Those Procrastinating Radionuclides

In all the discussion of nuclear power, there’s one bit that hasn’t been discussed in any of the summaries, which may be a good thing because I’m not confident that the general science media would get it right: How can you control the fission reaction in a reactor?

First, a bit of terminology. A critical reactor is one in which each fission result in one neutron, on average, inducing another fission. Which makes the fission rate from this chain reaction constant. So all those times you’ve seen on a TV show or in a movie, where a character shrieks, “OH my GOD! The reactor has gone CRITICAL!” it’s really no big deal. The population of neutrons from fission is constant over some period of time. If you are supercritical this population is increasing, and subcritical means it is decreasing. And the rate of fissioning is proportional to the neutron population.

The neutrons that come from fission (called “prompt neutrons,” for reasons which should become clear shortly) have a lot of energy — an MeV or so, typically, so they are called “fast,” — and they bounce around, scattering off nuclei and losing energy in those collisions. Most of the collisions are with the material that’s there for the express purpose of slowing the neutrons down — the moderator — and if the neutron gets down to thermal energies (“slow” or “thermal” neutrons) before it leaks out of the reactor or gets captured by some nucleus, it can be absorbed by the uranium and induce another fission. And this happens really quickly. A matter of a few tens of microseconds. It’s convenient to look at this in discrete steps, even though the reactions are continuous: each set of fissions releases neutrons which slow down or are lost, and these then induce more fissions. That constitutes a generation with some characteristic lifetime. If the lifetime were that of prompt neutrons alone there’s no way you could ever control a nuclear reactor. Because when a reactor is supercritical, the effect compounds: more than one neutron survives to cause a fission, which means more fissions, which gives you even more neutrons, and so on, ad infinitum. And if your time constant for doing this compounding is 25 microseconds, that’s of order 40,00 generations in just one second. Even if you had just a 0.01% increase in population per generation, you’d increase the population (and power) by a factor of 50 in just one second. There are no systems that could react fast enough to stay within reasonable limits.

But that’s not the whole picture. Not all neutrons come directly from the fission process. Some neutrons appear as the result of beta decays. Beta minus decay occurs in nuclei that have an overabundance of neutrons, and as you look at nuclei that are far from stability (that is, it takes several decays before you would end up with a stable nucleus) there is a tendency for the decays to release more energy and happen quicker.

In beta minus decay, a neutron changes into a proton and a positron and neutrino are emitted from the nucleus. This “reshuffles” the nucleus and the energy states it has; in a lot of cases, the daughter nucleus is not in the ground state, so a gamma is also emitted as it de-excites. For some nuclei far from stability, there is so much energy left over that the nucleus can emit a neutron instead of a gamma. But before this neutron can appear, we have to wait for the beta decay to happen, and that delay is on a time scale best measured in seconds. These are called “delayed neutrons,” and they comprise a little less than 1% of the neutrons from fissions in a critical reactor. But because they take so relatively long to appear, the effective generation time is much greater. Which means only a handful of neutron generations will occur in the time it would take for the system to respond — the reactor is actually subcritical from just the prompt neutrons, and any neutron population increase is relying on decays that won’t occur for around a second.

This works as long as the reactor is subcritical on prompt neutrons. If the reactor went “prompt critical” there would be a spike in power before the system could respond; this is what happened at Chernobyl, because safeguards were intentionally disabled and procedures violated in order to run a test. In a bomb the design is to be highly prompt supercritical using fast neutrons; you aren’t thermalizing neutrons or relying on delayed neutrons for anything. One of many ways a bomb is different from a reactor.

One thought on “Those Procrastinating Radionuclides

  1. This summation was easily absorbed (sorry – couldn’t resist the pun) and clarified my rather vague understanding of the process. Thanks!

Comments are closed.