The critical catastrophe revisited

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.

16 pages, 6 figures

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Cited by in corpus (11)

• Constraint Ornstein-Uhlenbeck bridges
• Stochastic interpolation of sparsely sampled time series via multi-point fractional Brownian bridges
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Neutron fluctuations: the importance of being delayed
• Conditioning diffusion processes with killing rates
• Percolation properties of the neutron population in nuclear reactors
• Space and time correlations for diffusion models with prompt and delayed birth-and-death events
• Clusters in the critical branching Brownian motion
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• Time-dependent Monte Carlo in fissile systems with beta-delayed neutron precursors
• Conditioning two diffusion processes with respect to their first-encounter properties