Anomalous diffusion processes in nuclear reactors

We have studied time-fractional telegrapher’s equation (FTE) for purely absorbing, heterogeneous and highly scattering media in nuclear reactor. In this approximation the neutron motion is based on a P1-approximation of the Boltzmann equation and a fractional constitutive equation of the neutron current. The propagation velocity of the neutrons predicted by FTE follows a power–law with exponent 1/3γ for 0 < γ < 1. The detrended fluctuation analysis (DFA) was applied to field data for estimating the anomalous diffusion exponent. Our results show that the scaling exponent is related to an anomalous diffusion exponent using the neutronic signals in a BWR nuclear reactor. Some connections between the scaling properties and neutron process in the BWR core are also discussed.

► Anomalous diffusion appears when particles are temporally trapped in complex media.
► The phenomenon is considered for modeling neutron transport in nuclear reactors.
► Anomalous diffusion plays an important role for short time scales.
► Important differences with classical diffusion models are found.