Neutronics analysis for cylindrical assembly using Green's functions

When designing a reactor a preliminary design is done in order to obtain a rough estimate of various reactor properties. These properties include the neutron flux, criticality condition, or distribution of material in the assembly. It is possible to obtain an analytic solution for the neutron flux for a reactor represented in cylindrical coordinates using a Green's function or Green's function matrix method for both one group and two group neutron diffusion. The analytic results for a two-dimensional cylindrical system are simplified by assuming a cosine flux shape in the horizontal direction. This assumption makes the flux in the horizontal direction a neutron sink term in the radial direction. From the neutron flux, expressions for the criticality condition and fuel distribution cross section can be obtained by specifying the form factor, which is equivalent to specifying the power shape. A specific form factor, such as a constant power shape or parabolic power shape allow for a comparision between the results obtained by using a one group diffusion model against a two group diffusion model