# The criticality of multiplicative processes

## TL;DR

This paper develops a mathematical framework to analyze multiplicative processes, especially in nuclear reactor simulations, providing estimates of the multiplication factor crucial for monitoring reactor criticality and applicable to natural processes.

## Contribution

It introduces a unified formalism for estimating the multiplication factor in multiplicative processes, enhancing understanding of particle growth in nuclear and natural systems.

## Key findings

- Two estimates of the multiplication factor are derived within the same framework.
- The relative positions of these estimates with respect to criticality are characterized.
- The approach is applicable to real-time monitoring of nuclear reactors and natural multiplicative phenomena.

## Abstract

Keeping in view applications to numerical simulations of the evolution of a nuclear reactor core around criticality, we use a general mathematical framework for describing the evolutions of multiplicative processes (processes involving particle creation) both in particle generations and in time. This framework allows us to obtain, within a same formalism, two corresponding estimates of the multiplication factor which describes the growth of particle numbers at large times. We obtain the relative positions of both estimates with respect to each other and to criticality. These relations may show particularly useful when simulating in a realistic way the monitoring of nuclear cores in subcritical states, such as is the case for Accelerator Driven Systems (ADS). More generally, this study applies to various multiplicative processes which can be found in nature.