Nuclear Fission Chain Reactions: Subcritical, Critical and Supercritical

One neutron in, more than one neutron out

When a slow (thermal) neutron strikes a U-235 nucleus, it can be absorbed and split the nucleus into two lighter fragments, releasing roughly 200 MeV of energy per fission — overwhelmingly from the fragments' kinetic energy — plus, critically, an average of about ν ≈ 2.4 new free neutrons. Each of those neutrons can go on to strike another U-235 nucleus and trigger another fission, which is the entire mechanism of a chain reaction: the simulation on this page renders exactly this cascade as a spreading field of particles.

The multiplication factor k

Whether the reaction dies out, sustains itself, or grows explosively is governed by a single number, the effective multiplication factor k: the average number of neutrons from one fission that go on to cause another fission in the next generation.

k < 1   subcritical   — each generation has fewer neutrons, reaction dies out
k = 1   critical      — steady state, generation count stays flat (reactors run here)
k > 1   supercritical — each generation has more neutrons, reaction grows

N(generation n) ≈ N₀ · kⁿ

A working power reactor is deliberately engineered and controlled to sit at k = 1, using control rods that absorb excess neutrons to trim k in real time; a weapon is engineered to jump k well above 1 as fast as possible and hold it there for as many generations as the assembly survives, which for a bomb is a few dozen generations completed in about a microsecond.

Enrichment: raising the odds of a fissile hit

Natural uranium is 99.3% U-238 and only 0.7% U-235; U-238 mostly just absorbs neutrons without fissioning (it captures them, becoming U-239 and eventually plutonium-239 through beta decay), which is why a chain reaction in natural uranium alone barely sustains itself. Enrichment raises the U-235 fraction — typically 3–5% for power reactors, over 90% for weapons — increasing the odds that any given neutron hits a fissile nucleus rather than being wasted on non-fissile capture, which is exactly the enrichment slider's effect on k in this simulation.

Moderation: why reactors want slow neutrons

Neutrons come out of fission fast, around 2 MeV, but U-235 fissions far more readily from slow, thermal neutrons (around 0.025 eV) than from fast ones — the fission cross-section for thermal neutrons is hundreds of times larger. A moderator (water, heavy water, or graphite in this simulation's terms) is a light-nuclei material that fast neutrons collide with elastically, losing a large fraction of their energy per collision, similar to a billiard ball losing more speed hitting an object of similar mass than a much heavier one. This is why raising the moderator fraction in the simulation pushes k up even at a fixed enrichment: more moderation means more neutrons reach thermal energies before they either escape the fuel or are non-productively absorbed.

Why this isn't a runaway explosion in a reactor

A crucial safety fact the k = 1 picture hides: not all neutrons from fission appear instantly. Roughly 99.35% do (prompt neutrons, within about 10⁻¹⁴ seconds of fission), but a small delayed fraction, around 0.65%, is emitted seconds later by the radioactive decay of certain fission fragments. Reactor control is engineered to keep k below what prompt neutrons alone would need to sustain (prompt-critical), relying on that slow delayed fraction to determine the actual response time of the reactor, which stretches the effective reaction timescale from microseconds to seconds — long enough for control rods and feedback mechanisms to respond before the reaction can run away.

Frequently asked questions

Try it live

Everything above runs in your browser — open Nuclear Fission Chain Reaction and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.