The survival probability of neutrons in supercritical convex bodies using a time-dependent collision probability method

We consider the probability of the survival of the neutron population when one neutron is injected into a supercritical fissile convex body. The formalism developed by Pal and Bell is used and the equations arising for the survival probability are solved by using a time-dependent collision probability technique. In principle, this method can be used for arbitrarily shaped convex bodies. A simple one-region case is seen to lead to reasonably accurate results when compared with the work of Gregson and Prinja [Gregson, M.W., Prinja, A.K., 2008. Time-dependent non-extinction probability for fast burst reactors. Transactions of the American Nuclear Society 98, 533 (Anaheim, CA)]. The calculations are extended to the case where a steady background neutron source is present. The time-dependent, self-collision probabilities are evaluated for slab, sphere and infinite cylindrical geometries. A method due to Lefvert [Lefvert, T., 1979. New applications of the collision probability method in neutron transport theory. Progress in Nuclear Energy 4, 97] for solving time-dependent collision probability equations is shown to give accurate results. The usefulness of diffusion theory to solve this problem is also investigated.