Analytical Solutions of the Neutron Transport Equation in Arbitrary Convex Geometry

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Abstract
The integral equation describing the transport of monoenergetic, isotropically scattered neutrons in a one‐, two‐, or three‐dimensional body of arbitrary convex shape, containing distributed sources, is considered. An exact representation of the neutron density ρ(r) is obtained, involving a superposition of functions belonging to the null space of a simple differential operator. In general, when a countable basis is chosen to span the null space, the coefficients in the expansion of ρ(r) satisfy a coupled system of singular integral equations which is reducible to a system of Fredholm equations. If no sources are present, an exact criticality condition is also obtained. Some techniques for evaluating the expansion coefficients are given and several examples are considered.