The basic idea is that these sorts of objects are routinely seeing spontaneous nuclear decays -- there might be billions per millisecond of these. What's important is that each nuclear decay is an explosion which releases debris that can cause other nearby nuclei to decay as a result. So it becomes important to know: what is the average number N of nuclei which fall apart as a direct result of getting hit by the shrapnel of one decaying nucleus?
Since nothing is terribly exact in physics there are two regimes to consider, N < 1 and N > 1. In that first regime we can roughly calculate that we need to multiply this baseline billions-per-millisecond rate of spontaneous decays by the number
1 + N + N² + N³ + ... = 1/(1 - N)
For N > 1 the same multiplier holds but it cannot be summed infinitely: instead we realize that each term takes a slightly longer time period and thus the growth goes something like e^(k t) for some k, it's an exponential growth towards a majority of the sample reacting.
For fissile materials like plutonium, an easy way to increase N is to just bring two plutonium rods closer together: free debris from explosions in the one now cause new explosions in the other. This is called forming a "critical mass" hence the language about "criticality". Another way is to bring in these "neutron reflectors" that reflect the debris back into the same sample, it's basically the same principle.
Plutonium, not so much.
I think it's in mentioned in Richard Feynman's account of his time in Loa Alamos in 'Surely you're joking Mr Feynman'.
> On May 21, 1946, physicist Louis Slotin and seven other Los Alamos personnel were in a Los Alamos laboratory conducting another experiment to verify the exact point at which a subcritical mass (core) of fissile material could be made critical by the positioning of neutron reflectors.
> It required the operator to place two half-spheres of beryllium (a neutron reflector) around the core to be tested and manually lower the top reflector over the core via a thumb hole on the top. As the reflectors were manually moved closer and farther away from each other, scintillation counters measured the relative activity from the core. Allowing them to close completely could result in the instantaneous formation of a critical mass and a lethal power excursion
> Under Slotin's unapproved protocol, the only thing preventing this was the blade of a standard straight screwdriver, manipulated by the scientist's other hand. Slotin, who was given to bravado, became the local expert, performing the test on almost a dozen occasions, often in his trademark blue jeans and cowboy boots, in front of a roomful of observers. Enrico Fermi reportedly told Slotin and others they would be "dead within a year" if they continued performing it. Scientists referred to this flirting with the possibility of a nuclear chain reaction as "tickling the dragon's tail", based on a remark by physicist Richard Feynman, who compared the experiments to "tickling the tail of a sleeping dragon".
An aside: It's this kind of shit that scares the crap out of me with regards to nuclear energy. Some - literal - cowboy completely disregards the rules, endangers him and his colleagues, and then someone gets injured or killed. All for the benefit of showing off.
We should do better than this, but incidents like this give me little faith.
Unsurprisingly, this experiment killed Slotin:
> On the day of the accident, Slotin's screwdriver slipped outward a fraction of an inch while he was lowering the top reflector, allowing the reflector to fall into place around the core.
> [Slotin] received a lethal dose of 1,000 rad (10 Gy) neutron and 114 rad (1.14 Gy) gamma radiation in under a second and died nine days later from acute radiation poisoning.
When I look at the steps I used to go through multiple times a day when working in Cat 2 and Cat 3 biological containment facilities to work with cells and pathogens, including double door airlocks under negative pressure, safety hoods, protective gear etc., stringent aseptic practice LANL seems quite lax in their practices. We all watched ourselves and each other for bad technique and careless infractions to maintain that discipline without the need for dedicated separate safety inspectors (though periodic inspections did occur). That good practice was also tied into self-preservation of self and others when working with dangerous stuff; no one wants infection by some horrible pathogen. It seems quite bad to be working with even more lethally hazardous materials with basically zero protection, and the description of the attitude of the management 2011 and the present day towards safety seems to be equally cavalier.
In all the academic and industrial environments I've worked in, we had rigorous inventory and tracking of all dangerous materials (biological and radioactive), so it seems odd that LANL fails so badly here. This was the first casting in four years, and they immediately failed: why wasn't there preparation and planning for moving the material before the casting even started? Is Pu randomly stored around with place? Is there no oversight at all? In the lab I currently work in, we have to track every last trace of radioactivity (mainly P, N for biological labelling I think; I'm not involved directly) and account for it for statutory reporting every quarter, and if you fail to do it properly there would be a massive investigation and you would be banned from working with it; the lab managers make a bit deal of it, and rightly so.
It's a little ironic that safety has been compromised in order to meet production targets, but this resulted in a complete shutdown. Had they worked safely and sensibly and avoided the shutdowns, they would have overall been vastly more productive even if this was slower than the management would have liked. I've seen this pattern several times now in multiple places, from factories, to research laboratories to software development. It all comes down to unrealistic management goals from the top which dictate working at a fast place with attendant quality and safety problems no matter that a better end goal could be realised by working at a slower place with a little more care and thought. We see the same problem every time software design or implementation is compromised by a tight deadline with no scope for doing it the right way for the longer term, purely to meet some unimportant (in the greater scheme) short term deliverable.
Slotin got himself killed after the war was over, but it was less than a year after, and I imagine that sort of "get it done at any cost" culture does not change overnight.
I wonder if that attitude is in fact the root of the trouble today. Especially since I bet that the "save the nation and damn the risks" attitude came back for at least a decade or two once the Cold War ramped up.
I've seen different cultures in various labs I've worked in or had contact with, and it can vary wildly from being extremely disciplined to extremely sloppy and both practices can be picked up by new people from the individuals concerned.
http://www.sciencemag.org/news/2017/06/near-disaster-federal...
Edit: Answered my own question:
> keeping bits of plutonium far apart is one of the bedrock rules that those working on the nuclear arsenal are supposed to follow to prevent workplace accidents. It’s Physics 101 for nuclear scientists, but has sometimes been ignored at Los Alamos