The effect of random geometry on the criticality of a multiplying system V influence of the reflector

A heterogeneous nuclear reactor is modelled using the source-sink method. By allowing the fuel plates to assume random positions in the core we build up a probability density function P(k) for the multiplication factor k. 106 simulations are performed for different positions and the mean and variance computed. The variation in P(k) is studied as a function of reflector thickness. It is found that P(k) narrows as the reflector thickness increases and this behaviour is quantified by a decreasing relative standard deviation. Results are given for 235U plates in graphite and water moderators