Percolation properties of the neutron population in nuclear reactors

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 us 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 with 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 superdiffusion equation. The analysis of this equation will reveal that nonnegligible departure from mean-field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.