Neutron flux fluctuations are a natural phenomenon of nuclear reactors. Approximately since 2001, pressurized water reactors built by Kraftwerk Union AG have exhibited an unexplained cycle-by-cycle change of the magnitude of these fluctuations. The change has also drawn attention to long-known but also unexplained spatial correlations of the fluctuations in these reactors. The thesis at hand aims to contribute to a better understanding of both the observed change in magnitude and the immanent correlations. Based on the findings of previous research and on the own analysis of measured raw data, a hypothesis was developed, which states that a synchronous coolant-flow driven vibration of major parts of the fuel-assembly ensemble triggers the main contribution to the observed neutron flux fluctuations. The fluctuation correlations are supposed to result from the correlations of the fuel-assembly vibration. This idea was tested using the time-domain reactor dynamics code DYN3D and complementary using the frequency-domain neutronic tool CORE SIM. For this purpose, simplified mechanical models of the synchronous fuel-assembly vibration and models coupling the vibration to the neutron kinetics were developed and implemented. Two effects are distinguished: In case of the “reflector effect”, all fuel assemblies vibrate synchronously, in a way that the main resulting perturbation acts in the radial reflector as a fluctuation of the water layer between the outer fuel assemblies and the core shroud. In case of the “fuel-assembly pitch effect”, the fuel assemblies are unequally involved in the synchronous vibration, in a way that the main perturbations are induced within the reactor core as fluctuations of the fuel-assembly gaps. Both the simulations with DYN3D and the simulations with CORE SIM showed that a synchronized fuel-assembly vibration is a possible main source of the concerned neutron flux fluctuations. In particular, the uniform fluctuation of the gaps between all fuel assemblies, corresponding to high-amplitude fuel-assembly vibrations in the core center and low-amplitude fuel-assembly vibrations in the outer core regions, gave the best approximation to the measured data. A C-like axial vibration-shape provides the best agreement. The simulation results show that the developed hypothesis should be further investigated. In particular, the proposed synchronized vibration of the fuel assemblies suggest correlations of the neutron flux fluctuations with mechanical signals, which have not been taken into account so far. The simulations presented here enable further improvements of the understanding of the neutron flux fluctuations in the concerned reactors by additional measurements involving also specific modes of reactor operation.

El análisis de las fluctuaciones en reactores nucleares es hoy día un valioso instrumento de diagnosis y control del reactor sus fundamentos teóricos están enmarcados en la melanica estadística del no equilibrio y en la teoría de procesos estocásticos. Bajo estos supuestos se estudia en primer lugar los fundamentos de una descripción estocástica con ruidos externos e internos. En segundo lugar analizamos modelos de reactores no lineales con efecto de temperatura y ruidos externos. Estudiamos también modelos de reactores no markovianos por métodos funcionales y de cumulantes. Por último se estudian propiedades asintóticas y haciendo hincapié en el cálculo de la probabilidad de extinción y fluctuaciones en la puesta en marcha. / Nowadays the analysis of fluctuations in nuclear reactors is a valuable tool for diagnosis and control. The basis of such a method is framed in the non-equilibrium statistical mechanics and stochastic process theories. Under these assumptions the basis of a stochastic description of the reactor using external and internal noise is firstly studied. Next, reactor models with non-linear effects due to temperature and external noise are studied. Non-Markovian reactor models are also analysed using functional methods and cumulants. Assymptotic properties are finally treated focusing on the calculation of extinction probabilities and start-up fluctuations.

Le bruit neutronique désigne les fluctuations de la population neutronique induites par des changements déterministes ou stochastiques des sections efficaces macroscopiques lors du fonctionnement à puissance nominale d’un réacteur nucléaire. Ces perturbations peuvent avoir des origines diverses comme une variation de densité du caloporteur ou une vibration d’un élément mécanique (barres de contrôle, assemblages ou crayons combustibles…). Dans les réacteurs de puissance, ces bruits neutroniques sont observables par les détecteurs de neutrons placés à l’intérieur et à l’extérieur du cœur. Lorsque ces bruits sont jugés anormaux, tout l’enjeu est de savoir identifier et localiser leurs sources afin de pouvoir mettre en place les mesures de sûreté éventuellement nécessaires au bon fonctionnement de l’installation. Ces bruits peuvent aussi être exploités pour déterminer certaines propriétés du caloporteur comme sa vitesse ou son titre vapeur, ou encore d’autres propriétés dynamiques globales comme le coefficient de température d’un réacteur à eau pressurisée.Les équations générales du bruit neutronique sont issues de la linéarisation et de la transformée de Fourier de l’équation de Boltzmann cinétique perturbée autour de l’état d’équilibre du cœur en suivant l’hypothèse de petites perturbations et en prenant en compte le couplage avec les équations des précurseurs. Ceci a pour résultat une équation à source dans le domaine fréquentiel. Résoudre cette équation complexe permet de prédire le bruit pour différents emplacements de détecteurs.Cette thèse a pour principal objectif de mettre en place des outils de calculs neutroniques en implémentant notamment un solveur de bruit neutronique dans le code de transport déterministe multi-filière APOLLO3® développé au CEA.Au cours de nos travaux, nous avons tout d’abord étudié et analysé la théorie classique du bruit neutronique. Il nous est apparu qu’il était plus judicieux de définir comme opérateur d’équilibre la moyenne temporelle de l’opérateur cinétique perturbé plutôt que l’opérateur de Boltzmann stationnaire. Ce nouvel opérateur d’équilibre, qui a été développé pour la théorie linéaire et non linéaire, permet en effet de prendre en compte le système de régulation de la puissance présent dans les cœurs de réacteurs qui contrebalance automatiquement tout surplus de réactivité introduit par des perturbations.Nous avons implémenté par la suite la résolution numérique des équations du bruit en théorie de la diffusion et du transport dans une maquette dite « fil » pour des géométries à une dimension en multigroupe. La résolution des équations non linéarisées du bruit en théorie de la diffusion a aussi été implémentée afin d’étudier les limites de la théorie linéaire. Deux méthodes Monte Carlo ont été implémentées dans cette maquette : une méthode proposée très récemment dans la littérature et une nouvelle méthode que nous avons mise en place afin d’améliorer cette dernière. Cette nouvelle méthode a vocation à être implémentée dans le code Monte Carlo de référence TRIPOLI-4® développé au CEA. À l’aide de cette maquette, nous avons de plus proposé une nouvelle façon de modéliser plus exactement une vibration mécanique, modélisation que nous avons comparée avec les diverses modélisations analytiques existantes.Enfin, nous avons implémenté la résolution des équations linéaires du bruit en théorie de la diffusion et du transport dans le code déterministe APOLLO3® (solveur réseau IDT). Afin de tester ce nouveau solveur, nous avons mené à bien des calculs de bruit sur un cœur complet de réacteur à eau légère et à baffle lourd à deux et trois dimensions. Ces simulations nous ont permis de conclure nos travaux en étudiant l’impact de certaines sources de bruit, une oscillation ou une vibration d’un assemblage par exemple, sur un système aussi réaliste que ceux étudiés en calculs stationnaires et ce en théorie de la diffusion et du transport à deux groupes d’énergie. / Neutron noise analysis addresses the description of small time-dependent flux fluctuations induced by small global or local perturbations of the macroscopic cross-sections. These fluctuations may occur in nuclear reactors due to density fluctuations of the coolant, to vibrations of fuel elements, control rods, or any other structures in the core. In power reactors, ex-core and in-core detectors can be used to monitor neutron noise with the aim of detecting possible anomalies and taking the necessary measures for continuous safe power production. Thus, neutron noise techniques are more and more used by the nuclear industry for non-invasive monitoring, control and detection of anomalies in nuclear power plants. They are also applied to the measurement of the properties of the coolant, such as speed and void fraction, or of global dynamic properties such as the moderator temperature coefficient of a pressurized water reactor.The general noise equations are obtained by assuming small perturbations around a steady state in the neutron field and by subsequently taking the Fourier transform in the frequency domain. The analysis is performed based on the neutron kinetic equations including the coupling with neutron precursors. For each frequency, the outcome of the Fourier transform analysis is a fixed-source equation for the perturbed neutron field, which can then be solved so as to predict noise measurements at detector locations.The objective of this thesis is to develop techniques for neutron noise analysis and especially to implement a neutron noise solver in the deterministic transport code APOLLO3® developed at CEA.First, we studied and analyzed the traditional neutron noise theory. In order to take into account the action of the regulating system which cancel the time-averaged reactivity added by a perturbation in a core, we found that it is preferable to choose as steady-state operator the time-averaged of the kinetic operator rather than the stationary Boltzmann operator. This new steady-state operator has been developed for the linear and the non-linear full theory.Then, we have implemented a neutron noise solver in diffusion and transport theory for a simple “rod” geometry in multigroup. A non-linear neutron noise solver has been also implemented in diffusion theory for this rod geometry in order to analyze the limits of the linear theory. Moreover, two Monte Carlo methods that solve the transport equations for the neutron noise in the frequency domain have been implemented for this rod geometry: one recently developed in the literature and a new Monte Carlo algorithm that we have developed so as to improve the latter. This new algorithm is supposed to be implemented in the reference Monte Carlo code TRIPOLI-4® developed at CEA. In addition, a new one-dimension vibration model has been developed and tested for the rod geometry in order to simulate a periodic vibration of a mechanical element and to determine the neutron noise generated by this perturbation.Lastly, a neutron noise solver has been implemented in diffusion and transport theory in the deterministic transport code APOLLO3® (IDT lattice solver). In order to test this new solver, we have performed neutron noise simulations in a large pressurized water reactor with heavy baffle in two and three dimensions. Thus, we have concluded our work by analyzing the neutron noise induced by different noise sources, an oscillation or a vibration of one assembly for example, in a case as realistic as ones used in stationary calculations. These simulations have been performed in diffusion and transport theory with two energy groups.

O presente trabalho propõe o desenvolvimento de uma nova metodologia para a medida da reatividade no reator IPEN/MB-01 baseada nas técnicas de análise de ruído microscópico e macroscópico e no modelo de duas regiões das equações de cinética pontual. Diferentemente dos demais modelos teóricos da cinética pontual, o modelo de duas regiões adotado neste trabalho considera o reator como um sistema acoplado, sendo possível explicitar o núcleo e o refletor matematicamente nas equações de cinética. O estudo do efeito do refletor e da sua contribuição na reatividade é inédito e, para que seja viável, os parâmetros cinéticos relacionados ao refletor devem ser obtidos. A principal vantagem da metodologia proposta é a obtenção dos parâmetros cinéticos do refletor de modo puramente experimental. Com a finalidade de validar este novo método, uma série de experimentos envolvendo diferentes tipos de refletores foi realizada no reator IPEN/MB-01. Foram utilizados os refletores de água leve, aço inox (SS-304) e de água pesada. Utilizou-se a técnica de análise de ruído Rossi-α em vários estados subcríticos para a obtenção dos parâmetros do refletor. Empregou-se também a técnica de Densidades Espectrais para a comparação entre os dados experimentais. Além disso, foi utilizado o código computacional de física de reatores MCNP-5, com a biblioteca de dados nucleares ENDF/B-VII.0, para o cálculo da reatividade a partir do fator de multiplicação efetivo (keff) para cada uma das configurações realizadas experimentalmente. A partir das equações de cinética pontual do modelo de duas regiões foram obtidas as expressões teóricas, que foram utilizadas para o ajuste por mínimos quadrados aos dados experimentais. O tempo de vida dos nêutrons no refletor (τr) e no núcleo (τC) e a fração desses nêutrons que retornam ao núcleo (f) foram obtidos como parâmetros do ajuste e utilizados para o cálculo da reatividade a partir da equação Inhour de duas regiões. São apresentados os resultados experimentais e teóricos referentes ao núcleo padrão com refletor de água leve, refletor de aço inox e refletor de água pesada. Todos os experimentos utilizaram a configuração de 26x28 varetas combustíveis com detectores operando em modo pulso. / This work proposes the development of a new methodology for measurement of the reactivity in the IPEN/MB-01 research reactor facility, based on microscopic and macroscopic noise experiments and the Two-Region point kinetic equations model. Differently from the other point kinetic theoretical models, the Two-Region model assumed in this work takes into account the nuclear reactor how a coupled system, which constitute the theoretical basis of all mathematical development, contemplate both regions of the reactor (core and reflector).The study of the reflector effect and its impact in the reactivity is an original fact and, to make possible the viability of this study, the kinetic parameters related to the reflector must be obtained. The main advantage of this new methodology is to obtain the kinetic parameters from the reflector in a purely experimental way. In order to validate this new method, a series of experiments involving different types of reflectors was performed in the IPEN/MB-01 reactor. The reflectors constituted by Light Water, Stainless Steel (SS-304) and Heavy Water were employed. The Rossi-α neutron noise technique were applied in several subcritical states to obtain the parameters of the reflector. Furthermore, the Auto Power Spectral Densities were also used for a comparison between the experimental data. Moreover, the MCNP-5 nuclear reactor physics code with the ENDF/B-VII.0 library neutron data was employed to calculate the reactivity through the keff multiplication factor for each experimental configuration. In this way, from the Two-Region point kinetic equations model were obtained the theoretical expressions in which were used for least squares fit of the experimental data. The neutron lifetimes in the reflector (τr) and in the core (τC), and the neutron return fraction from the reflector to the core (f) were obtained as least squares fitted parameters and then employed for the reactivity calculation through the Inhour two region equation. The presented experimental and theoretical results are referring to the standard core configuration with aforementioned reflectors of Light Water, Stainless Steel (SS-304) and Heavy Water. For all experiments the 26x28 fuel rod configuration was employed with the detectors operating in pulse mode.

O presente trabalho propõe o desenvolvimento de uma nova metodologia para a medida da reatividade no reator IPEN/MB-01 baseada nas técnicas de análise de ruído microscópico e macroscópico e no modelo de duas regiões das equações de cinética pontual. Diferentemente dos demais modelos teóricos da cinética pontual, o modelo de duas regiões adotado neste trabalho considera o reator como um sistema acoplado, sendo possível explicitar o núcleo e o refletor matematicamente nas equações de cinética. O estudo do efeito do refletor e da sua contribuição na reatividade é inédito e, para que seja viável, os parâmetros cinéticos relacionados ao refletor devem ser obtidos. A principal vantagem da metodologia proposta é a obtenção dos parâmetros cinéticos do refletor de modo puramente experimental. Com a finalidade de validar este novo método, uma série de experimentos envolvendo diferentes tipos de refletores foi realizada no reator IPEN/MB-01. Foram utilizados os refletores de água leve, aço inox (SS-304) e de água pesada. Utilizou-se a técnica de análise de ruído Rossi-α em vários estados subcríticos para a obtenção dos parâmetros do refletor. Empregou-se também a técnica de Densidades Espectrais para a comparação entre os dados experimentais. Além disso, foi utilizado o código computacional de física de reatores MCNP-5, com a biblioteca de dados nucleares ENDF/B-VII.0, para o cálculo da reatividade a partir do fator de multiplicação efetivo (keff) para cada uma das configurações realizadas experimentalmente. A partir das equações de cinética pontual do modelo de duas regiões foram obtidas as expressões teóricas, que foram utilizadas para o ajuste por mínimos quadrados aos dados experimentais. O tempo de vida dos nêutrons no refletor (τr) e no núcleo (τC) e a fração desses nêutrons que retornam ao núcleo (f) foram obtidos como parâmetros do ajuste e utilizados para o cálculo da reatividade a partir da equação Inhour de duas regiões. São apresentados os resultados experimentais e teóricos referentes ao núcleo padrão com refletor de água leve, refletor de aço inox e refletor de água pesada. Todos os experimentos utilizaram a configuração de 26x28 varetas combustíveis com detectores operando em modo pulso. / This work proposes the development of a new methodology for measurement of the reactivity in the IPEN/MB-01 research reactor facility, based on microscopic and macroscopic noise experiments and the Two-Region point kinetic equations model. Differently from the other point kinetic theoretical models, the Two-Region model assumed in this work takes into account the nuclear reactor how a coupled system, which constitute the theoretical basis of all mathematical development, contemplate both regions of the reactor (core and reflector).The study of the reflector effect and its impact in the reactivity is an original fact and, to make possible the viability of this study, the kinetic parameters related to the reflector must be obtained. The main advantage of this new methodology is to obtain the kinetic parameters from the reflector in a purely experimental way. In order to validate this new method, a series of experiments involving different types of reflectors was performed in the IPEN/MB-01 reactor. The reflectors constituted by Light Water, Stainless Steel (SS-304) and Heavy Water were employed. The Rossi-α neutron noise technique were applied in several subcritical states to obtain the parameters of the reflector. Furthermore, the Auto Power Spectral Densities were also used for a comparison between the experimental data. Moreover, the MCNP-5 nuclear reactor physics code with the ENDF/B-VII.0 library neutron data was employed to calculate the reactivity through the keff multiplication factor for each experimental configuration. In this way, from the Two-Region point kinetic equations model were obtained the theoretical expressions in which were used for least squares fit of the experimental data. The neutron lifetimes in the reflector (τr) and in the core (τC), and the neutron return fraction from the reflector to the core (f) were obtained as least squares fitted parameters and then employed for the reactivity calculation through the Inhour two region equation. The presented experimental and theoretical results are referring to the standard core configuration with aforementioned reflectors of Light Water, Stainless Steel (SS-304) and Heavy Water. For all experiments the 26x28 fuel rod configuration was employed with the detectors operating in pulse mode.