A reactor is steered by one number: the multiplication factor k, the ratio of one neutron generation to the last. Drive the control rods and the fuel enrichment below, and watch k, the reactor period and the thermal power answer together on a live trace.
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.
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.
Start with the insertion slider, because everything else follows it. Each percent of rod you push into the core removes 40 pcm of reactivity, and the panel converts that straight into k through ρ = (k − 1) / k. At the default 50 percent the arithmetic lands on exactly zero: the trace runs flat and the power holds at 3,000 MW. Nudge one percent either way and it stops holding. That is the point of the control: k = 1 is a knife-edge, not a setting, and an operator holds a reactor there by continuously correcting, not by parking a lever.
The stable period readout is where the lesson gets sharper. Pull the rods back to 45 percent and the period reads about 29 seconds: the neutron population multiplies by e every 29 seconds, slowly enough to watch and to catch. Keep pulling and that number falls off a cliff — roughly 4 seconds at half a dollar, and well under a second as the reactivity closes on β. That collapse is why the reactivity is printed in dollars as well as pcm: one dollar is β, so the figure tells you how much margin is left before the period stops being a human timescale.
Cross that line and the PROMPT CRITICAL lamp latches. It means the prompt neutrons alone now sustain the chain reaction, the delayed ones no longer set the pace, and the response time drops from tens of seconds to a prompt generation time of 10-4 seconds. Nothing you can do with a slider is fast enough to follow that. The lamp stays lit after you back away, because in reactor operation a state you passed through briefly still happened.
Now press SCRAM and watch what the trace refuses to do. The rods slam fully in, the neutron population collapses through several decades — and the power line separates from it and levels out. Five minutes later the core is still producing tens of megawatts. That is decay heat from fission products that do not care the chain reaction has stopped, and it is the misconception this tool exists to break: shutting a reactor down does not switch it off. Cooling it is a problem that outlives the neutrons by days. For the physics underneath the controls, read How a Nuclear Reactor Works; for where the fuel's energy came from in the first place, compare the two routes in Nuclear Fission vs Fusion, or put the missing mass through the E = mc² calculator.
k is the multiplication factor: the number of fissions in one neutron generation divided by the number in the generation before it. At k = 1 each generation exactly replaces the last and the power holds steady, which is what the simulator calls critical. Above 1 the population grows, below 1 it shrinks. Reactivity is just k expressed as a fraction of itself, rho = (k - 1) / k, because that difference is the quantity the physics actually responds to.
A dollar is one delayed neutron fraction, so one dollar equals a reactivity of beta, which this simulator takes as 0.0065 or 650 pcm. The unit exists because beta is the natural yardstick for reactor control: below a dollar the chain reaction still depends on delayed neutrons and moves on a timescale of seconds, and at exactly a dollar it no longer does. Reading the reactivity in dollars tells you how close you are to that edge, which a raw pcm figure does not.
Because most of the neutrons a reactor runs on arrive late. About 99.35 percent are prompt and appear within roughly a ten-thousandth of a second, but the remaining 0.65 percent are emitted seconds to minutes later by decaying fission products. That small late fraction sets the pace of the whole system: it stretches the response from microseconds out to the tens of seconds you see in the period readout. Move a rod and the power does not jump, it leans.
It means the reactivity has reached beta, so the prompt neutrons alone are enough to sustain the chain reaction and the delayed ones are no longer needed. Below that point the delayed neutrons act as a brake and the reactor is steerable. At or above it the brake is gone and the power rises on the prompt generation time instead, which is far too fast for any operator or control system to follow. The lamp latches so that a state you passed through briefly is still reported afterwards.
Set the enrichment to its lowest setting, 0.7 percent, pull every rod fully out, and the reactivity still reads about -970 pcm. That is the correct result for this model and it is not an accident of the numbers: natural uranium is roughly 0.72 percent uranium-235, and in an ordinary light-water core that is not enough fissile material to replace each neutron generation. Real reactors solve it either by enriching the fuel, as here, or by changing the moderator to heavy water or graphite, which the simulator does not offer.