A Three-Dimensional P_N Spherical Harmonics Theory in Cylindrical Geometry

A cylindrical system of finite height is being considered, consisting of a series of homogeneous, concentric annular zones surrounded by moderator in the radial direction. For this system, a complete solution of the monoenergetic, stationary neutron transport equation is found in the P_N spherical harmonics approximation. In the moderator, the scalar flux converges asymptotically towards the solution of the diffusion equation. When coupled with the heterogeneous (source-sink) theory, the method yields the scalar flux in a reactor and, after minor modifications, also applies to the exponential assembly.