Passage of thermal neutrons through a medium with localized heterogeneities

The passage of thermal neutrons through heterogeneous diffuse medium in the terms of mean (macroscopic) flux is considered. The effect of a great number of blocks on the neutron distribution is investigated at the assumption that the neutron flux perturbation caused by a separate block is known. The blocks may constitute periodical cell or be chaotic disposed in the volume of the diffuse medium. To take into account the heterogeneities an effective supplement is introduced in the kernal of the kinetic equation. The kernal is determined by the statistical properties of the diffuse medium and also by the scatering properties of the separate block. A formalism is developed that allows the effective diffusion parameters of heterogeneous medium with an arbitrary disposed blocks and arbitrary amplitude of the oscillation of the transverse cross-section to be determined taking into account the non-diffusion corrections and the neutron thermalization. From the general formula an equation is deduced for the time constant of the attenuation of a macroscopic flux from a stationary source in a heterogeneous medium (characteristic or dispersion equation) in one speed approximation. (author)