Neutron fluctuations: The importance of being delayed

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, have actually a key impact on the fluctuations, and their contribution is very effective in quenching the spatial clustering.

Large deviation of long time average for a stochastic process: an alternative method

“…The dPGFk method can easily be extended to investigate multi-step processes. As an illustration, consider a simple generalization of the chemical process considered in subsection III A, describing now RNA productions with bursts [10] or the dynamics of neutron production in nuclear reactors [11]. The transition rates are :…”

Neutral aggregation in finite-length genotype space

“…Note that the probability that two individuals from the same parent are at distance k = 2 is aλ 2 and therefore it has been neglected in relation (9). It should also be noted that because we suppose λ ≪ 1,…”

“…It can be shown however [2][3][4][5]that diffusion is not enough to efficiently dilute the correlation creation at short distances for spatial dimensions d ≤ 3 and large system size extension. This phenomena is called neutral clustering (see [6] for a review); it has been demonstrated experimentally [7] and the main concept has been applied to other systems such as neutrons in nuclear reactors [8,9] and evolution of bimolecular networks [10].…”

Patchy snapshots of nuclear chain reactions

“…The key ingredient behind clustering is the asymmetry between death occurring everywhere and birth being only possible close to a parent particle; particle diffusion has a smoothing effect on the wild spatial patterns induced by the parent-child correlations [10]. The occurrence of clustering is the signature of strong deviations from the expected behavior of such systems, and has been shown to be enhanced in low-dimensional systems (d = 1 or d = 2), especially when the population is fairly diluted: a deterministic description would be thus meaningless, since the typical size of the fluctuations might be of the same order of magnitude as the average particle density [11,12]. The evolution of the neutron population in a nuclear reactor is also subject to random displacements (diffusion), births (fission events on heavy nuclei leading to secondary neutrons), and deaths (capture events on nuclei leading to the disappearance of the colliding neutrons).…”