Application of the Wiener-Hermite Functional method to a linear feedback model of point reactor kinetics driven by random reactivity noise

The Wiener-Hermite Functional (WHF) method is applied to a linear feedback model of point reactor kinetics in a second-order approximation. The neutron kinetics model is driven by Gaussian reactivity white noise under stable reactor operating conditions. It contains explicitly one group of delayed neutrons. In addition to the instantaneous negative power-reactivity feedback, the case of a positive feedback is included with a Greenʹs function which has the characteristics of a narrow-band resonance filter. A first-order perturbation calculation is applied to solve approximately the system of non-linear integral equations resulting in the frequency domain for the determination of the neutron steady-state value and the power spectral density (PSD) of the neutrons. Under certain conditions the appearance of a (small) harmonic peak can be observed in the PSD