Two-point theory for the differential self-interrogation Feynman-alpha method

Abstract

A Feynman-alpha formula has been derived in a two region domain pertaining the stochastic differential self-interrogation (DDSI) method and the differential die-away method (DDAA). Monte Carlo simulations have been used to assess the applicability of the variance to mean through determination of the physical reaction intensities of the physical processes in the two domains. More specifically, the branching processes of the neutrons in the two regions are described by the Chapman -Kolmogorov equation, including all reaction intensities for the various processes, that is used to derive a variance to mean relation for the process. The applicability of the Feynman-alpha or variance to mean formulae are assessed in DDSI and DDAA of spent fuel configurations.

A multi-region multi-energy formalism for the Feynman-alpha formulas

“…In the present study, we further generalize the results in Anderson et al (2012) and Pal and Pzsit (2012), and introduce a multi-region multi-energy formalism (for a general number of both regions and energy groups) of the relevant stochastic transport equation, resulting with a multi-region multi-energy Feynman-Y function. For an N-regions M energy groups model, construction the relevant set of equation may be reduced to the following problem: consider a N regions nuclear system (under an M energy groups approximation), and a set of detectors operational in a time interval of duration T -referred to as the target interval -opened after the system has reached saturation. The goal is to calculate the mean and the variance of the number of detections in the target interval.…”

“…In the present study, the formalism and some of the notations introduced by Pal & Pazsit in Anderson et al (2012) (where the analysis was carried out for a two region problem), will be often used and further developed.…”

“…As in Anderson et al (2012), each ''region'' will be defined by a spatial location which is both homogeneous and large enough, so that the branching process is determined only by the number on neutrons in the entire region and their energies, and therefore the dynamics of the system is well defined by the following set of intensities: -the fission multiplicity, defined as the probability that a fission in the i th region and j th energy group, will produce k neutrons in the l th region and m th energy group 1 . ðS i;j Þ i¼N;j¼M i¼1;j¼1 -The source rate, defined as the probability (per time unit) for a source event in the i th region and j th energy group.…”

“…In the work presented in Anderson et al (2012) and Pal and Pzsit (2012), dynamics through time (the master equation) was given only in terms of the neutron population, and the relation between the moments of the population size distribution and the moments of the detection distribution is evaluated once the first were fully computed. In that sense, both papers described a single-detector setting.…”

“…However, in recent years, there is a growing academic effort, from a large number of contributors, to generalize the results to more elaborated settings: in Anderson et al (2012) a two region model was suggested, and in Pal and Pzsit (2012) a two energy-groups model was developed. The two were combined in Chernikova et al (2013).…”