Decay of Fast Neutron Pulses in Uranium Assemblies

The multigroup diffusion equation is solved for the pulsed problem and the time-dependent energy spectra are obtained using the eigenfunction expansion method. It is shown that complete spectral equilibrium can be obtained beyond 2000 ns in a 40-cm cube (B² ∼ 0.015 cm^-2) of natural uranium. This time is found to increase with increasing assembly size. The earlier exponential decays observed in a pulsed uranium system are traced to the establishment of the pseudo-equilibrium condition due to the trapping of neutrons in certain energy groups. It is shown that such a pseudo-decay corresponds to the establishment of the first higher mode of decay and the time range in which it is established is a function of B².