The Effect of Random Geometry on the Criticality of a Multiplying System II: Extension to Resonance Absorption

In an earlier paper a method was developed for calculating the probability distribution of the multi- plication factor in a reactor in which the fuel elements are randomly distributed across the core. In this paper the method is extended to include resonance absorption and also to the case where the fuel elements have random values of enrichment. As before the Feinberg-Galanin-Horning source-sink method is used. The probability distribution P(ke€) is calculated for a bare reactor containing from 1 to 10 fuel plates. We observe that ke€ lies in the range (ke€ min ke€ max) and we also note that as the number of fuel plates increases the form of P(ke€) becomes Gaussian-like but can never be exactly Gaussian because of the ®nite limits on ke€. We have also discovered that the general rule put forward by previous workers in this ®eld namely that hke€i for the spatially random medium is always greater than the corresponding deterministic value no longer holds in general. Further calculations with 235U and Al plates suggests that the presence of resonance absorption may be the cause of this discrepancy. There is also the fact that in this work a realistic slowing down model is used whereas previous workers used one-speed theory. Some new results for basic source-sink theory are also reported.