Theory and Analysis of the Feynman-Alpha Method for Deterministically and Randomly Pulsed Neutron Sources

In future planned accelerator-driven subcritical systems, as well as in some recent related experiments, the neutron source to be used will be a pulsed accelerator. For such cases the application of the Feynman-alpha method for measuring the reactivity is not straightforward. The dependence of the Feynman Y(T) curve (variance-to-mean minus unity) on the measurement time T will show quasi-periodic ripples, corresponding to the periodicity of the source intensity. Correspondingly, the analytical solution will become much more complicated. One can perform such a pulsed Feynman-alpha measurement in two different ways: either by synchronizing the start of each measurement block with the pulses ("deterministic pulsing") or by not synchronizing ("random pulsing"). The variance-to-mean has been derived analytically for both cases and reported briefly in previous publications. However, two different methods were used and the two cases were reported separately. In this paper we give a unified treatment and a comparative analysis of the two cases. It is found that the stochastic pulsing leads to an analytic solution that is much simpler than that for the deterministic case, and the relationship between the pulsed and continuous source is much more straightforward than in the deterministic case. However, the amplitude of the ripples, constituting a deviation of the pulsed Feynman Y curve from the smooth curve corresponding to the traditional constant source case, is much larger for the stochastic pulsing than for the deterministic one. The reasons for this are also analyzed in the paper. The results are in agreement with recent measurements, made by other groups in the European Community-supported project MUSE.