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The point kinetics model replaces the spatially and spectrally distributed neutron field by a single amplitude $n(t)$, effectively assuming a fixed or sufficiently slowly varying flux shape. The source amplitude is $s$. A single effective delayed neutron precursor population $c(t)$, delayed neutron fraction $\beta$ and decay rate $\lambda$ stand in for many precursor species with different lifetimes. $\Lambda$ is the prompt neutron generation time and $\rho$ the specified reactor reactivity.

The displayed equations omit explicit thermal-hydraulic, fuel-temperature and isotope-composition feedback. For the stated constant-coefficient transients, $\rho ,\beta ,\Lambda ,\lambda$ are prescribed rather than being solved as evolving fields. The model is useful for an elementary timescale calculation; it does not establish the spatial stability or operating limits of an actual core.

At equilibrium, precursor production balances precursor decay:ThereforeThe delayed neutron precursor population can exceed the instantaneous neutron population even when the delayed neutron fraction is small: the delayed neutron precursor reservoir persists much longer than an individual prompt-neutron generation.

After the short prompt adjustment, the prompt jump approximation takes the neutron amplitude to remain nearly in balance with the slowly changing delayed neutron precursor reservoir. For the source-free model,Substitute this quasi-steady relation into the precursor equation:For constant coefficients,The approximation is meaningful in the stated delayed-neutron regime with $\rho <\beta$ and a separated fast transient. The delayed neutron precursor reservoir remains continuous across an idealized instantaneous reactivity step; the approximation does not resolve the short prompt adjustment itself.

A reduced time-dependent model for a neutron population amplitude coupled to delayed neutron precursor populations. Spatial and spectral shape changes are neglected or represented through prescribed effective coefficients. Such a model illustrates timescale separation without establishing the spatial behaviour or operating limits of an actual reactor.

A timescale-separation approximation that eliminates the rapidly adjusting neutron amplitude in favour of the slower delayed neutron precursor reservoir. It describes behaviour after the short prompt transient and need not resolve the initial adjustment.