Percolation properties of the neutron population in nuclear reactors

TL;DR

This paper models neutron population in nuclear reactors as a percolation process, revealing that super-diffusion better describes neutron spread than traditional diffusion, which questions current numerical methods' accuracy.

Contribution

It introduces a stochastic percolation-based model of neutron transport, linking critical phenomena to super-diffusion in reactor physics.

Findings

Neutron transport exhibits super-diffusion rather than classical diffusion.

Critical exponents indicate departure from mean field behavior.

Current numerical schemes may lack sufficient accuracy due to these effects.

Abstract

Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled stochastic systems however require to define intermediate quantities (e.g. the temperature field), which are bridging the gap between the stochastic neutron field and the deterministic feedback. By interpreting the branching random walk of neutrons in fissile media under the influence of a feedback mechanism as a directed percolation process and by leveraging on the statistical field theory of birth death processes, we will build a stochastic model of neutron transport theory and of reactor physics. The critical exponents of this model, combined to the analysis of the resulting field equation involving a fractional Laplacian will show that the critical diffusion equation cannot adequately describe the spatial distribution of the neutron population and shifts instead to a critical super-diffusion equation. The analysis of this equation will reveal that non-negligible departure from mean field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.