General formulation of neutron noise for fast reactor systems

A general space- and energy-dependent formalism is developed in order to analyze zero-power neutron noise experiments in fast reactor systems. A generalized dispersion equation is combined with theoretical expressions for the experimentally measured power spectral density and variance-to-mean ratio which makes it possible to express these quantities in terms of a double moment of the Laplace and Fourier transformed Green's function of a slowing-down operator rather than those of the full Boltzmann operator. Several spatial approximations are analyzed in the context of the general formalism. In each case, the power spectral density and variance-to-mean ratio are written in terms of an appropriate fast reactor dispersion law for the medium which can be calculated from the solution to a simple slowing-down equation. The resultant expression for the power spectral density are analyzed for various combinations of neutron migration descriptions, slowing-down kernels, fission spectrum and cross section models, and detector geometries. The combinations are chosen so to determine the effects of the diffusion theory approximation, detector geometry, reactor geometry, and energy-dependent neutron migration descriptions on the power spectral density, and to evaluate the significance of various space and energy effects in the determination of subcritical reactivity from power spectral density measurements. The results of these analyses demonstrate that energy-dependent descriptions of neutron migration are extremely important in the determination of reliable and accurate subcritical reactivities from power spectral density measurements in fast reactor systems