Thermal-Neutron Wave Propagation in Finite Assemblies of Beryllium and Beryllium Oxide

Using multigroup diffusion theory with energy-dependent boundary conditions, the propagation of thermal-neutron waves has been studied in finite assemblies of beryllium and beryllium oxide. At different frequencies, we have calculated α and ξ for the discrete (or pseudo-discrete) mode as well as effective values of α(z) and ξ(z) (which include the effect of the source and higher modes) at a distance, z, from the source plane. In the case of beryllium, the results are in agreement with experimental findings of Miles et al. As observed by Miles et al., we find oscillations in the calculated values of α(z) and ξ(z) in a certain distance range beyond a certain frequency, which decreases with the decrease of transverse size of the assembly. Furthermore, in conformity with the experimental results of Miles et al., we find that with a decrease in the transverse dimensions of the assembly, the oscillations become larger, until one goes to very small assemblies, where these oscillations tend to smooth out. In the case of beryllium oxide, since no agreed value of Debye temperature exists and since the energy distribution of source neutrons is not known, only a qualitative comparison with the experimental results of Ritchie and Whittlestone has been possible.