Why can operators control a nuclear reactor at all, when neutrons live only milliseconds? The secret is delayed neutrons — and the point-kinetics equations reveal it.
Reactor Point KineticsLive
power, reactivity & period
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A small step in reactivity does not blow the power up instantly, because a fraction of neutrons are released with a delay. Those delayed neutrons slow the response to a controllable timescale — the reactor period. But push reactivity past the delayed fraction β and it goes prompt-critical, growing on the neutron lifetime — millisecond-fast and uncontrollable.
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How it works
Point reactor kinetics tracks power against a step change in reactivity. A small fraction of neutrons emerge with a delay of seconds, stretching the response to a controllable reactor period. But if reactivity exceeds the delayed fraction β, the reactor goes prompt-critical and power surges on the millisecond neutron lifetime — the runaway regime operators must never enter. Educational model.
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