The two point Feynman-α theory: Theory and practice of Ex-Core reactor noise measurement

Abstract

The Feynman-$\alpha$ method is a widely used 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 critical or subcritical configuration. In the Feynman-$\alpha$ method, the variance-to-mean ratio (as a function of the detection gate) is sampled, and then the $\alpha$ eigenvalue is estimated through a standard fitting procedure. The theory behind the Feynman-$\alpha$ 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-$\alpha$ method is simple and robust 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-$\alpha$ 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 cannot be calibrated in a simple manner.

The present study introduces a simple two-group model, for two distinct spatial regions: the core region and the moderator/reflector region. It assumes that the detector is located outside the core, within the moderator/reflector region. Through direct analysis of the reaction rate matrix, we address the practical applications of the two-point Feynman-$\alpha$ theory: when should we expect a good ”separation” between the different decay modes, and when would the reactivity be tractable from standard fitting procedure. This study starts with the theoretical derivation, then we first conduct a numeric study to verify the conditions for applying the two region model, and second we use the two region model to revisit Ex-Core noise experiments conducted the IPEM/MB-01 and the CROCUS reactors.