A SPATIAL AND ANGULAR MOMENTS ANALYSIS OF THE MONOENERGETIC PENCIL BEAM PROBLEM

We consider the time-independent, monoenergetic, normally incident pen cil beam (searchlight) problem for a homogeneous, source-free, finite thickness, purely scattering slab. By adopting a cylindrical coordinat e system to describe this problem, exact equations are developed for t he radial and azimuthal Fourier cosine moments of the angular flux. Th e analysis is carried out for both the full integral scattering desrip tion as well as its Fokker-Planck differential approximation. Assuming that the beam remains nearly collimated as it passes through the slab , these moment equations are analysed using an additional (in this cas e asymptotic) moments method in the polar angle. The resulting set of coupled, one-dimensional (in the depth variable) ordinary differential equations are used to construct asymptotic power series representatio ns for certain radial moments of the scalar flux. These one-dimensiona l series are then used to improve earlier descriptions, due to Fermi a nd Jette, of the radial and depth variations of the beam scalar flux. (C) 1997 Elsevier Science Ltd.