Nuclear Reactor Control

Drive the control rods and the fuel enrichment to set the multiplication factor k. The trace shows how the neutron population and the thermal power answer — and how long they take about it.

Multiplication factor k

1.0000

reactivity 0 pcm · $0.00

−5000 pcm0+5000

CRITICAL

Prompt criticality was reached. Past this point the chain reaction no longer needs delayed neutrons and no operator can follow it. Press Reset to clear this warning.

Stable period

steady

power is holding

Neutrons n/n₀

1.000

at rated flux

Thermal power

3,000 MW

100.0% of rated

Control rod insertion50%

Fuel enrichment4.0%

Time speed5×

One-group point kinetics. Λ = 1.0 × 10^-4 s · β = 0.0065 · λ = 0.0767 s^-1. Rated power 3,000 MW at n/n₀ = 1.

The rods and enrichment are mapped to reactivity by a deliberately simple teaching rule, not by a neutron transport solve: ρ = 2000 + 900(e − 4.0) − 40 i pcm, for enrichment e in percent and insertion i in percent.

No temperature feedback is modelled. In a real core the fuel heats, and that alone pushes ρ back down; here nothing stops a rising trace, so treat anything far above rated power as a curve, not a plant.

Try it: park the rods at 50% and the reactor sits still. Pull them to 45% and watch how slowly the power climbs — that lag is the delayed neutrons, and it is the only reason a reactor can be steered at all.