The effect of random geometry on the time constant of a multiplying system

Methods developed in a series of earlier papers for calculating the probability distribution of the multiplication factor when reactor properties and geometry are randomised, are extended to the time decay constant. To illustrate the method, we choose a one-dimensional reactor with plate type fuel elements which can be analysed by the source-sink method. Two types of randomness are studied: (1) when the plates are fixed in position and their enrichments vary randomly and (2) when the plates have a fixed enrichment and their positions in the core vary randomly. We present the probability distribution P(w) for the time decay constant w for the different realisations, which are chosen by means of a random number generator. The mean value and variance are calculated for an N plate reactor where N takes the values, 1, 2, 5, 10. We also obtain the associated marginal probability P(w>0), i.e. the probability that the decay constant is positive and we have a supercritical system. Some exact analytical results are obtained for P(w) for some special cases and these are used to check the accuracy of the simulations as well as giving guidance on the expected forms for the more complex geometrical multiplying assemblies.