Limit theorems for the neutron transport equation

TL;DR

This paper establishes rigorous moment results for neutron populations in transport equations, introduces a benchmark for Monte Carlo code verification, and advances understanding of importance sampling in reactor physics.

Contribution

It provides new theoretical results on neutron population moments and introduces a benchmark configuration for Monte Carlo method validation.

Findings

Derived exact solutions for neutron population moments.

Established rigorous moment bounds for asymptotic neutron populations.

Proposed a benchmark for Monte Carlo code verification.

Abstract

Over the last decade, ingenuous developments in Monte Carlo methods have enabled the unbiased estimation of adjoint-weighted reactor parameters expressed as bilinear forms, such as kinetics parameters and sensitivity coefficients. A prominent example is the Iterated Fission Probability method, which relies on the simulation of the fission chains descending from an ancestor neutron: the neutron population at an asymptotic fission generation yields an estimate of the importance function (and hence of the adjoint fundamental eigenmode) at the phase-space coordinates of the ancestor neutron. In this paper we first establish rigorous results concerning the moments of the asymptotic neutron population stemming from a single initial particle, with special focus on the average and the variance. Then, we propose a simple benchmark configuration where exact solutions are derived for these moments, which can be used for the verification of new functionalities of production Monte Carlo codes involving the Iterated Fission Probability method.