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Hi! I'm a nuclear engineer. I just wanted to do a small drive-by clarification/lecture.

There are a lot of feedbacks that are considered when designing a nuclear reactor, it's not just a single void coefficient. There are thermal feedbacks, feedbacks related to the decay of fission products, feedbacks related to the burnup of fuel, the burnup of the neutron poisons, the activation of the water in the primary loop, etc etc. When designing a nuclear reactor, all of these effects must be examined. Generally, this involves finding the transfer function and confirming that all the poles of the transfer function have real part less than 0. (This is where the "negative" part comes in, they're complex numbers in general, but as long as the real part is less than zero this corresponds to a decaying exponential.)

An aside on criticality. We are quite fortunate in that due to a quirk of nuclear physics, fission reactors are possible. We call the time difference between one fission and the next from the neutrons produced a "generation." If we had to react on the timescales of a "generation" based on the simple model where one fission leads directly to another, then we'd have to react in milliseconds, and this just wouldn't be possible to make a reactor safe, even with an extremely well designed system of feedbacks. However, some fission products will decay and release a neutron, these so-called delayed neutrons make controlling a nuclear reactor on human time scales possible (minutes and hours instead of milliseconds), and it makes these feedback loops far more stable. So we aim to keep the criticality below 1 for "prompt" neutrons, and slightly above 1 for delayed neutrons, then we rely on the feedback systems (primarily thermal and fission products) to keep the criticality oscillating very slowly around 1.

For specifically Chernobyl, there is a more broad idea that we concentrate on in reactor design, that of overmoderation vs undermoderation. Reactivity has a relative peak at a particular amount of moderation, and we want to design the reactor in such a way that it can never get more moderated than that peak, because that would give a positive feedback loop if increasing the power led to a concomitant decrease in moderation (which is normal, the density of liquid water decreases with increasing temperature). Because Chernobyl was graphite moderated and steam cooled, we had an especially bad case of this where the core flooded and was massively overmoderated, and in order to get the water out of the core they attempted to turn the reactor all of the way up and boil it out, but in doing so this caused the reactivity to go massively supercritical as the moderation was reduced from absolutely smothering the reaction to just right. It was so supercritical that it was supercritical only with the prompt neutrons, so-called prompt supercriticality, which is why you read things like the power went up 1000x in a second.

The United States does not, and did not even at the time, allow certification of designs where it is possible for this to occur. All reactors must have negative reaction coefficients for all major feedbacks in all operating scenarios, and, in fact, due to this stringent process there are only 4 reactor types that the NRC has currently certified for new nuclear reactors (with 3 more currently under review), (and each design has to be certified jointly with the location where it will be built, so something like Fukushima, where the backup generators are in the basement in a flood zone, would not pass certification review in the US.)

Anyway, I hope this was interesting and educational.