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

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).