Prompt-Neutron Kinetics of a Spherical-Cavity Reactor

A simple kinetics model is proposed that describes time dependence of the prompt-neutron population in a cavity reactor in terms of a linear, first-order differential equation for the net thermal-neutron current at the cavity wall. The model is applicable if the cavity albedo changes slowly during a neutron lifetime and does not exceed a specified maximum value. This range of applicability is defined by deriving the kinetics equation on the basis of an age-diffusion theory approximation that describes the time dependence of the thermal-neutron flux at the cavity wall in terms of a Volterra integral equation of the second kind. The method of deriving the kinetics equation suggests a means of experimentally determining the effective multiplication factor and average neutron lifetime-to-fission for more complex cavity geometries by measuring thermal-neutron absorption rate in a nonmultiplying gas in the cavity.