysis of the GCFR-PROTEUS reference lattice generally yields good agreement – within 1σ measurement uncertainty – with experimental values and with the Monte Carlo simulations. As shown by the analysis, the predictions were in somewhat better agreement in the case of the adjusted ERALIB1 library. The applicability of ERANOS-2.0/ERALIB1 as the reference neutronics tool for the GFR analysis could thus be demonstrated. Furthermore, neutronics aspects related to the novel features of the GFR, for which new experimental investigations are needed, were highlighted. In the second phase of the research, the CA pattern was developed for the GFR, based on iterative neutronics and thermal-hydraulics calculations, 2D and 3D neutronics models for the reactor core having first been set up using the reference ERANOS-2.0/ERALIB1 computational scheme. For the thermal-hydraulics analysis, the CEA code COPERNIC was used. This design work was followed by the study of an appropriate CA implementation scheme (number of CAs and corresponding positions within the core). Detailed neutronics studies revealed the existence of large CA interaction effects, so-called shadowing/anti-shadowing effects leading to an amplification/reduction of the CA worth. The interactions between the absorber pins within a CA, and between the CAs themselves, were investigated in detail, with the goal to optimize the CA efficiency, in terms of the absorber fraction and minimization of the associated heterogeneity effects. The proposed CA pattern consists of 54 absorber pins placed in a triangular lattice. Each absorber pin is a stainless-steel tube filled with highly enriched 10B boron carbide pellets. As a result of the detailed investigations, the absorber pin diameter could be chosen such as to minimize the pin-to-pin influence within the assembly. In particular, a central part of the CA was designed without any absorber pins (zone filled with stagnant helium). A final reduction of the heterogeneity effect (difference between homogeneous and heterogeneous treatments) to 13% was achieved through this feature. Of special importance, the neutronics investigations performed for the reference GFR core ("2004-Core"), especially those related to the CA interactions, have directly contributed to a new core design ("2007-Core"), with the height-to-diameter ratio having been increased to 0.6, compared to 0.3 for the reference core. During the third phase, detailed coupled, 3D neutron-kinetics (NK) and 1D thermal-hydraulics (TH) models were developed for the GFR core, the aim being to arrive at an in-depth understanding of the 3D core behavior during CA driven transients, especially from the viewpoint of spatial effects. The coupled models were developed using the PARCS code for the 3D NK and the TRACE code for the 1D TH modeling. Particular attention was paid to have each individual fuel sub-assembly and CA represented, in order to allow the analysis of local deformations of the 3D distributions of power and safety related parameters, such as the coolant, cladding and fuel temperatures. The validation of the coupled full-core models was performed against reference ERANOS-VARIANT calculations. In particular, the CA worth and reactivity feedbacks were benchmarked, the discrepancies being shown to be relatively low (

CEA develops and makes use of miniature fission chambers (MFCs, with radius down to 1.5 mm) for reactor physics conducted in experimental reactors such as EOLE and MINERVE zero power reactors (CEA Cadarache). When measuring fission rate, it is known that the neutron spectrum in the irradiation channel can be modified by the detector and the detector fixture. So the result of the measurement does not give a direct access to the desired quantity (fission rate, neutron flux,etc.) To overcome this problem, it is possible to make use of Monte Carlo calculations based on a detailed modeling of the detector. It could then be included in the 3D reactor model but this leads to large and time consuming calculations. In this case, measurement results can be combined directly with calculated values to produce the desired quantity. Another possibility is to calculate correction factors to apply to the biased measurement, i.e. to perform two-step calculations. Those factors depend on the detector geometry, the neutron spectrum and the fissile isotope at stake. A method to determine those factors is presented in this paper. The previously calculated neutron spectrum is fed to a simplified calculation route that includes only the detector and its close environment. Correction factors are obtained from two calculations results (with and without the detector fixture). In this case, the measured fission rates are corrected before being further processed. This paper details a parameter study on the impact of MFC parts and its environment (cable, connector) on the observed fission rate. Precise models of CEA-made MFCs have been developed for that purpose and used to produce correction factors for various fissile isotopes and neutron spectra. It is shown that fission rates can be greatly underestimated because of neutron radiative capture in MFC parts close to the fissile coating (9% in the worst case). The impact on standard reactor physics measurements is then discussed.

2014