Two-point theory for the differential self-interrogation Feynman-alpha method

TL;DR

This paper derives a two-region Feynman-alpha formula for the stochastic self-interrogation method, using Monte Carlo simulations and Chapman-Kolmogorov equations to evaluate neutron reaction processes in spent fuel.

Contribution

It introduces a novel two-point theoretical framework for the Feynman-alpha method applicable to DDSI and DDAA, incorporating detailed reaction intensities.

Findings

Derived a new variance-to-mean relation for two-region neutron processes.

Validated the applicability of the formula through Monte Carlo simulations.

Assessed the method's effectiveness in spent fuel configurations.

Abstract

A Feynman-alpha formula has been derived in a two region domain pertaining the stochastic differential self-interrogation (DDSI) method and the differential die-away method (DDAA). Monte Carlo simulations have been used to assess the applicability of the variance to mean through determination of the physical reaction intensities of the physical processes in the two domains. More specifically, the branching processes of the neutrons in the two regions are described by the Chapman - Kolmogorov equation, including all reaction intensities for the various processes, that is used to derive a variance to mean relation for the process. The applicability of the Feynman-alpha or variance to mean formulae are assessed in DDSI and DDAA of spent fuel configurations.