Prompt Criticality
Below 1.0$ of reactivity, delayed neutrons keep the chain reaction manageable. Above 1.0$, prompt neutrons take over and the reactor becomes uncontrollable in milliseconds.
Delayed Supercritical, Approaching Limit
At 0.50$, the reactor period is 12.5 seconds. Delayed neutrons still dominate, but the margin to prompt criticality is shrinking. Power doubling time: 8.7s.
Delayed vs Prompt Neutrons
About 99.35% of neutrons from fission appear instantly (prompt neutrons). The remaining 0.65% come from fission product decay with delays of seconds to minutes (delayed neutrons). This tiny fraction is what makes nuclear reactors controllable, the effective response time is seconds, not microseconds.
The delayed neutron fraction is expressed as β (beta). When reactivity ρ is measured in units of β, called dollars, the critical threshold is clear: below 1.0$ the reactor responds on a timescale of seconds; above 1.0$ it responds in milliseconds.
The Chernobyl Connection
The RBMK-1000's positive void coefficient could inject several dollars of reactivity in seconds. When the AZ-5 emergency shutdown was triggered but the graphite displacers added even more reactivity, the total exceeded 1.0$, prompt critical. Power surged from 200 MWt to over 30,000 MWt in under a second. The fuel fragmented, the pressure tubes burst, and the 1,000-tonne reactor lid was blown off.