Mean Square Instability in Boiling Reactors

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Abstract
The dynamic behavior of boiling water reactors at high powers is investigated with a model in which the reactor system is represented by a second-order differential equation with a random damping factor and a random driving function. It is found that the mean square value of power becomes divergent (instability in the mean square sense) at a power level which is lower than the instability threshold usually predicted by the conventional transfer function analysis (instability in the mean). A method for predicting the mean square instability threshold during the initial power rise is also described, which consists of plotting the inverse of the root mean square of the power fluctuations as a function of the average power level, and determining the power at which the extrapolated curve intersects the x axis. The observed occurrence of oscillatory wave trains in the power fluctuations is also accounted for. Some of the results of the model are verified by analogue computer studies.

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