Analysis of infinite domain criticality zones in finite reactors

A reactor that is infinitely large has two ideal properties: (1) the fission rate density and, hence, the power are uniform throughout; and (2) the fuel density needed for criticality is minimum. A finite reactor loaded in this way would be subcritical and would have to contain additional fuel to compensate for neutron leakage to sustain criticality. The performance of two reactor models is analyzed on the basis of the multi-group diffusion approximation. Both models comprise a primary inner core zone which would be critical if it were infinite in extent. In the first model, the primary core zone is surrounded by a secondary core which is loaded to achieve a specific power density (i.e., fission rate density). The exact solutions of the multi-group diffusion equations are obtained for up to four energy groups. In the second model, the primary core zone contains a ''thin'' spherical fission plate. The exact solutions of the one- and two-group diffusion equations are obtained