Stability of Moments in a Simple Neutronic System with Stochastic Parameters

The exact expressions for the first- and second-order moments of neutron density and the delayed-neutron precursor density are derived for a neutron multiplying system, with time-dependent stochastic perturbations in the reactivity and white noise source. The effect of finite correlation time of the reactivity on the stability of moments is discussed. For asymptotically long times, the moments are found to be stable. The exact expressions of the moments in the limiting case, when the reactivity correlation time becomes zero, are also derived. It is found that the expressions for this limiting case differ from the corresponding expressions of Williams.