On the solution of the monoenergetic neutron Boltzmann equation in cylindrical geometry

Abstract

In this paper the F-transform Boltzmann equation for monoenergetic neutrons is first derived, in the stationary case, for arbitrary three-dimensional geometries. After some general results, the F-transform equation, which is in order in the case of a homogeneous cylinder of infinite height in critical and subcritical conditions, is considered. A monodimensional linear integral equation for a function, which is related to the F-transform of the total non-virgin flux, is obtained and then proved to be of the Fredholm type. The solution of such an equation is cast into a series expansion, whose coefficients satisfy an infinite linear algebraic system. The vanishing of the determinant of such a system yields the criticality condition for the physical system under consideration. Finally the solution of the transformed equation is inverted to give the space-angular neutron flux distribution.