Feedback Theory for Linear Reactivity Transients in a Point Reactor

The effect of a reactivity insertion in a point reactor is formulated as a linear feedback process, and a simple exponential mode representation is proposed as an analytical solution that is valid at small times. The solution contains a fast transient mode as well as slow ones, and it resolves the stiffness problem in a very simple way. With a ramp reactivity insertion as an example, it is shown that this analytical solution is valid for a time interval that is much longer than the time-step size used in the conventional numerical integration, and it is thus useful in reducing computing time.