On some one-speed neutron transport problems revisited and reformulated

Abstract

The solution of a number of one-speed neutron transport problems involving infinite media have been re-considered in the light of a transformation first used by Wallace (Wallace, P.R., 1944a. Boundary Conditions at Thin Absorbing Shells and Plates I. Canadian National Research Council Report MT-34; Wallace, P.R., 1944b. On the Thermal Utilisation of Plates in the Presence of Linear Anisotropic Scattering. Canadian National Research Council Report MT-63). The outcome of this transformation is that the infinite medium problem can be reduced to one in terms of an integral equation involving finite regions only. For example, in the case of an infinitely reflected slab, the infinite reflector is removed and its presence transferred to the kernel of a new integral equation. These kernels turn out to be the point or plane kernels of the corresponding infinite medium problem in the pure reflector material. In this paper the method is extended to slabs with arbitrary anisotropic scattering in slab and reflector; it is also applied to reflected spheres. In this case however, there is a limitation that the total mean free path in sphere and reflector be the same. Finally, we comment on the physical meaning of the standard anisotropic formalism and show that a more realistic eigenvalue exists which is directly related to the isotropic fission source. Some numerical results are given to illustrate our conclusions.