Kinetics of the Reactor without Feedback

So far we have considered only the steady state critical reactor where the neutron flux does not vary with time. We now extend the discussion to cover the case where an initially critical reactor is rendered sub- or supercritical by some change such as the movement of a control rod. The dynamic response to changes in the multiplication factor is of obvious importance to the practical operation of the reactor and in particular to the assessment of its safety under operational conditions. 

Initially, the discussion will be restricted to the reactor without feedback that is, we assume that the changes in reactor power level consequent on the applied change in multiplication factor do not themselves produce further changes in multiplication. During the commissioning of a power reactor, for example, the reactor is often operated at very low powers 

In discussing the dynamic behavior of a reactor, it is found convenient to introduce a new variable, the reactivity, which is related to the multiplication factor, /Cejy, as shown below  

The reactivity, like the multiplication factor, is dimensionless. It is frequently expressed as a percentage, a reactivity of 1 % corresponding to a value of 0.01 for the ratio above. The critical reactor, of course, has zero reactivity, since is equal to unity in that case. 

This simplified picture is known as the point reactor model. 

---