Possibilities of applying boundary functionals of random processes to nuclear safety problems

TL;DR

This paper explores how boundary functionals of random processes can be applied to improve nuclear safety analysis, especially in scenarios with significant neutron behavior changes.

Contribution

It introduces the use of boundary functionals of random risk processes to enhance nuclear safety assessments and calculations of protection settings.

Findings

Boundary functionals enable precise power quantile calculations.

They provide a mathematical link between percolation theory and safety engineering.

Neutron behavior distributions shift from normal to stable or limiting types in certain scenarios.

Abstract

The potential for using boundary functionals of random risk processes to solve nuclear safety problems at nuclear power plants is assessed. In certain situations (MSRs (Molten Salt Reactors), High-Temperature Gas-Cooled Reactors (HTGRs), pulverized fuel reactors, reactor startups, and accident analysis (core collapse)), neutron behavior changes significantly. Neutron clustering begins to play an important role, and the distributions characterizing neutron behavior change. The normal distribution is replaced by stable, but also limiting, distributions. Boundary functionals allow for precise calculation of the power quantile and provide a mathematical bridge between abstract directed percolation and engineering calculations of protection settings.