As can be seen from the solution of exact point kinetics equation, any reactivity insertion (ρ
) 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 long-term behaviour (asymptotic period) and not interested in the details of the prompt jump, we can simplify the point kinetics equations by assuming that the prompt jump takes place instantaneously in response to any reactivity change. This approximation is known as the Prompt Jump Approximation (PJA) in which the rapid power change due to prompt neutrons is neglected, corresponding to taking dn/dt |0 = 0 in the point kinetics equations. That means the point kinetics equations are as follows:
From the equation for neutron flux and the assumption, that the delayed neutron precursor population does not respond instantaneously to a change in reactivity (i.e. Ci,1 = Ci,2), it can be derived that the ratio of the neutron population just after and before the reactivity change is equal to:
The prompt-jump approximation is usually valid for smaller reactivity insertion, for example, for ρ < 0.5β. It is usually used with another simplification, the one delayed precursor group approximation.