Critical conditions in an infinitely reflected, multiplying slab using two-group, integral transport theory

A two-group formulation of the integral transport equation has been carried out for the infinitely reflected critical slab. The coupled integral equat ions that arise are re-formulated using a special transformation so that th e problem is reduced to an integration over the slab only. The effect of th e infinite reflector is incorporated into a modified kernel of the integral equation. The new integral equations are solved numerically and some compa risons are made with published experimental and theoretical critical sizes. Some conjectures are made about the agreement obtained. The calculations a re illustrated by graphs showing the fast and thermal fluxes. Finally, we c alculate some values of Galanin's constant for the slab and study its conve rgence as the accuracy of the numerical method is improved. (C) 2001 Elsevi er Science Ltd. All rights reserved.