%0 Journal Article
%T Two-Group Theory of the Feynman-Alpha Method for Reactivity Measurement in ADS
%A L¨¦n¨¢rd P¨¢l
%A Imre P¨¢zsit
%J Science and Technology of Nuclear Installations
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/620808
%X The theory of the Feynman-alpha method, which is used to determine the subcritical reactivity of systems driven by an external source such as an ADS, is extended to two energy groups with the inclusion of delayed neutrons. This paper presents a full derivation of the variance to mean formula with the inclusion of two energy groups and delayed neutrons. The results are illustrated quantitatively and discussed in physical terms. 1. Introduction Methods of online measurement of subcritical reactivity, in connection with ADS, have been studied over a decade by now. Both deterministic methods, such as the area ratio or Sj£¿strand method [1] (pulsed measurements), and stochastic or fluctuation-based methods (Feynman- and Rossi-alpha methods) have been investigated. What regards the latter class of methods, the theory of classical systems, based on a stationary source with Poisson statistics, had to be extended to the case of nonstationary (pulsed) source with compound Poisson statistics (spallation source, generating several neutrons simultaneously in one source emission event). Regarding the pulsed sources, both narrow (instantaneous) as well as finite width pulses with various pulse shapes were considered, both with ¡°deterministic¡¯¡¯ (synchronised between source emission and counting interval) and stochastic (nonsynchronised) pulse injection. An overview of the field can be found in [2]. The most general treatment of all the above mentioned cases is found in Degweker and Rana [3] and Rana and Degweker [4, 5]. In this paper, we will discuss another aspect of stochastic reactivity measurement methods, which is related more to the system properties than those of the source. The new aspect is to take into account the energy dependence of the neutrons by the use of a two-group approach. All work so far in which compact analytical results could be obtained in this area (calculation of the Feynman- and Rossi-alpha formulae) was made by the use of one-group theory. This is justified by the fact that the methods were used in thermal systems, where the neutron population and hence its dynamics is dominated by thermal neutrons. However, many of the planned ADS concepts will use a core with a fast spectrum, in which the dominance of thermal neutrons will be significantly reduced. In terms of a two-group approach, unlike in a thermal system where there is one time or decay constant in a pulsed experiment, there will be two components in the temporal response with two different time constants and with comparable amplitudes. One indication for this possibility comes from
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