THE TWO POINT FEYNMAN-α THEORY: A PRACTICAL POINT OF VIEW ON EX-CORE DETECTORS

The Feynman-α method is perhaps the most basic realization of the so-called”reactor noise” theory, where static and kinetic parameters of the core are estimated by sampling statistical properties of the neutron count distribution in a sub critical configuration. In the Feynman-α method, the variance to mean ratio (as a function of the detection gate) is sampled, and then through a simple fitting procedure, the α eigenvalue is estimated. The theory behind the Feynman-α method relies on a single-group analysis. From a practical point of view, the single group model requires that the detector be located within or next to the reactor core. Implementation of the Feynman-α method is simple due to three facts: first, although the dynamics are determined by (at least) 5 parameters, the fit is done only for a two-parameter function. Second, these parameters are well separated: one is a constant multiplier and the second is an exponential coefficient. Third, the exponential coefficient has a clear and simple physical interpretation, which can be easily used to estimate the reactivity of the core. In the past decade, the classic Feynman-α theory has been extended to a multi-group setting, using the probability generating function formalism. However, in the resulting formulas, it seems, the above mentioned properties are often lost: implementation would require a fit on a multi-exponential function, whose decay modes are defined by the eigenvalues of a certain”reaction rate” matrix, which may not be explicitly computed, and would depend on parameters that can not be calibrated in a simple manner. The outline of the present study is to analyze a simple two region model: Core and moderator/reflector, were the reactor is located outside the core, within the moderator/reflector. In particular, through direct analysis of the reaction rate matrix, we address the practical implementation of the two point Feynman-α theory: when should we expect a good”separation” of the different decay modes, and when would the reactivity be tractable from the variance to mean ratio.