Sub-critical mass determination for cylindrical systems of ²³³U, ²³⁵U and ²³⁹Pu

Calculated values are reported for sub-critical masses (SCMs) of ²³³U, ²³⁵U and ²³⁹Pu in a cylindrical geometry. This work is motivated by the need to ensure criticality safety for materials stored in a configuration with cylindrical containers of 13.5 cm diameter stacked in a cylindrical pipe of 15 cm diameter. The storage configuration was evaluated in a parametric study to determine optimal water moderation. SCM values of 356 g ²³³U, 688 g ²³⁹Pu and 855 g ²³⁵U were calculated. The result that the SCM for ²³⁹Pu is almost twice that of ²³³U would not be predicted from the common understanding that ²³⁹Pu has the smallest minimum critical mass. As such, the calculation method was verified via determination of SCMs for ²³³U and ²³⁹Pu for known configurations, i.e., spherical water moderated systems, which have available standard data. Thus, the reactivity of a fissionable material system is determined by a complex relationship between the geometry and the participating materials, and especially that in certain geometric configurations, ²³⁹Pu is not the most reactive fissile nuclide, but ²³³U. (author)