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Andrea Zoia - One of the best experts on this subject based on the ideXlab platform.

  • Monte Carlo power iteration: Entropy and spatial correlations
    Annals of Nuclear Energy, 2016
    Co-Authors: Michel Nowak, Jilang Miao, Benoit Forget, Anthony Onillon, Kord Smith, Eric Dumonteil, Andrea Zoia
    Abstract:

    The behaviour of Monte Carlo criticality simulations is often assessed by examining the convergence of the so-called entropy function. In this work, we shall show that the entropy function may lead to a misleading interpretation, and that potential issues occur when spatial correlations induced by fission events are important. Additional information can be extracted from the analysis of the higher-order moments of the entropy function, or from the center of mass of the Neutron Population. Within the framework of a simplified model based on branching processes, we will relate the behaviour of the spatial fluctuations of the fission chains to the key parameters of the simulated system, namely, the number of particles per generation, the reactor size and the migration area. Numerical simulations of a fuel rod and of a whole core suggest that the obtained results are quite general and hold true also for real-world applications.

  • Monte Carlo power iteration: Entropy and spatial correlations
    Annals of Nuclear Energy, 2016
    Co-Authors: Michel Nowak, E. Dumonteil, Jilang Miao, Benoit Forget, Anthony Onillon, Kord Smith, Andrea Zoia
    Abstract:

    Abstract The behavior of Monte Carlo criticality simulations is often assessed by examining the convergence of the so-called entropy function. In this work, we shall show that the entropy function may lead to a misleading interpretation, and that potential issues occur when spatial correlations induced by fission events are important. We will support our analysis by examining the higher-order moments of the entropy function and the center of mass of the Neutron Population. Within the framework of a simplified model based on branching processes, we will relate the behavior of the spatial fluctuations of the fission chains to the key parameters of the simulated system, namely, the number of particles per generation, the reactor size and the migration area. Numerical simulations of a fuel rod and of a whole core suggest that the obtained results are quite general and hold true also for real-world applications.

  • Neutron fluctuations: The importance of being delayed.
    Physical Review E, 2015
    Co-Authors: Bahram Houchmandzadeh, E. Dumonteil, Alain Mazzolo, Andrea Zoia
    Abstract:

    The Neutron Population in a nuclear reactor is subject to fluctuations in time and in space due to the competition of diffusion by scattering, births by fission events, and deaths by absorptions. As such, fission chains provide a prototype model for the study of spatial clustering phenomena. In order for the reactor to be operated in stationary conditions at the critical point, the Population of prompt Neutrons instantaneously emitted at fission must be in equilibrium with the much smaller Population of delayed Neutrons, emitted after a Poissonian time by nuclear decay of the fissioned nuclei. In this work, we will show that the delayed Neutrons, although representing a tiny fraction of the total number of Neutrons in the reactor, actually have a key impact on the fluctuations, and their contribution is very effective in quenching the spatial clustering.

  • The critical catastrophe revisited
    Journal of Statistical Mechanics: Theory and Experiment, 2015
    Co-Authors: Clélia De Mulatier, E. Dumonteil, Alberto Rosso, Andrea Zoia
    Abstract:

    The Neutron Population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole Neutron Population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total Population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the Neutrons may display a wild patchiness (clustering). On the contrary, imposing a Population control on the total Population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of Population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the Neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time.

E. Dumonteil - One of the best experts on this subject based on the ideXlab platform.

  • Patchy nuclear chain reactions
    2020
    Co-Authors: E. Dumonteil, R. Bahran, T. Cutler, B. Dechenaux, T. Grove, J. Hutchinson, G. Mckenzie, A. Mcspaden, W. Monange, M. Nelson
    Abstract:

    Stochastic fluctuations of the Neutron Population within a nuclear reactor are typically prevented by operating the core at a sufficient power, since a deterministic behavior of the Neutron Population is required by automatic safety systems to detect unwanted power excursions. Recent works however pointed out that, under specific circumstances, non-Poissonian patterns could affect Neutron spatial distributions. This motivated an international program to experimentally detect and characterize such fluctuations and correlations, which took place in 2017 at the Rensselaer Polytechnic Institute Reactor Critical Facility. The main findings of this program will indeed unveil patchiness in snapshots of Neutron spatial distributions -- obtained with a dedicated numerical twin of the reactor -- that support this first experimental characterization of the 'Neutron clustering' phenomenon, while a stochastic model based on reaction-diffusion processes and branching random walks will reveal the key role played by the reactor intrinsic sources in understanding Neutron spatial correlations.

  • Neutron clustering: spatial fluctuations in multiplying systems at the critical point
    2017
    Co-Authors: A. Zoia, E. Dumonteil
    Abstract:

    We investigate the spatial fluctuations of a Neutron Population close to criticality the interplaybetween random births and deaths leads to a spontaneous clustering of the diusing individuals. By resortingto a statistical mechanics approach, we determine the behaviour of the average Neutron Neutron density, thepair correlation function and other relevant physical observables. When the individuals are left free to evolve,their ultimate fate is the so-called critical catastrophe, i.e., extinction. When a global constraint is imposed onthe total number of individuals, the impact of clustering on diusion depends on the competition between thetime required for a Neutron to explore the whole reactor, and the time over which the Population has undergonea full generational renewal. In order to illustrate these results, exact formulas and scaling functions are derivedfor a simple model of nuclear reactor and are compared to Monte Carlo simulations.

  • Monte Carlo power iteration: Entropy and spatial correlations
    Annals of Nuclear Energy, 2016
    Co-Authors: Michel Nowak, E. Dumonteil, Jilang Miao, Benoit Forget, Anthony Onillon, Kord Smith, Andrea Zoia
    Abstract:

    Abstract The behavior of Monte Carlo criticality simulations is often assessed by examining the convergence of the so-called entropy function. In this work, we shall show that the entropy function may lead to a misleading interpretation, and that potential issues occur when spatial correlations induced by fission events are important. We will support our analysis by examining the higher-order moments of the entropy function and the center of mass of the Neutron Population. Within the framework of a simplified model based on branching processes, we will relate the behavior of the spatial fluctuations of the fission chains to the key parameters of the simulated system, namely, the number of particles per generation, the reactor size and the migration area. Numerical simulations of a fuel rod and of a whole core suggest that the obtained results are quite general and hold true also for real-world applications.

  • Neutron fluctuations: The importance of being delayed.
    Physical Review E, 2015
    Co-Authors: Bahram Houchmandzadeh, E. Dumonteil, Alain Mazzolo, Andrea Zoia
    Abstract:

    The Neutron Population in a nuclear reactor is subject to fluctuations in time and in space due to the competition of diffusion by scattering, births by fission events, and deaths by absorptions. As such, fission chains provide a prototype model for the study of spatial clustering phenomena. In order for the reactor to be operated in stationary conditions at the critical point, the Population of prompt Neutrons instantaneously emitted at fission must be in equilibrium with the much smaller Population of delayed Neutrons, emitted after a Poissonian time by nuclear decay of the fissioned nuclei. In this work, we will show that the delayed Neutrons, although representing a tiny fraction of the total number of Neutrons in the reactor, actually have a key impact on the fluctuations, and their contribution is very effective in quenching the spatial clustering.

  • The critical catastrophe revisited
    Journal of Statistical Mechanics: Theory and Experiment, 2015
    Co-Authors: Clélia De Mulatier, E. Dumonteil, Alberto Rosso, Andrea Zoia
    Abstract:

    The Neutron Population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to absorption events. When the reactor is operated at the critical point, and fissions are exactly compensated by absorptions, the whole Neutron Population might in principle go to extinction because of the wild fluctuations induced by births and deaths. This phenomenon, which has been named critical catastrophe, is nonetheless never observed in practice: feedback mechanisms acting on the total Population, such as human intervention, have a stabilizing effect. In this work, we revisit the critical catastrophe by investigating the spatial behaviour of the fluctuations in a confined geometry. When the system is free to evolve, the Neutrons may display a wild patchiness (clustering). On the contrary, imposing a Population control on the total Population acts also against the local fluctuations, and may thus inhibit the spatial clustering. The effectiveness of Population control in quenching spatial fluctuations will be shown to depend on the competition between the mixing time of the Neutrons (i.e., the average time taken for a particle to explore the finite viable space) and the extinction time.

Antonio Carlos Marques Alvim - One of the best experts on this subject based on the ideXlab platform.

  • A stochastic model for Neutrons simulation considering the spectrum and nuclear properties with continuous dependence of energy
    Progress in Nuclear Energy, 2013
    Co-Authors: Dayana Q. De Camargo, Bardo E. J. Bodmann, Marco Tullio De Vilhena, Sérgio Q. Bogado Leite, Antonio Carlos Marques Alvim
    Abstract:

    Abstract In this work we developed a stochastic model to simulate Neutron transport in a heterogeneous medium, considering continuous Neutron spectra and the nuclear properties with its continuous dependence on energy. This model was implemented using the Monte Carlo method for the propagation of Neutrons in different media. Due to restrictions with respect to the number of Neutrons that can be simulated in reasonable computational time we introduced a variable control volume together with (pseudo-) periodic boundary conditions in order to overcome this problem. This study allowed a detailed analysis of the influence of energy on the Neutron Population and its impact on the life cycle of Neutrons. From the results, even for a simple geometrical arrangement, we can conclude that there is need to consider the energy dependence and hence defined a spectral effective multiplication factor per Monte Carlo step.

Dayana Q. De Camargo - One of the best experts on this subject based on the ideXlab platform.

  • A stochastic model for Neutrons simulation considering the spectrum and nuclear properties with continuous dependence of energy
    Progress in Nuclear Energy, 2013
    Co-Authors: Dayana Q. De Camargo, Bardo E. J. Bodmann, Marco Tullio De Vilhena, Sérgio Q. Bogado Leite, Antonio Carlos Marques Alvim
    Abstract:

    Abstract In this work we developed a stochastic model to simulate Neutron transport in a heterogeneous medium, considering continuous Neutron spectra and the nuclear properties with its continuous dependence on energy. This model was implemented using the Monte Carlo method for the propagation of Neutrons in different media. Due to restrictions with respect to the number of Neutrons that can be simulated in reasonable computational time we introduced a variable control volume together with (pseudo-) periodic boundary conditions in order to overcome this problem. This study allowed a detailed analysis of the influence of energy on the Neutron Population and its impact on the life cycle of Neutrons. From the results, even for a simple geometrical arrangement, we can conclude that there is need to consider the energy dependence and hence defined a spectral effective multiplication factor per Monte Carlo step.

William Emrich - One of the best experts on this subject based on the ideXlab platform.

  • Neutron Balance Equation and Transport Theory
    Principles of Nuclear Rocket Propulsion, 2016
    Co-Authors: William Emrich
    Abstract:

    The time rate of change of the Neutron Population in a nuclear reactor depends upon the rate at which Neutrons are produced in the reactor as compared to the rate at which Neutrons are lost from the reactor. During steady-state operation, the production and loss rates in the reactor exactly cancel and the Neutron Population remains constant. The Neutronics calculations necessary to determine the exact spatial dependence of the Neutron Population in the reactor generally require a calculational technique called transport theory. Transport theory is challenging from a calculational standpoint; however, an approximation to transport theory called diffusion theory is often used to perform the needed Neutronics calculations. Diffusion theory has been found to be acceptable when high accuracy is not required or when the Neutron Population gradients in the reactor are not very large.

  • Neutron Flux Energy Distribution
    Principles of Nuclear Rocket Propulsion, 2016
    Co-Authors: William Emrich
    Abstract:

    During fission an atomic nucleus generally splits into two fission products and between two and three Neutrons. These Neutrons are extremely energetic having energies in the low MeV range. These Neutrons lose energy through scattering collisions, and if they are not captured by a nucleus will eventually reach thermal equilibrium at energies of a fraction of an eV. It is found that light nuclei such as hydrogen and beryllium are the most effective at slowing-down Neutrons. During this slowing-down process, the Neutron Population will take on a spectrum of energies which will depend upon other things, the amount of fissionable material, the probability of the Neutrons being scattered as opposed to being absorbed, and so on.