Solutions of the Reactor Kinetics Equations for Time Varying Reactivities

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Abstract
The solutions of the reactor kinetics equations for constant (step-function) reactivities are straight-forward and well known. For time dependent reactivities, however, only approximate solutions (excluding machine results) peculiar to the individual need are generally available. To obtain solutions for time dependent reactivities, the reactor kinetics equations are combined into a single integral equation of the Volterra type. The kernel of the integral equation characterizes the particular reactor through the decay properties of the six groups of delayed neutrons plus the prompt neutron generation time. A simple iterative procedure for hand computation of the solutions for general time dependent reactivities is given. Curves for two types of such reactivities (linear and ≃∫0vtsin2kxdx) are included.

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