Probability of Initiation in Coupled Multiplying Assemblies

Neutron chain survival and ultimate divergence in coupled multiplying assemblies, linked by intercepted leaking neutrons, are considered. Nonlinear equations are formulated for the dynamic probability of survival and static probability of initiation (POI) with assembly intercept fractions computed using a view factor model. Numerical solutions are obtained for up to four coupled assemblies, revealing a sensitive dependence on interassembly coupling strength. The results indicate that a chain will not diverge with certainty in a subcritical or critical system but that divergence will occur with some probability POI > 0 that increases with coupling strength. Additionally, at k_eff = 1, the stable subcritical solution branch is observed to bifurcate into two branches, one of which is shown through linear stability analysis to be unstable.