An Analytical Solution for the Two-Group Diffusion Theory Analysis of Multiregion Source-Driven Systems

An analytical solution of the two-group diffusion equations is derived for multiregion source-driven subcritical systems in spherical geometry. An analytical formulation for the calculation of the effective multiplication factor is also presented. Using typical two-group cross sections characterizing source, buffer, and blanket regions, parameters such as neutron amplification, source efficiency, and blanket fast flux peaking factor are calculated. The criticality solution is utilized to calculate the effective multiplication factor and the neutron source efficiency. The dependency of the calculated global parameters on design variables like the source, buffer, blanket thicknesses, and subcriticality level is studied. Thin source regions result in very high neutron amplification, at the expense of high blanket fast flux peaking factors. If a buffer region is put between the source and the blanket regions, flux peaking could be reduced at the expense of reduced neutron amplification. If the subcriticality level can be reduced without jeopardizing safety, the neutron amplification increases and the fast flux peaking is reduced.