The Effect of Fuel Depletion on Stochastic Behaviour in Supercritical Systems

Abstract

Extensive studies have been carried out of the probability distribution of neutron number in multiplying systems and a comprehensive list of references is available! Essentially, the procedure involves the construction of a probability balance equation for P(n,t), the probability that exactly n neutrons are present in the system at time t. Various extensions to this distribution may easily be developed which include delayed neutron precursors, number of counts recorded, etc. An aspect of this general problem that has by and large been neglected is the inclusion of burn-up of the fissile material. That is, the destruction of nuclei that occurs when fission takes place. The justification for such neglect is that during the time of measurement the number of nuclei destroyed is negligible compared with those remaining. This is indeed true except in one special case; namely that of a nuclear explosion. In this case, the time scale is such (10^-7s) that a large fraction of the fissile material is consumed before the period of interest is over.