Stochastic Point Kinetics Model of Circulating-Fuel Reactors under Perfect Mixing Approximation

TL;DR

This paper develops a stochastic modeling framework for circulating-fuel reactors that captures low-population dynamics and precursor transport, providing insights into variance estimation and reactivity loss under perfect mixing assumptions.

Contribution

It introduces a stochastic point-kinetics model with two perfectly-mixed volumes, deriving equivalent discrete-event and SDE formulations, and compares two numerical solvers for CFR dynamics.

Findings

AMC and SDE mean solutions match deterministic results

SDE underestimates DNP variances in some regimes

Reactivity loss estimator is negatively biased

Abstract

We present a stochastic framework for low-population dynamics in circulating-fuel reactors (CFRs) that captures delayed-neutron precursor (DNP) transport without delay terms. Starting from a modified point-kinetics model with two perfectly-mixed volumes, we derive equivalent discrete-event dynamics and an It\^o stochastic differential equation (SDE) system. Two solvers are implemented: an analog Monte Carlo (AMC) engine and a semi-implicit Milstein SDE solver. Transient benchmarks demonstrate perfect agreement of AMC/SDE means with deterministic solutions, while revealing that the SDE approach underestimates DNP variances in selected regimes, potentially due to the neglect of DNP noise. We further recast reactivity loss due to precursor drift in this stochastic setting and show that its estimator is negatively biased. Overall, the developed framework provides a minimal yet representative model for CFR low-population kinetics. Future work will re-derive and test SDE noise terms and apply the framework to selected transient applications such as start-up analyses of CFRs.