Characterization of Neutron Leakage Probability, k_eff, and Critical Core Surface Mass Density of Small Reactor Assemblies Through the Trombay Criticality Formula

The Trombay criticality formula (TCF) has been derived by incorporating a number of well-known concepts of criticality physics to enable prediction of changes in critical size or k_eff following alterations in geometrical and physical parameters of uniformly reflected small reactor assemblies characterized by large neutron leakage from the core. The variant parameters considered are size, shape, density and diluent concentration of the core, and density and thickness of the reflector. The mass-to-surface-area ratio of the core, is essentially a measure of the product ρr extended to nonspherical systems and plays a dominant role in the TCF. The functional dependence of k_eff on σ/σ_c, the system size relative to critical, is expressed in the TCF through two alternative representations, namely the modified Wigner rational form and the exponential form as follows: where is the k_∞ of the critical system. The quantity in the square brackets is close to unity and Z is a parameter weakly dependent on both the physical and geometrical properties of the core, where θ = ln[/( - 1)] and ε is a parameter introduced to account for the steep rise in the net leakage probability for highly subcritical cores. The applications of the TCF range from the quick computation of the k_eff of a lump of fissile fuel having arbitrary shape and density through the study of k_eff of highly enriched fissile materials during transportation accidents to an estimation of the void and fuel expansion coeffficients of reactivity in high leakage systems.