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When reactor physics meets game theory

​An international collaboration involving the CEA-Irfu and the CEA's Energy Directorate has revealed a subtle neutron clustering mechanism by rigorously combining nuclear reactor experiments, modelling and simulations, all of which are extremely demanding. This result goes beyond the scope of just nuclear safety.

Published on 12 October 2021

Anyone who continually bets a fixed amount on a coin toss will sooner or later go broke. This can be explained by the fact that one's resources fluctuate more and more until the ultimate loss.

At first glance, there is nothing in common between the gambler's ruin and the startup of a nuclear reactor ... and yet, the operator injects neutrons to start the fission reactions, like so many "bets" for a "game".

Indeed, a neutron can cause an atom to split and give rise to several neutrons in a winning "bet", or on the contrary, it can be absorbed and disappear in a losing "bet". While the losing players disappear, leaving many empty spaces, a few very lucky players accumulate winnings. In a similar way, one observes an increasing heterogeneity of the neutron content within the reactor, with the progressive formation of zones having high and low neutron densities (neutron clustering).

Researchers were able to demonstrate this neutron clustering phenomenon using reactor physics experiments that took place in 2017 at the Reactor Critical Facility (RCF) at Rensselaer Polytechnic Institute (USA).

The analysis of the experiments was based on an intensive three-year simulation campaign that included a "digital twin" of the reactor. For the first time, realistic statistics of the reactor neutrons could be simulated by a high-fidelity neutron code.

The theoretical predictions of a particular model of neutron clustering developed from the mathematical model of "branching random walks" are clearly confirmed.

These results are also reproduced with the help of Monte Carlo simulations of neutron transport that describe the fluctuations inherent in the fission process. The simulations calibrated with the experiments reveal very strong clustering effects when the neutron population is "radiographed" at a given time.

For the experiments, the researchers used detectors that allow one-dimensional neutron mapping with very good temporal resolution (NeutrOn Multiplicity 3He Array Detector, NOMAD) – a technology developed by the Los Alamos National Laboratory. These detectors, positioned in pairs, one on top of the other, provide instantaneous snapshots of the neutron population covering the entire size of the reactor.

This work is primarily of interest for nuclear safety. The configuration of a nuclear reactor in the startup phase, with very few neutrons, is likely to favor a clustering effect. If the reactor was affected by local overcriticality effects, the diagnosis of these anomalies could be more complicated in the presence of clustering at startup and only be revealed during the power increase of the core.

In the field of fundamental physics, this research opens perspectives concerning stochastic modeling and the use of Monte Carlo simulation for the understanding of diffusive phenomena such as the study of the initial phase of epidemics or the understanding of the decoherence phenomenon in quantum mechanics.

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