Theory of neutron fluctuations in source-driven subcritical systems

Neutron fluctuations are investigated in a subcritical system driven by a non-Poisson (correlated) source. Such sources arise in e.g. accelerator-driven systems (ADS) where several neutrons are born simultaneously with a certain fluctuation in the spallation process. The second moment of the neutron number and of the detector counts is calculated. In particular, the Feynman-alpha formula is derived both by a master equation technique and with a heuristic approach. It is shown that the dependence of the variance-to-mean of the counts on the time gate is the same as in the traditional case (Poisson source), but its magnitude is enhanced by the source fluctuations and multiplicity. Thus, the presence of a correlated source is beneficial for the application of the Feynman technique. Consequently, it may be possible to perform measurements with deeper subcriticalities than in the traditional case.