Neutron clustering: spatial fluctuations in multiplying systems at the critical point

A. Zoia (1) , E. Dumonteil (2)

1 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
2 IRSN - Institut de Radioprotection et de Sûreté Nucléaire

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.

Keywords: Clustering; neutron noise; Monte Carlo

Domains: Nuclear Experiment [nucl-ex]; Nuclear Theory [nucl-th]

A. Zoia, E. Dumonteil. Neutron clustering: spatial fluctuations in multiplying systems at the critical point. M&C 2017 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Apr 2017, Jeju, South Korea. ⟨cea-02434555⟩