Constant Delayed Neutron Source Approximation
As can be seen from the solution of exact point kinetics equation, any reactivity insertion (ρ < β) causes at first a sharp change in prompt neutrons population and then the neutron response is slowed as a result of the more slowly changing number of delayed neutrons. The rapid response is a result of the small value of prompt neutron generation time in the denominator of point kinetics equation.
If we are interested in short-term behaviour and not interested in the details of the asymptotic behaviour, we can simplify the point kinetics equations by assuming that the production of the delayed neutrons is constant and equal to the production at the beginning of the transient. This approximation is known as the Constant Delayed Neutron Source Approximation (CDS) in which changes in the amount of delayed neutrons is neglected, corresponding to taking dCi(t)/dt = 0 and Ci(t) = Ci,0 in the point kinetics equations. That means the point kinetics equations are as follows:
The above equation can be solved analytically and assuming that the reactivity is constant the solution is given as: