Determination of reactor stability in case of dual oscillations

In a recent paper by van der Hagen et al. (1994), a novel instability phenomenon. observed in the Swedish Ringhals I BWR, was analysed. The new feature of the instability was that the decay ratio, calculated either from single detector signals (LPRMs) or from spatially averaged signals (APRMs), appeared to behave discontinuously, i.e. showing a jump. when the operating point was changed smoothly on the power-flow map. It was found that a global (reactor-wide or in-phase) and a regional (first azimuthal harmonic, "out-of-phase") mode were existing concurrently, with the same resonance frequency, but with differing stability properties and signal amplitudes. In this paper it is investigated in a simple phenomenological model whether or not a co-existence of two oscillations can explain such a discontinuous behaviour of the decay ratio of the total signal. Explicit formulae are derived for the decay ratio of such a composite signal, as a function of the decay ratios of its constituents. It is shown how the above mentioned jump-like behaviour arises when one of the two components approaches instability. The use of the asymptotic decay ratio is suggested for the determination of the largest decay ratio, i.e. the one corresponding to the most unstable mode