Some aspects of random geometry and absorption in multiplying systems and the pulsed neutron problem

Abstract

The effect of random displacements of absorbers in a homogeneous multiplying medium is studied via the source sink method. Simulation is used to build up a statistical history sufficiently accurate to obtain the probability density function P(k) of the multiplication factor k. In addition, we examine the effect of randomly placed absorbers in the classic pulsed neutron problem in a pure moderator. In this case the probability density function P(λ) is constructed for the decay constant λ. These two problems are repeated using fixed absorber position but random absorber strength: the associated forms of P(k) and P(λ) are obtained. In order to assess the usefulness of perturbation theory to study such stochastic problems we have obtained, for varying degrees of plate absorption, the mean value and standard deviation of λ in the pulsed neutron experiment. Tables of results are given which give some guidance on the accuracy of perturbation theory and also illustrate some pitfalls that can arise if the method is used indiscriminately.