The Chain Reaction
Nuclear fission releases 2–3 neutrons per split uranium-235 nucleus. If exactly one of those neutrons causes another fission, the reaction sustains itself at constant power — the reactor is critical. This deceptively simple balance is the central problem of nuclear engineering: maintaining k-effective at precisely 1.000 while the fuel depletes, fission products accumulate, and temperatures fluctuate.
The Six-Factor Formula
The effective multiplication factor k_eff is the product of six probabilities tracing a neutron's life from birth to the next fission. Each factor — fast fission, resonance escape, thermal utilization, reproduction, and two non-leakage probabilities — depends on geometry, materials, temperature, and isotopic composition. Changing any one parameter ripples through the entire neutron economy.
Delayed Neutrons: The Gift of Control
If all fission neutrons were emitted instantly (prompt neutrons), a reactor with k=1.001 would double in power in milliseconds — impossibly fast to control mechanically. Nature provides a saving grace: about 0.65% of neutrons are delayed, emitted seconds to minutes later from fission product decay. This tiny fraction stretches the effective neutron generation time from microseconds to seconds, making control rod adjustment feasible.
Temperature Feedback and Safety
This simulation models k-effective as a function of enrichment, moderation, control rod absorption, and temperature feedback. Adjust parameters to explore how the reactor transitions between subcritical, critical, and supercritical states. Watch how the Doppler effect at high temperatures provides inherent negative feedback — the single most important passive safety mechanism in thermal reactor design.