The critical catastrophe revisited

TL;DR

This paper investigates the spatial fluctuations of neutron populations in nuclear reactors at criticality, analyzing how population control mechanisms influence clustering and stability through the interplay of mixing and extinction times.

Contribution

It provides a detailed analysis of how population control affects spatial fluctuations and clustering in neutron populations at criticality, highlighting the importance of mixing and extinction times.

Findings

Population control suppresses spatial clustering of neutrons.

The effectiveness of control depends on the ratio of mixing time to extinction time.

Uncontrolled systems exhibit wild spatial patchiness.

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.