Derivation of two-group two-region Feynman-alpha formulas and their application to Safeguards and accelerator-driven system (ADS)

The theory of the Feynman-alpha method was extended to two-energy groups and two-regions by the use of the Chapman - Kolmogorov equation with complete description of various processes including all reaction intensities for neutrons. This paper presents a full derivation of the variance to mean formula with the forward approach, as well as quantitative evaluation of the formula with regards to applications in safeguards and accelerator-driven system. The quantitative assessment was made through MCNPX and MCNP-PoliMi simulations. The motivation for this work is related to the fact that the traditional one-group (and one-region) variance to mean formula was elaborated and used for thermal systems in which the thermal flux and the lifetime of thermal neutrons dominates. However, this approach does not fully describe the fast neutron systems, as well as heavily reflected thermal systems, since the effects of the reflector play a significant role in the latter. Thus, a two-group two-point master equation approach might lend the possibility of treating a fast multiplying material surrounded with a reflector in a more accurate way, by treating the counts separately in the fast and the thermal groups (or in the fissile and reflector regions). Investigation of this problem has a methodological value of its own since, for example, two-group calculations with the master equation technique when both thermal and fast fissions are included, have not been performed earlier