Critical Parameter for Spatially Inhomogeneous Slabs

The critical problem in a finite plane slab is studied by an appropriate extension of the integral transform method. For a given optical thickness, the value of the scattering ratio (or mean number of secondaries per collision) that makes the system critical is determined as an eigenvalue of a Fredholm integral equation, in which a continuous position dependence of the scattering ratio itself has been taken into account. The integral equation is solved by a suitable projection technique, and numerical results are presented and briefly discussed for a parabolic trend of the fuel enrichment inside the slab.