New equilibrium state of a perturbed nuclear reactor with negative feedback

Nonlinear analysis has shown that when the buckling of a nuclear reactor with negative feedback is increased, the flux, under appropriate conditions, will proceed to a new asymptotically stable state. This contrasts with the linear theory which predicts a runaway. In this work, the method of "coordinate stretching" has been used to obtain the asymptotic solution of a nonlinear nuclear reactor under the combined effect of an initial positive disturbance and a negative feedback based on the Newton's law of cooling.The minimum stability condition is derived by requiring that a bounded new equilibrium state exist. This condition sets an upper limit to the magnitude of the initial disturbance beyond which an equilibrium solution does not exist. Furthermore, the magnitude of the equilibrium flux is determined explicitly in terms of several relevant physical properties of the system: feedback coefficient, energy production rate, and rate of energy transfer to coolant.