Collision probability calculations of multiplication factors for lattices

Abstract

A multigroup version of the method of successive generations is used to determine the multiplication factors of unmoderated and unreflected periodic lattices of identical fissile components. The lattice components must be one-dimensional (i.e. spheres, infinitely long cylinders or infinite slabs). Lattices of nearly one-dimensional components (cubes or long cylinders) may, however, be approximately treated. The lattice components may be arranged in a linear, planar or cuboidal manner; the permissible component arrangements being limited by the lattice component geometry. The computation traces successive neutron collisions in the lattice, starting from a uniform neutron-source density distribution in each lattice component. The initial source density energy distribution is specified in a 16-group format which is obtained from S 4 transport equation solutions. The method satisfactory predicts the critical pitch of two experimentally measured lattices and, to this degree of confidence, is used to compute the critical parameters of other similar lattices. The method is also used to find the reactivity temperature coefficient of thermal expansion for several just-critical arrays. This coefficient is found to be positive for large arrays of small elements which have a high interaction factor.