The issue of recriticality in the damaged reactors at Fukushima pops up every now and then (a few examples link1, link2, link3, link4). Perhaps it is worth taking a look at what recriticality means, how likely it is and what it would mean if the cores goe critical. These posts will contain some maths and give some insight into basic reactor physics. Despite what most people think it is actually quite easy as long as one can follow the solution of some simple differential equations.
We will look at two different cases, in the first case the core has melted completely and is as a molten puddle or bed of “gravel” at the bottom of the vessel. In the second case the fuel rods are still mostly geometrically intact while the control rods have melted. If I have energy I might throw in a section about criticality in spent fuel pools as well at the end. We start with the completely molten core because it is easier and highlights all the relevant physics.
What exactly is criticality?
Fission is a reaction whereby a incoming neutron hits a nucleus, the nucleus then has a certain probability (depending on the energy of the neutron, what nucleus it is etc) of splitting into two roughly equally large pieces and in the process emit 2-3 new neutrons. Those neutrons can in turn hit new nuclei that causes more fissioning and voila, we have a chain reaction. If we assume we have a system where nothing is happening and we send in a burst of neutrons, those neutrons, that we will call the first generation, will cause an initial amount of fission reactions that produce a second generation of neutrons which goes on to create a third generation etc. Criticality is simply defined as the ratio between a subsequent generation with the one preceding it, it is usually designated by the letter K.