Every induced fission event produces two or more neutrons. These neutrons can go on to induce more fission, or they can be absorbed without producing fission or lost from the surface of the reactor core.

To keep the reactor self-sustaining at least one neutron must go on to produce one fission for every fission event.

Let us consider starting up a nuclear reactor. Initially, there are a lot of control rods inserted into the core. The control rods absorb neutrons and therefore stop the reaction from being self-sustaining.

If we add neutrons to this system then they may cause a few atoms to fission, but not enough neutrons will be produced to keep the system self-sustaining. For example, you may only get 0.80 neutrons going on to produce fission from every fission event. For convenience, we are going to call this number k. Here k=0.80

Now we start to move control rods. This time we may get 0.95 neutrons going on to produce fission from every fission event (i.e. k=0.95). Move the control rods even further and we reach a state where k=1 – the reaction is self-sustaining.

If we have pulled the control rods out too far and have k=1.001 then the number of neutrons will continue to increase with a similar increase in the number of fissions and hence energy generation. At some point we are going to get a problem since the cooling system will no longer be able to cope and the fuel rods will overheat.

So OK we can push the control rods back down again to bring it back to k=1.

How Long Have We Got?

This depends on how long we have to wait until the neutrons are produced and go onto to induce more fission. If this time is too short, then we will not be able to react quickly enough before we have a problem.

The neutrons that are produced by fission are generated very quickly and are called prompt neutrons. If we just relied on prompt neutrons, then we would not be able to control a nuclear reaction.

However, a very small percentage of the neutrons are produced by other processes, such as some of the decays of fission products. These can take several seconds to appear and are called ‘delayed neutrons’. Although they are less than 1% of the neutrons produced, the long delay has a big impact on the amount of time we have to respond.

If we pulled out the control rods too far then there would be many more prompt neutrons and the time we have would be much less. This happened at the SL-1 reactor¹. Therefore control rods must be moved quite slowly.

PWRs and Prompt Criticality

You often see it stated that PWRs (pressurised water reactors) cannot reach the state of ‘prompt criticality’². This is based on the fact that the level of enrichment (3-5%) is not great enough to make a critical mass. However, this is irrelevant. If we did take all the nuclear fuel and bung it into a big lump, it is true that it would not support a self-sustaining reaction. However, it can produce a self-sustaining reaction (k=1) or increase reaction (k>1) when placed in a reactor core with a moderator.

Xenon-135

Xe-135 is a fission product and is also produced by the decay of Iodine-135 and Techetium-135. It has a very high neutron capture cross-section. In a running reactor, the amount of Xe-135 is very small, since it almost immediately captures a neutron to form Xe-136. However, after reactor shutdown or if the reactor runs at low power, then the Iodine-135 continues to decay to Xe-135.

With no or insufficient number of neutrons about, this is not transformed and builds up. It has a half-life of a few hours and so eventually decays away.

What happens when you start a reactor before most of it has decayed? You pull the control rods up until you reach k=1. However now the Xe-135 rapidly disappears via neutron capture. This means that suddenly there are a lot more neutrons about because they are not longer being captured by the Xe-135 and k becomes much larger than 1.

You now do not have anywhere near enough time to control the reaction and you have a bit of a problem. This is probably what cause the accident at Chernobyl.

It is also one of the reasons why nuclear power plants cannot vary their output much and why they take a long period to restart after they have been shut down.

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¹ SL-1, wikipedia (http://en.wikipedia.org/wiki/SL-1#Accident_and_response)

^2  I personally do not like the term ‘prompt criticality’. Although you can define a point where the rate of production of prompt neutrons equals the rate of loss this does not have any real relevance. Delayed neutrons still play an important part after prompt criticality is reached and you can still have large increases in power below prompt criticality – it just means you have more time to respond to them.