The Effect of Random Geometry on the Criticality of a Multiplying System

A method has been developed for calculating the probability distribution of the multiplication factor in a reactor in which the fuel elements are randomly distributed across the core. The method is also applicable to waste storage drums in which lumps of fissile waste material are stored in a background matrix. The procedure is based upon the Feinberg-Galanin-Horning method of heterogeneous reactors, in which the fuel element or fissile lump is replaced by a point, line or plane sink of thermal neutrons and a similar source of fast neutrons. The fuel element positions are chosen to lie randomly in the core and for each realisation a criticality calculation is carried out. Thus a large number of values of keff is obtained and reduced to a probability distribution P(keff). We observe that keff lies in the range kefJ,min, keff.max), where the very small value keff.min arises when all elements lie on the reactor boundary, and the value of kefJ,max when all elements are fortuitously in the position of minimum critical mass. A further simulation is carried out in which the fuel elements are notionally at a fixed position in a regular lattice but are allowed to vary randomly about the position by 10% of the lattice pitch. In this case, the distribution in keff is found to be highly symmetrical about the critical value of keff = I and the distribution appears to be Gaussian. The methods developed will also be useful for safety assessments arising in the storage of fissile material and general problems in radioactive waste disposal. An analytical method has been developed for calculating P(keff ) for N randomly distributed plates and illustrated for the case of a reactor containing one plate. The agreement between the simulation and the analytical method is excellent. It also seems likely that P(keff) becomes Gaussian-like as the number of plates increases.