I always thought the material had to be forced together at high pressure for the chain reaction to start. Crazy that just dropping it had such dire consequences.
[0] - https://en.m.wikipedia.org/wiki/Nuclear_chain_reaction#Prede...
It's also been discussed numerous times on this board.
> Los Alamos was going to make the bomb, but at Oak Ridge they were trying to separate the isotopes of uranium ... he saw them wheeling a tank carboy of water, green water - which is uranium nitrate solution. He says, “Uh, you're going to handle it like that when it's purified too? Is that what you're going to do?" They said, “Sure -- why not?" "Won't it explode?" he says. Huh! Explode?" ... he noticed certain boxes in big lots in a room, but he didn't notice a lot of boxes in another room on the other side of the same wall ... what you would have to do to fix this. It's rather easy. You put cadmium in solutions to absorb the neutrons in the water, and you separate the boxes so they are not too dense ...
https://calteches.library.caltech.edu/34/3/FeynmanLosAlamos....
In the case of Slotin, the thing he dropped onto the core was a neutron reflector so it redirected neutrons back into the core.
https://www.science.org/content/article/near-disaster-federa...
This is an interesting read, it's a story about a more recent near criticality that took place in 2011.. You can see a picture in the article of the dangerous configuration -- it's just a few rods of plutonium near each other. Any closer, if one tips over into the other, and they might go hot and release a huge amount of radiation.
This part is confusingly worded.
Once the dangerous configuration was noticed what was the right thing to do?
Not an argument against your main point but doesn’t geometry actually have quite a bit to do with chemistry?
If you look at the energy per unit mass, e.g., J/kg, of different materials, you'll note that curiously many fuels (hydrogen, methane, petrol) and explosives (gunpowder, TNT, ANFO), you'll find that the former are roughly ten times (or more) greater.
What makes explosives, well, explosive isn't the total energy contained within them, it's the rate at which it's released. Jet fuel contains ten times the energy per unit mass than C4, and can in fact melt (or at least significantly weaken) steel beams, but it does so by burning over time.
What explosives do is to combine oxidiser and fuel in the same package (as with gunpowder and ANFO), or contain chemically-unstable bonds with high potential in a state which can be triggered by a sharp shock (TNT, C-4/RDX). The total energy released is smaller, but the rate of release is far greater.
It may be possible to use more conventional fuels to generate explosions. This happens with hydrogen gas, particularly in a stoichiometric combination with oxygen, with petrol within an internal combustion engine (the fuel burn is explosive), and in a fuel-air bomb (a/k/a thermobaric weapon), in which a fuel is widely dispersed in the atmosphere and then ignited. The blast generated is typically far weaker than of an equivalent conventional explosive, but can still be explosive rather than a deflagration (rapid combustion not generating a shock wave). Incidentally, virtually all cinematic "explosions" are in fact deflagrations, often using either flammable gas or suspended powder. There are also relatively frequent dust explosions involving powdered foodstuffs (grain, flour, sugar, etc.) which are a hazard where large quantities of such materials are stored or processed (grain silos, processing plants).
USCSB investigative video of an explosion at Imperial Sugar: <https://yewtu.be/watch?v=Jg7mLSG-Yws>
Raw video of the blast: <https://yewtu.be/watch?v=LQZGWjVwN58>
In particular, storage combinations of potential fuels and oxidisers in close proximity can lead to explosions.
There's also the case of spontaneous combustion particularly of oil-soaked rags or compost piles which shares some characteristics with criticality incidents. That's where heat release which in smaller concentrations would be benign reaches the ignition point of the materials involved. Large heaps of freshly-mown grass in particular can spontaneously ignite. I've had the experience of moving a large pile of woodchips which had been left in sub-freezing weather and discovering that the core of that pile was literally steaming hot, and was melting snow and evaporating water which had flowed in toward it. The chips weren't charring, but they were distinctly warm.
nuclear reactors also do not force material together at high pressure, but nevertheless achieve criticality
If you have a small amount of material but enough to be critical and say, generate enough heat to melt itself into a puddle in a minute, it doesn't explode or anything, but before it melts and likely starts itself on fire, everybody nearby is going to get a lethal dose every few seconds.
In other words, there's a lot of room between "self-sustaining nuclear reaction" and "bomb".
Even storage of materials in warehouses has to be done carefully because too much too close can cause dangerous amounts of reactions.
You might be conflating that condition with prompt criticality.
Geometry and mass matters here because the "default" thing a neutron does is "misses all the nucleii and exits the device", unless the device is fairly big, simply because as electrically neutral particles neutrons do no interact with electrons and only interact with nucleii when very close, so most material looks mostly like empty space to them.
So in principle if you just form a large enough ball of Pu-239, it would go critical. The reason you need explosives is that in order to form that ball, you need to go from a state where there is not enough material together to go critical to a state where there is, and the criticality will immediately start releasing very large amounts of energy. This energy then heats things and drives them apart, preventing a chain reaction where the entire core goes up.
In the criticality accidents listed above, that is precisely what happened. In Slotin's case, the upper half of the core kept falling on the lower half and then pushed apart.
Don't neutrons lose some energy as they transit through the material? That would make this bounded in some respect anyway.
The scenario was that the size of the material can increase until you guarantee a sufficiently high rate of collision, and I'm asking whether neutrons really do not lose energy as they travel prior to collision (as the scenario seems to assume).
I suppose it does eventually, as the number of undecayed nuclei falls, but that wouldn’t be a significant effect until the criticality reaction had very significantly progressed. In other words the reaction can’t go on forever.
Because if the problem is that neutrons are escaping the object before hitting a nucleus, and we are adding more nuclei so the likelihood that they hit something increases, the new collision candidates will be further away than the old ones.
In other words, adding material to the edge of the object does not affect the per distance probability of collision. It only affects the overall probability of collision. Since the per distance probability does not change while the overall probability does, the probability increase must lie outside of the average path length of a neutron through the original object.
Consider that the wavelength of the neutron is a function of its energy, and that the cross sections for interaction between nuclei and neutrons are strong and complex functions of energy.
If the cross section for the interaction of interest gets smaller with decreasing energy, then it would be the case that the neutrons mean free path length would increase as energy decreased.
Sorry, I said something subtle and easy to miss and also made a confusing typo, writing too fast.
"average distance a [nucleus-hitting neutron]"
As in, as more material is added, the percent of neutrons that successfully collide and don't just fly out increases. But, for the class of nucleus-hitting neutrons, the average distance prior to collision increases.
If the neutron loses energy as it travels, then as the average distance increases I suppose the probability of splitting the collidee nucleus decreases. So as the class increases in size, its rate of nucleus splitting may fall below the threshold, which bounds the useful size increase.
Perhaps this doesn't occur until the object has grown in size way past the point of basically guaranteed criticality, I haven't done the math, just curious since GP's statement sounded as if neutrons do not lose energy across any distance and the object could therefore could be increased to an arbitrary size while maintaining the same qualitative per-iteration behavior, and I find that surprising.
Excluding collisions, it does not. As far as the neutron is considered, it's traveling through empty space, just as if it was in vacuum.
> I suppose the probability of splitting the collidee nucleus decreases.
In this regime, probability of splitting a nucleus goes up as energy decreases.
Neutrons lose energy by colliding with things of similar mass, such as hydrogen nuclei (often in water). If they collide with a heavy nucleus, such as plutonium, they just bounce off without losing speed. (Or fission or capture.)
Think of billiards. The cue ball may slow or stop after hitting another ball, since they have similar masses. But hit the rail and it just bounces off, at the same speed, because the table is so much heavier.
If there are no light nuclei in the environment, then the neutrons won’t slow down.
If you kept criticality to a stable level and let energy of fuel release over e.g. 20 years, it's called a nuclear power plant. If you let it run away and let the material melt itself, it's called a meltdown situation. If you instead take highly purified fissile material and compressed it instantly into size of a peanut or however small you could, the material compressed experience nuclear chain reaction everywhere inside that peanut, and spontaneous release of that insane amount of energy resemble behaviors observed with conventional chemical explosive material exploding, and such a contraption that do this is somewhat metaphorically called an atomic "bomb".
A nuclear chain reaction occurs where more neutrons enter into a fissible mass than leave it, where those neutrons trigger additional fission events.
"Criticality" is the point at which that neutron emission is just balanced: the same number are added as are consumed. This is often fairly stable, and can be further controlled with moderating systems (e.g., control rods, circulating water, or neutron reflectors which increase neutron flow). There's also the matter of "prompt" vs. "delayed" neutrons. The first, prompt neutrons, are emitted immediately following a fission event, the latter occur after some delay, from milliseconds to minutes or longer. The ratio of prompt to delayed neutrons also matters in controlling a nuclear reaction.
A nuclear reaction at criticality is not a bomb, at least not necessarily. What it is however is sustained, which is to say that the nuclear reaction will continue unless circumstances change.
A nuclear bomb, and specifically a fission bomb, requires not only a critical mass but a supercritical one, with a large amount of the material going critical at once. The challenge for the engineer is that nuclear reactions release so much energy that the explosive material itself can be blown apart before enough of it has time to react. So the trick is to transition between subcritical and supercritical masses quickly.
For Uranium-235, the reaction is slow enough that a "bullet-style" design is sufficient. A supercritical mass is arranged in two pieces, which are separated until detonation is desired, at which point one (usually smaller) mass is shot into the other, like a bullet down a gun-barrel. Plutonium-239 is so fissile that this would result in premature criticality and only a small fraction of the material would fission before being blown apart. Instead, an implosion design is used, in which a subcritical mass of plutonium is surrounded by explosive charges which, when detonated, compress the core sufficiently that it does achieve criticality, and the much larger nuclear explosion follows.
The Uranium bullet-style device was considered sufficiently reliable that it was not tested. The Hiroshima bombing was the first detonation of this style of weapon. The Trinity test was to confirm the theory of a plutonium implosion-style design, and Nagasaki saw the second explosion of such a weapon.
In the case of the Hiroshima (uranium) bomb, about 1 g of matter was converted to energy, and about 660 g of a total fissile mass of ~51 kg actually reacted, or about 1.3% of the total mass. Essentially the bomb was already coming apart before any more material could engage in fission. See: <https://old.reddit.com/r/askscience/comments/1546rcv/why_did...>
I believe values are about the same for the Nagasaki weapon.
More on fission weapon designs: <https://nuclearweaponarchive.org/Nwfaq/Nfaq4-2.html>