A Stochastic Calculation of Fast Reactor Generation Times

Multigroup calculations for fast reactors are basically static in character, based on a representation of the system in which 25 or fewer groups are used to describe 5 or 6 decades in energy. While most of the uncertainty in calculations (as exemplified by generation times which are consistently 10 to 20% too low) is due to errors in cross sections, errors may also arise in averaging over broad groups; and in the treatment of elastic scattering by means of computed elastic removal cross-sections. Also, the multigroup method does not.permit convenient detailed study of the physics of slowing down in fast reactors. In this paper a new approach to calculation of fast reactor temporal and integral properties is described. With this method the neutron slowing down process is treated approximately as a discrete time, discrete state Markov process. Starting with an initial condition of a pulse of neutrons distributed with a fission spectrum, the neutron density as a function of energy and time over a large number ( >100) of energy 'sates' or 'groups' is evolved at discrete time steps. From this discrete representation of the time-energy dependent neutron density one is able to calculate a finely resolved discrete approximation to the distribution of slowing down times to first generation fission. The first time moment of this function is the generation time. Convolution of this distribution yields a function proportional to the time dependent response of a counter after a burst of fission spectrum neutrons. It is this function which is sampled in the Rossi-α experiment. Compared to the usual multigroup calculations the method has the advantage of not being directly dependent on spectral or adjoint calculations, and of being able to account for elastic scattering very accurately. Further, it is a dynamic calculation which follows the evolution of the neutron slowing down process in detail, as opposed to the usual calculations based on static fluxes. The method is versatile and may be applied to fast spectral and criticality calculations, and the usual spectral indicators such as central core fission ratios. Example calculations using the discrete state Markov method have been performed in systems with simple geometry. These calculational results are compared to those of other methods. (author)