Reactor Inhour & Reactivity Period Calculator
Nuclear kinetics: Solve the 6-group precursor Inhour equation relating reactivity insertion (ρ, $) to stable reactor period (T) and power doubling time.
Reactivity Insertion & Nuclear Kinetics
Reactor Period & Power Evolution
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Frequently Asked Questions
Why do delayed neutrons make nuclear reactors controllable?
Prompt neutrons emitted directly during fission appear within 10⁻¹⁴ seconds, resulting in a mean generation time of only ~30 microseconds. If reactors relied solely on prompt neutrons, any small positive reactivity would double reactor power in milliseconds, faster than any mechanical control rod can move. Delayed neutrons (0.65% in U-235) emitted by decaying fission fragments (like Br-87 and I-137) stretch the effective neutron generation time to ~0.1 seconds, giving operators and automatic systems seconds to minutes to respond.
What is the definition of one "Dollar" ($) of reactivity?
One Dollar ($1.00) of reactivity is equal to the total effective delayed neutron fraction (β_eff). At exactly $1.00 of reactivity (ρ = β), the reactor becomes "prompt critical," meaning the chain reaction can sustain itself purely on prompt neutrons without waiting for precursor decay, initiating an instantaneous power pulse.
Why does a shut-down reactor power level decline on a -80 second asymptotic period?
When control rods scram into a critical reactor, prompt neutrons disappear instantly. However, delayed neutron precursors already present in the core continue decaying and feeding neutrons into the subcritical multiplier. The longest-lived precursor group (Group 1, primarily Bromine-87) has a radioactive half-life of 55.6 seconds (λ₁ = 0.0124 s⁻¹). Its decay governs the longest stable asymptotic period: T = -1 / λ₁ ≈ -80.6 seconds.