Harmonic Analysis of Stochastic Descriptors and the Interpretation of ²⁵²Cf Neutron Source Experiments

The harmonic expansion of the detector field of view in terms of direct and adjoint kinetic eigenfunctions together with the use of a modified version of the Schottky prescription of the equivalent source of noise make possible the harmonic analysis of stochastic descriptors used in the measurement of kinetic parameters. The results are general in the sense that they do not depend on the approximations of the Boltzmann operator, the distribution of fissile materials, or the multiplicity of the neutron source that drives the subcritical system. The results are applied to analyze the particular case of a system driven by a ²⁵²Cf source, with the californium deposited in one of the electrodes of a fission chamber and monitored by two sets of neutron detectors. This analysis is oriented toward the interpretation of experiments to measure reactivities with the stochastic method of the ²⁵²Cf source (ratio method). The theory is then used to synthesize stochastic observables using a simple approximation of the Boltzmann operator, i.e., two-point kinetics, which show the general features of the spatial effects observed experimentally.