Effect of Small Perturbations on Pile Period

Abstract

A perturbations theory is developed for calculating the change of the pile period caused by the introduction of small amounts of extraneous materials into the pile, such as impurities, additional fissionable material, etc. It is shown that the effect can be calculated in first approximation most easily by solving the adjoint of the pile equation. This leads to the definition of an “adjoint neutron density”, also depending on the position and the energy of the neutron. The weight factor for a perturbation is the product of the ordinary neutron density and the adjoint density. The adjoint equation is developed both for the two group and the ordinary pile theory and solved in both cases for a simple pile without reflector. The purpose of the work is to find a method for calculating the effect of small perturbations on composite piles and to separate the effects on fast, resonance and slow neutrons.