The exact point kinetics equations, that can be derived from the general neutron balance equations without making any approximations are:
- n(t) is the neutron density in the core (which is proportional to the detector count rate)
- Ci(t) is the precursors density of delayed neutrons of group i
- Λ is the prompt generation time
- ρ is the reactivity
- the constants βi and λi are the fraction and decay constant of delayed neutron precursor of group i
- S(t) is the source term, which characterizes number of neutrons (source neutrons) added to the system from an external source. As can be seen, the source term does not influence the dynamics of the system, since it does not influence the reactivity of the system.
According to Seiji TAMURA, the Inverse Kinetics equations (flux ⟶ reactivity) for discrete time series data can be derived from the ordinary point kinetics equations (reactivity ⟶ flux) assuming that the reactor power change for the interval of Δt is as n(t)=nj-1exp(μjt), where μj = log(nj/nj-1)/Δt:
When the reactor power is at a steady state no, there are seven initial conditions that can be obtained as:
The equation for ρj provides a real time reactivity calculation for successive reactor power data. When the reactor is operating at sufficiently high power level the last term of the right side, the source term, may be neglected, because it becomes negligible.
For operation at low power levels or in the sub-critical domain (e.g. during criticality approach), the contribution of the neutron source must be taken into account and this implies the knowledge of a quantity proportional to the source strength, and then it should be determined. Otherwise zero reactivity will be obtained for any subcritical reactor condition (after the transition phenomena have died out). The source term can be determined using data from a transient state after the introduction of a given reactivity. The source term can be determined from data from rod drop experiment using the Least Squares Inverse Kinetics Method (LSIKM).
Special reference: M. Itagaki, A. Kitano, “Revised source strength estimation for inverse neutron kinetics,” Preprints 1999 Fall Mtg., At. Energy Soc. Jpn., Hiroshima, Japan, G20, (1999)
Special reference: Renato Yoichi Ribeiro Kuramoto, Anselmo Ferreira Miranda. SUBCRITICAL REACTIVITY MEASUREMENTS AT ANGRA 1 NUCLEAR POWER PLANT. 2011 International Nuclear Atlantic Conference – INAC 2011. ISBN: 978-85-99141-04-5.