Multifractality, percolation threshold and critical point of a nuclear reactor

TL;DR

This paper employs a multifractal model to analyze neutron behavior in nuclear reactors, exploring percolation thresholds and critical points, and linking fractal properties to reactor criticality and chain reactions.

Contribution

It introduces a multifractal framework to describe neutron dynamics and identifies critical percolation thresholds related to reactor criticality.

Findings

Neutron behavior exhibits multifractal characteristics.

Percolation probability correlates with reactor criticality.

Fractal analysis helps identify critical regions in reactor operation.

Abstract

A multifractal model is used to analyze neutron evolution within a reactor. For chain reactions, various characteristics of multifractal neutron behavior have been determined. These include the dimension of the multifractal carrier, information and correlation dimensions, the entropy of the fractal set, maximum and minimum dimension values, and the multifractal spectrum function. The geometric features of a multifractal allow for the description of a stochastic system consisting of hierarchically subordinate statistical ensembles, which are characterized by Cayley trees. A stationary distribution over hierarchical levels is established, which follows the Tsallis power law. The text also points out some potential applications of fractal patterns in nuclear reactor theory. The chance of percolation, which is when we see a state in the Bethe lattice where there's at least one continuous path through neighboring conducting nodes all the way across, is similar to the likelihood of a self-sustaining fission chain reaction happening. When this probability hits a critical point, we get a (conditionally) infinite cluster of neutrons forming. The percolation probability, influenced by how long the reactor has been running and its size, is linked to the reactor's criticality. We take a look at how the neutron multiplication factor behaves over time. We especially focus on the early stages of a self-sustaining nuclear fission chain reaction. We also highlight the ways to identify the boundaries of the critical region.