The variance-to-mean ratio in subcritical systems driven by a spallation source

In a previous work, we have derived a formula for the variance-to-mean ration, used in the Feynman-alpha method, of the neutron counts in a subcritical system driven by a correlated (multiple or non-Poisson) source (such as a spallation or a 252Cf one). The formal derivation as made by assuming prompt neutrons only in the fission chain, and the results were extended to include delayed neutrons by intuitive arguments. To confirm this procedure and the validity of the former result, in this paper the variance-to-mean formula has been derived by using a master equation technique including one group of delayed neutrons. The result shows, in agreement with the previous work, that both the prompt and the delayed neutron terms include the effect of the correlated source in form of additive factors, multiplying the corresponding time dependent terms. It is thus also confirmed that the presence of a correlated source with large multiplicity, such as in the case of a spallation source in an accelerator driven system, is very beneficial for the application of the Feynman alpha technique because it enhances the prompt alpha component from which the prompt neutron time constant is determined. Hence, in such systems the reactivity may be monitored with larger subcriticalities than in conventional systems