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 variousprocesses including all reaction intensities for neutrons. This paper presents a full derivationof 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. Themotivation 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 thermalflux 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 ofthe reflector play a significant role in the latter. Thus, a two-group two-point master equationapproach might lend the possibility of treating a fast multiplying material surrounded with areflector in a more accurate way, by treating the counts separately in the fast and the thermalgroups (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 equationtechnique when both thermal and fast fissions are included, have not been performed earlier.