A discrete ordinates operator for the diffuse transmission of a mixed neutron beam through a multilayered medium

Abstract

In this article the transport model and inductive approach reported in a recent work have been extended, and a discrete ordinates operator for the diffuse transmission of a mixed neutron beam through a multilayered medium is derived. At first, a mathematical description of the mixed beam transport problem that we are concerned with is given. The resulting mathematical problem is, according to Chandrasekhar, decomposed into uncollided and diffuse problems. After treating the uncollided problem analytically, a discrete ordinates formulation of the diffuse problem is considered. A set of spatially discretised equations that are free from spatial truncation error is then introduced. Finally, a discrete ordinates operator that replaces the entire multilayered medium in diffuse neutron transmission computations is derived inductively. To the best of our knowledge, such an operator has never been reported previously in neutron transport literature. Numerical results for a four-layer medium are presented to illustrate the computational merit of a computer code based on our diffuse transmission operator.