Axial propagation of neutron waves in heterogeneous media

A theoretical study of the axial propagation of plane-thermalneutron waves in a semi-infinite heterogeneous subcritical assembly containing cylindrical fuel rods in a square pattern is performed in the framework of the P-1 approximation to the Boltzmann equation. The method is based on a modified form of heterogeneous reactor theory due to Feinberg and Galanin. The analysis is first carried out in the one group P-1 approximation and then extended to age diffusion theory. Axial propagation of neutron waves is studied, analytically and numerically, by analyzing the time dependent part of the moderator flux in the assembly. On oscillating plane source of thermal neutrons placed at one face of the assembly is assumed to inject a plane wave of thermal neutrons which propagate along a direction parallel to the fuel rods. The thermalization effect is considered by assuming a time delay prior to appearance of the fission neutrons in the thermal group. The analysis predicts that the phase interference between the modes of propagation in the axial direction may five rise to resonances in the frequency response of the asymptotic moderator flux. A standing-wave-pattern is also predicted in the amplitude distribution of the oscillating part of the moderator flux in the axial direction. The relationship between the resonances and the system parameters are investigated. An experimental method which can be useful for the determination of the system parameters is suggested for systems in which the frequency response (of the amplitude and the phase) and the standing-wave-pattern can be measured