Time-Dependent Single-Collision Kernels for Integral Transport Theory

Abstract

The authors discuss time-dependent integral transport equation single-collision kernels for one-dimensional geometries corresponding to the steady-state single-collision kernels found in the available literature calculated by making use of the Laplace transform technique, simple geometric transformation relationships, and point kernel integrations. Using the convolution theorem, the time-dependent scalar flux is obtained by convoluting the single-collision kernel with the time-dependent source. Using the multiple collision formulation of the integral transport solution isotropic sources thar are delta distributions in time are considered in several examples. Analytical solutions for the uncollided and first-collided scalar fluxes are obtained for a boundary source having an isotropic angular distribution directed into a semi-infinite medium and into a slab of thickness b and for a point source at the origin of an infinite medium and finite sphere of radius a.