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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.

With no delayed neutrons, set $\beta =0$ and omit the precursor equation. The source-free model reduces to $\dot{n}=(\rho /\Lambda )n$, givingThe delayed-neutron model's dominant e-folding time is about $121$ times larger. This comparison illustrates why a small delayed neutron fraction strongly alters the kinetics. It is a comparison of the supplied idealized models at the same imposed positive reactivity, not a control prescription or a claim that every transient has the same timescale.