Last time I promised you a fire deliberately held at the exact edge of running away.
A nuclear reactor at steady power is the most deliberate standing wave in this archive. Nothing in it stays: uranium nuclei split, throw out neutrons, and are gone. What holds still is a ratio. Each fission of uranium-235 releases two or three neutrons — on average 2.42 — and for the power to hold level, exactly one of them must go on to split another nucleus. Call that number k. Steady power is k = 1. Not 1.001. One, held there for eighteen months while the fuel burns away underneath it.
Why that should be impossible
A neutron born in a water-cooled reactor spends about twenty millionths of a second slowing down, wandering, and finding a nucleus to split. That is one generation: fifty thousand of them a second.
Now nudge k up by one part in ten thousand. The power grows by a factor of e every fifth of a second; four seconds later it is a hundred million times what it was.
No control rod moves that fast, and no operator thinks that fast. On those numbers a reactor is not a machine you run. It is something that happens once, briefly.
The ones that are late
Not all of the neutrons come out of the split.
About two-thirds of one percent come out of the wreckage instead, some time afterwards. Fission leaves fragments so overloaded with neutrons that a few, having shed an electron and become a different element, are left holding more energy than it costs to throw a neutron away — so they throw one away. The emission is instantaneous; the waiting is the parent’s half-life. The main one is bromine-87, which takes 55.6 seconds to decay to half.
There are dozens of such precursors. In 1965 G. R. Keepin and his colleagues collapsed them into six groups fitted to measured decay curves, with half-lives running from about a fifth of a second to about fifty-six. For uranium-235 the whole late fraction, written β, is 0.0065.
What six neutrons in a thousand buy
Average the generation time over all the neutrons. The prompt 99.35 per cent contribute 0.9935 × 20 microseconds — two hundredths of a millisecond. The late 0.65 per cent contribute 0.0065 × thirteen seconds, which is eighty-five milliseconds. Add them: 0.085 seconds, essentially all of it from the sliver.
The overwhelming majority of the neutrons in a reactor contribute some four thousand times less to its clock than the handful running late. The response time of the machine belongs almost entirely to neutrons which, at the moment the operator touches the rods, do not exist yet. They are still inside bromine atoms.
Take that same nudge again. The power now grows by a factor of e every 850 seconds. Fourteen minutes, instead of a fifth of a second.
The unit is the distance to the cliff
Because the steerable range is exactly β wide, reactor people measure reactivity not in percent but in dollars, where one dollar is β — a name Louis Slotin is credited with proposing, and which stuck.
Zero dollars is critical. One dollar is the edge: at k = 1 + β the prompt neutrons alone close the loop, the latecomers stop mattering, and the clock snaps back to twenty microseconds. For a typical pressurised-water reactor that edge sits at k ≈ 1.006. Everything a control room has ever done happened inside a window six-tenths of a percent wide, and the unit exists to say how far across it you are.
No. 62’s sandpile also sits at a critical angle, but nobody put it there — pour grain on and it finds the angle by avalanching, with no set point and no operator anywhere. This is the opposite arrangement: the critical point is a place people hold the thing, against a budget, with instruments. No. 112’s cochlea is the nearer cousin, an amplifier parked just under its own runaway — but the ear tunes itself, and when it tips over it sings. Here the far side of the line is not a sound.
The window closes as you use it
β is not a property of the reactor. It is a property of what is being split, and what is being split does not stay the same. A uranium core breeds plutonium-239 out of its own uranium-238 as it runs, until plutonium can be supplying something like half the fissions — and plutonium-239’s delayed fraction is roughly a third of uranium-235’s.
So the core’s late fraction falls across a fuel cycle. The dollar gets smaller. The window a reactor is steered inside narrows the longer it runs, and it narrows because it has been running.
Nothing in the core is waiting for anybody. The minutes an operator has are made out of atoms coming apart on their own schedule, one bromine nucleus at a time, thrown off a minute ago by a fire that is trying very hard to go faster.
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One loop I’m watching
Next: a thermostat with no thermostat in it — rain, rock and volcanoes arranged so that a hotter planet buries more of its own carbon dioxide and a colder one buries less. It has held an ocean liquid since long before there was anyone to notice, and it is far too slow to help anyone who does. Next time.