Remark on the role of the driving force in BWR instability: In memory of George Kosály† 1933–2009

Simple models of BWR instability, used e.g. in understanding the role of the various oscillation modes in the overall stability of the plant, assume that each oscillation mode can be described by a second order system (a damped harmonic oscillator) driven by a white noise driving force. Change of the decay ratio (DR) of the observed signal is, as a rule, associated with the changing of the parameters of the damped oscillator, mainly its damping coefficient, and is interpreted in terms of the change of the stability of the system. However, conceptually, one cannot exclude cases when the change of the response of a driven damped oscillator is due to the change of the properties of the driving force. In this work we investigate the effect of a non-white driving force on the behaviour of the system. A question of interest is how changes of the spectrum of the driving force influence the observed autocorrelation function (ACF) of the resulting signal. Hence we calculate the response of a damped harmonic oscillator driven by a non-white driving force, corresponding to the reactivity effect of propagating density fluctuations in two-phase flow. It is shown how in some special cases such a driving force, when interpreting the neutron noise as if induced by a white noise driving source, can lead to an erroneous conclusion regarding the stability of the system. It is also concluded that in the practically interesting cases the effect of the coloured driving force, arising from propagating density fluctuations, is negligible.