Derivation of two-group two-region Feynman-alpha formulas and their application to Safeguards and accelerator-driven systems.

摘要

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 evalua- tion 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 de- scribe 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 method- ological 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.