Multigroup Diffusion with Periodic Arrays of Line Sources

A multigroup diffusion theory is formulated for heterogeneous reactors having periodic arrays of line discontinuities. These discontinuities are idealized cylindrical internal boundaries of an otherwise homogeneous moderating medium, and appropriate mixed-group or multiplying boundary conditions at such boundaries allow Floquet solutions to be found for the neutron fluxes in the moderator. Real superpositions of such Floquet solutions can then give the physical fluxes in finite reactors. The requirement that a Floquet solution in the moderator have the proper thermal flux behavior at a cylindrical internal boundary, to match the thermal flux actually inside a fuel rod, leads to a “criticality” condition, the solutions of which give the spectrum of allowed Floquet solutions. For each of these a relation between material bucklings B_x², B_y², and B_z² is obtained which is, in general, anisotropic.