The Covariance and Biocovariance of the Stochartic Neutron Field

The use of stochastic neutron field theory (neutron noise) for the measurement of reactor physics parameters goes back to the early work of Serber, Feynmann, and Orndoff. Since then, a large variety of methods and applications has been developed. In the majority of these methods, some form of modified one-point reactor kinetics was used for the interpretation of the measurements. In fact, the high level of sophistication of the instrumentation used was not matched by the theory. In 1965, Bell developed a general theory of the stochastic neutron field, and in 1987, Munoz-Cobo et al enlarged this treatment to include the effect of the detectors in the neutron field. In both instances, the complexity of the theoretical results were beyond the computing capabilities then available thus, the mismatch between experimental and theoretical methods remained in existence because the powerful Monte-Carlo methods then at work, were only applicable to static neutron fields. This problem was eliminated by the development of a time-dependent Monte-Carlo code specially written by T. E. Valentine for the analysis of stochastic measurements that gave them relevance to the results of the general theory. The purpose of this work is to illustrate the derivation of observables of the stochastic neutron filed from its general treatment