Correlation functions of non-linear nuclear reactor models

The steady-state correlation function of a non-linear point nuclear reactor model with instantaneous temperature feedback, reactivity fluctuations and omission of delayed neutrons is calculated by means of a continued fraction expansion method. Near criticality, where other methods fail, this method gives good results for early times. A first-order truncation gives a spectral density with two corner frequencies. Results are given for a non-vanishing independent neutron source. In this case no exact results are known. For a vanishing source our results are compared with exact ones and with those of a linear analysis and a system size expansion. The necessity of a proper treatment of non-Markovian effects for non-white reactivity fluctuations is pointed out. The existence, in the spectral density, of a corner frequency associated with the correlation time of the noise is shown. (author)