Derivation of Pál-Bell equations for two-point reactors, and its application to correlation measurements

For the analysis of noise problems in zero-power coupled-core reactors, one-energy group multipoint Pal-Bell equations are derived and their applications are illustrated. The illustration is made for the neutron correlation experiments of loosely-coupled two-core systems. We first derive a two-point version of the Pal-Bell equations for the neutron detection probability generating functions, and then derive the formulae of Feynman-alpha and Rossi-alpha (Orndoff type) experiments for a coupled-core system, using the factorial moment and cumulant expansions. With these formulae the following coupled-core kinetic parameters can be evaluated from neutron correlation experiments: coupling delay time, coupling coefficient and neutron generation time. The simplicity in the present derivation of Pal-Bell equations is pointed out.