Disclaimer: I am not an expert. These are notes I made while trying to figure stuff out. Work in progress.
There are at least 5 cases to consider:
| | Prompt | | Delayed | | |
| Weapon: | | few nanoseconds | | n/a | |
| Fast reactor: | | ≈ 100 nanoseconds | | 13 seconds | |
| Moderated reactor: | | ≈ 100 microseconds | | 13 seconds | |
Delayed neutrons are super-important, because without them the typical(*) reactor would be unmanageable; the reaction rate would be increasing exponentially or decreasing exponentially, much too quickly. Anything that happens on a “prompt” timescale is much quick to be manageable using control rods.
Therefore a reactor is designed to be operated at the point where it is just barely delayed critical. It must be constantly adjusted to keep it there.
In a reactor, increasing the reactivity by 7% makes the thing go prompt critical, which is generally a Bad Thing.
Every moderation scheme has “some” negative temperature coefficient of reactivity, based on properties of neutrons and uranium, no matter what the properties of the moderator. That’s because the cross section for absorption of a neutron by U-235 scales inversely with the neutron velocity, hence inversely with the square root of temperature. So when the moderator heats up, the reactivity goes down. If the reactor was only moderately supercritical, this gives you some hope. Perhaps the thing will stabilize before you get a meltdown. Perhaps you will get a meltdown rather than a huge explosion.
A TRIGA reactor is particularly interesting for this reason. It is cleverly designed so that if it goes prompt critical, the moderator very quickly becomes hot enough to be ineffective but not hot enough to cause a meltdown.
The RBMK-1000 at Chernobyl was uncleverly designed. Among its many design faults, it was overmoderated by massive blocks of graphite, the runaway chain reaction could proceed relatively far before “disassembly” occurred. (That’s a euphemism for “explosion”.) For a list of prompt critical accidents, see reference 1.
A fast-neutron reactor is scarier than a moderated-neutron reactor. That’s because the lack of a moderator makes it harder to create a strongly negative temperature coefficient of reactivity.
The vapor pressure produced by graphite is a steep function of temperature. It’s reportedly 108 Atm at 4600 K, which is the triple point. It’s probably around 1 Atm at 3900 K, although this is hard to measure. So I don’t think you can make a big explosion that relies on sublimation of graphite. It would become ineffective as a moderator long before then.
Graphite in air ignites at about 920 K
The melting point of Zircaloy-4 is about 2123 K
One disadvantage of metallic zirconium is in the case of a loss-of-coolant accident in a nuclear reactor. Zirconium cladding rapidly reacts with water steam above 1,500 K (1,230 ∘C).[15][16] Oxidation of zirconium by water is accompanied by release of hydrogen gas. This oxidation is accelerated at high temperatures, e.g. inside a reactor core if the fuel assemblies are no longer completely covered by liquid water and insufficiently cooled.[17] Metallic zirconium is then oxidized by the protons of water to form hydrogen gas according to the following redox reaction:
Zr + 2 H2O –> ZrO2 + 2 H2
A normal BWR has a negative void coefficient of reactivity. Because the RBMK-1000 at Chernobyl was overmoderated, it to only a small extent affected by the loss of moderation from the water, but was to a greater extent affected by the loss of absorption. It had a positive void coefficient of reactivity. Terrible design.
What’s worse, it had absorber that could leave (water) and moderator that couldn’t leave (graphite).
Also, the water was the coolant. So a loss of water resulted in loss of cooling as well as increased reactivity.
You could guarantee a negative void coefficient of reactivity by using heavy water. Comparable moderation, less absorption. Loss of coolant would still be a horror show, probably resulting in a meltdown, but probably not a huge explosion.
Iodine pit. Xenon poisoning.
Iodine-135 yield about 6%. It decays to Xenon-135 with a lifetime of 6.6 hours. Stupendous neutron poison. Cross section of 2 point something million bars. The cross section for U-235 is about 2 barns.
Suppose you start up a reactor without any iodine or xenon. You set the control rods to operate at 100% of rated power. Over the next six hours, as iodine accumulates and produces xenon, you will have to adjust the rods. In the long term steady state, 6% of the neutrons you produce will go toward burning off the xenon that is the grand-daughter of reactions that took place 6.6 hours ago. The fuel flow will be 106% of what it was at the start.
Xenon-135 has a half-life of its own, so if you shut off a reactor and wait a few days, the xenon-135 will go away and you can restart afresh.
Now suppose you don’t shut down and wait. Suppose you want to drop the power by a factor of 16. That is you want to operate at 6% of rated power. You still have to burn off the xenon, which was put into play 6.6 hours ago. So the fuel flow rate will have to be 12% of what it was for the full-power reactor. Not 6% but 12%.
Before pulling out the control rods to make up for xenon poisoning, ask what will happen when the xenon goes away. Think about what happens if you are burning away the xenon faster than it’s being created. If that would take you outside the 7% margin between delayed critical and prompt critical, pulling the rods creates a time bomb. When the xenon goes away, the reactivity will increase, possibly faster than you can respond by re-inserting the control rods.
The xenon burn-out will happen non-uniformly in the loosely-coupled enormous core. 190 metric tons of fuel. Low enrichment (only 2% U-235).
Chain of causation. But so many faults that fixing one of them might not have been sufficient.
190 metric tons of fuel in the RBMK-1000.
Low-enriched uranium. About 2% enrichment.
There are currently 94 nuclear power plants licensed to operate in the United States (63 PWRs and 31 BWRs). They generate about 20nation’s electrical use.
When designing a weapon, a great deal of effort goes into keeping all the fuel together in one place long enough for the reaction to go to completion, more or less, before the thing blows itself apart.
On the other hand, if a reactor has gone prompt critical and is about to blow up, you’d rather have disassembly occur sooner rather than later. It sounds weird to say it, but it’s true: You’d prefer a meltdown rather than an explosion, and you’d prefer a small explosion sooner rather than a humongous explosion later.
Reactor loosely coupled. A small part went prompt supercritical. Neutrons are diffusing into the rest of the core at the speed of sound. A shock moving at supersonic speed is disassembling the core.
Nobody knows exactly what happened, but this scenario fits the facts as I know them, and it’s hard to come up with a better explanation.
Start with primary cosmic rays. Mostly protons. Some with ridiculously high energy. One of them strikes a nucleus in the upper atmosphere and blasts it to smithereens. The debris includes some loose neutrons.
The neutrons start out with high KE. As we know from reactor physics, those are not very reactive. When they hit a nucleus, they mostly go in one side and out the other without reacting.
However, by bouncing around for a while, they gradually lose their KE and become /thermal/ neutrons.
Thermal neutron meets a 14N nucleus. It reacts to form 15N. The neutron didn’t have appreciable KE to begin with, but it picks up a lot of energy falling into the potential well of the strong nuclear force. So what you actually get is 15N*, where the * indicates "excited state". Generic 15N is stable, but 15N* not so much.
It was easy for the neutron to waltz in, because it sees no Coulomb barrier. On the other side of the same coin, a proton has an easier time leaving, because it gets a push from the Coulomb potential. That’s in addition to whatever energy it can get from the excitement of the aforementioned excited state.
According to my limited understanding, this happens fairly quickly and easily, because it does /not/ involve any weak interactions. Making a proton via decay of a neutron requires weak interactions and neutrinos and such, but we don’t need to do that. There’s plenty of protons in the nitrogen nucleus, ready to leave as soon as they get a bit of a push.
At this point we have a loose proton plus an electron that the carbon doesn’t want. Sooner or later that averages out to make hydrogen, which isn’t important to our story.
The rest of the story you know. The radiocarbon reacts with oxygen to make CO2. Rain washes it to the ground. Living things take up the radiocarbon. Dead things don’t. So the amount of radiocarbon tells you how long it’s been dead. Calibrate tree rings against radiocarbon /and/ vice versa to eliminate any uncertainty.