Collision probabilities for plate geometry cells with an approximate treatment of plate edge regions

Abstract

A method of allowing for plate edge effects in the calculation of the neutron flux in the plate geometry cells of zero-power fast critical assemblies is developed and evaluated. Each layer contains a central region and an edge region and an approximate method for calculating the collision probabilities relating regions in different layers is developed. Collision probabilities are first calculated for a number of directions, i (having direction consines, μ i , relative to the normal to the plates). These are then combined with Gaussian weights, ω i . Escape, collision and transmission probabilities for each layer are calculated assuming that the neutrons travel only in one type of material within the layer. These material types are the central region material, the edge region material and a mixture of the two (which depends on the material fractions within the layer and the angle, i). The fraction of the neutrons travelling in each material type depends on the angle and the layer material fractions. The method is compared with Monte Carlo calculations made for single energy groups, and is used to calculate a number of zero-leakage plate geometry test zones for which measurements have been made in the ZEBRA facility.