Most Critical Geometry of a Fuel Solution Based on the Transport Boundary Perturbation Theory

The methodology for obtaining optimal free surface geometry of a fuel solution which maximizes the neutron multiplication factor is presented using the concept of "boundary importance". Optimal geometries for a two-dimensional planar fuel solution are demonstrated with a multigroup, finite element, discrete ordinates transport code, TRIPLET. A new concept, "interface importance", is defined so that the optimal geometry of an interior boundary between dissimilar media can be obtained. The optimal interface geometry is accomplished by letting the interface importance be identical along the interface concerned. The requirements, that an optimal interface geometry can exist, are discussed.