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On the Stability of Homogeneous Nuclear Reactors with Non-Linear Reactivity Dependence on Temperature


Nuclear Science and Engineering

Volume 11 / Number 4 / December 1961 / Pages 428-433


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The stability and instability properties of homogeneous nuclear reactors with a single temperature coefficient of reactivity which is temperature dependent are studied by means of Liapounoff's Second Method. The special case of a temperature coefficient linearly dependent on temperature is solved completely for a space-independent model and it is shown that all solutions are bounded and tend asymptotically to a constant if the reactivity decreases as the temperature approaches large values. In some conditions, the reactor has two stable equilibrium points (bistable).

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