Nuclear reactor kinetics with a continuous slowing-down model

The present paper is devoted to deriving an analytical solution to a simple but physically significant and paradigmatic problem in local reactor kinetics, i.e. the one where the effects of the neutron migration during the slowing-down process, from fission to thermal energies, are taken into account by means of a dynamic generalization of the stationary Fermi continuous slowing-down approach. The attention is focused essentially on the influence of the space displacement and time delay undergone simultaneously by prompt and delayed fission neutrons and the analysis is restricted to the situation where the space asymptotic reactor theory may be applied. The Laplace transform technique is used throughout all the work. The solution is written down initially as a power series of the delayed-neutron fraction β, which is easy to handle and rapidly convergent within a time interval as long as a few slowing-down times after the perturbation event. Later on the adoption of a quite simple asymptotic form of the inverse Laplace transform may be fully justified. Therefore, by means of these two fully analytical forms of the solution to the local dynamics of a bare multiplying structure, within the frame of the quasi-continuous slowing-down model, it is possible to describe the neutron population evolution over the whole time axis. (author)