Astronuc said:
A subcritical (k < 1) system decreases in power to some low level which is that left by spontaneous fissions or other neutron sources. A subcritical system would not cause a steam explosion.
I must be using the wrong terms. Presumably your k is the expected number of first-generation children of a single neutron introduced in the mass. If k > 1, as you say, the number of fissions increases exponentially in time, and we get a standard nuclear explosion.
On the other hand, if k < 1, then a spontaneous neutron created within the mass will generate T = k + k^2 + k^3 + ... = k/(1 - k) fissions in total, before all neutrons get lost. When k << 1, T is approximately k and therefore small too. However, as k aproaches 1 the number of fissions T created by one spontaneous neutron gets arbitrarily large. For k = 0.9, each initial neutron generates 9 fission events, on the average; for k = 0.99, it is 99 fissions. The chain reaction for
one initial neutron indeed will die off, but a steady supply of N spontaneous neutrons per second will produce N*T fissions per second.
Of course this ignores the effects of energy, direction, and location within the mass. But the point is that fission can generate an arbitrarily large amount of heat power even if k < 1. Indeed, in a woking reactor the goal is to keep the net k below but very close to 1. Isn't that so?
(Wikipedia says that in a reactor one has "delayed criticality", i.e. k > 1 but secondary fissions are "delayed" so that the process becomes stable. This does not seem right: if the net k is greater than 1, delaying the children fissions will still yield an exponential growth with a smaller but still positive rate, growing ever faster without limit. Isn't that so?)
Astronuc said:
The famous bare critical sphere demonstration, e.g., the one in which Louis Slotin died, was a supercritical assembly with nearly pure fissile material. Such material is not used in power reactors.
Did Stotin's configuration really get supercritical? As I understand, it would be hard to tell the difference between (k slighty below 1) and (k slightly above 1) for a very short time. In both cases the rate of fission would be very high. The difference is that in the second case the radiation
would have increased exponentially
if the assembly had not been undone; whereas in the first case the reaction would remain at a high but constant level indefinitely.
Astronuc said:
Only if a system went supercritical and achieve a certain power density very rapidly, would there be a possibility of a steam explosion, and likely the system would have to be prompt critical with a significant amount of positive reactivity (i.e., k >> 1.006), which is not the case at Fukushima.
What I was thinking is the fllowing. I am assuming a dense rack design like that in the Czech re-acking paper, with walls of boral (boron carbide powder clad in aluminum) sandwiched in steel around each assembly.
0. Pool cooling pumps stop.
1. Pool water boils off, and the assemblies become partly dry.
2. The dry parts of the assemblies slowly get hotter by decay heat (k still <<1).
3 When the temperature reaches 660C, the aluminum in the boral melts.
4. The boron carbide powder shifts inside the steel walls, creating "neutron holes".
5. As neutron absorption decreases, the k factor starts to increase.
6. Larger k means increased heat production that means more boral melting and larger k.
8. As k approaches 1 the temperature of the fuel slugs shoots up to >>1800C.
9. A few seconds later, fuel tubes and steel jackets melt.
10. The molten mass falls onto the remaining water causing a steam explosion.
11. The explosion blows away the overheated fuel and stops the chain reaction.
Note that this scenario does not require k>1, but only k large enough for fission to cause fast heating of (some part of) the fuel, from ~700C to over 1800C.
Does it make sense?
