Non-linear response of point-reactors to stochastic inputs

Abstract

Statistical properties of the non-linear response of a point reactor to a white Gaussian reactivity insertion and an external source are investigated through the general Fokker-Planck theory for linear systems with random coefficients. The autocorrelation function and power spectral density of the reactor power are obtained, and the effect of non-linearities on the corner frequencies is discussed. The response to a Gaussian (not necessarily white) reactivity insertion and an arbitrary neutron source is also considered in the absence of delayed neutrons.