The solution to the nuclear reactor kinetic equations with a continuous slowing down model using numerical Laplace transform inversion

In an attempt to better understand the influence of prompt and delayed neutrons on nuclear reactor dynamics, a continuous slowing down model based on Fermi age theory was developed several years ago. This model was easily incorporated into the one-group diffusion equation and provided a realistic physical picture of how delayed and prompt neutrons slow down and simultaneously diffuse throughout a medium. The model allows for different slowing down times for each delayed neutron group as well as for prompt neutrons and for spectral differences between the two typed of neutrons. Because of its generality, this model serves not only a a useful predictive tool to anticipate reactor transients, but also as an excellent educational tool to demonstrate the effect of delayed neutrons in reactor kinetics. However, because of numerical complications, the slowing down model could not be developed to its full potential. In particular, the major limitation was the inversion of the Laplace transform, which relied on a knowledge of the poles associated with the resulting transformed flux. For this reason, only one group of delayed neutrons and times longer than the slowing down times could be considered. As is shown, the new inversion procedure removes the short time limitation as well as allows for any number of delayed neutron groups. The inversion technique is versatile and is useful in teaching numerical methods in nuclear science