Could you cause a nuclear explosion by simply manually sticking two subcritical masses of radioactive material together?
Or energy exerted would quickly throw them apart without anything serious happening (apart from emission of very deadly doses of radiation for those in the closest proximity)?
No.
You would be killed by the release of radiation, but at worst you would get small “fizzle” and vaporized material.
OP, think of it this way–you cannot have an explosion without explosives.
That’s the main difference between a nuclear bomb and a nuclear power plant.
Chernobyl and Fukushima didn’t have any conventional explosives, but plenty blew up (not nuclear bomb level, but plenty). Expanding steam can do plenty of damage when you heat up water with a nuclear reaction.
Wikipedia’s article on criticality accidents gives a bunch of examples of what happens when you get enough fissile material together: Criticality accident - Wikipedia
AFAIK, both were due to hydrogen gas.
Chernobyl was a steam explosion. Fukushima was an explosion of hydrogen gas that accumulated in the secondary structure surrounding the main reactor vessel. Neither was comparable to what happens in an actual nuclear bomb.
To quote from the article: “Though dangerous and frequently lethal to humans within the immediate area, the critical mass formed is still incapable of producing a nuclear detonation of the type seen in fission bombs, as the reaction lacks the many engineering elements that are necessary to induce explosive supercriticality.”
In other words, the results would be ugly, and probably lethal to anyone in the vicinity, but you wouldn’t get a full blown nuclear explosion.
I recall seeing (long ago) a movie where a critical element of the plot was the amateur construction of a nuclear bomb. The bomb was a sphere of fissile material with a cylindrical hole. (It was Pu IIRC) A second piece was a cylinder of the same material that fit snugly inside the hole to complete the sphere. The bomb was supposed to work by inserting the cylinder into the sphere to achieve critical mass.
It was good for illustrating to the uninitiated the principle of critical mass but is I believe fraught with problems for the commencement of a chain reaction and nuclear explosion.
That bomb design would, and has, worked just fine.
ASSUMING they’ve designed a way to shove the cylinder into the sphere’s cavity fast enough. Where “fast enough” is on the order of handfuls of milliseconds at most, and more probably handfuls of microseconds for a good conversion fraction.
Actually, That design would only work for U-235.
PU-239 has a high enough spontaneous fission rate that the only workable design is an implosion device.
That movie was The Fourth Protocol. It was a “gun” type bomb and not all that amateur of a construction. I suppose you could use the word “inserting” the slug but I’d use “shooting” because it was propelled by an explosive charge. And there were 2 discs involved also, one was polonium, I think, and I don’t recall what the second one was. They were there as a neutron source to speed along the fission. And it was uranium, not plutonium. It was a smaller version of the same device used over Hiroshima.
TV drama never was bettered. - YouTube
Accurate too.
Cool. Thanks.
So, how many here could sketch out a crude, but effective fusion bomb? Fission?
What would you need that can’t be readily bought online - let’s not be cynical. few of us can get Pu or U238 over the web.
Back in the early 80’s a high school kid in what became Silicone Valley submitted a design as a Science Fair or some such project. One of the teachers knew a fellow at Lawrence-Livermore Lab.
Crude, but it would have worked.
How widespread is the “crude, but effective” knowledge at this point.
Lawrence (his widow spent her life trying to get his name removed) Livermore (location - a used-to-be way-out-of-the-way town in CA) Laboratory designs nukes and builds the detonators (Fusion, aka “Atomic”) bombs…
Ah, no it isn’t. A nuclear power plant and a nuclear bomb work in completely different ways. There is absolutely, positively no possible way a nuclear power plant could ever explode as a nuclear explosion. Actually, there is one way: Bring a nuclear bomb inside the plant and set it off! 
A nuclear power plant simply does not have the pure, weapons-grade, fissionable material concentrated into anything nearly like a critical mass anywhere in the facility to cause a nuclear explosion.
A BLEVE (Boiling Liquid Expanding Vapor Explosion) requires no explosives - and indeed in the past the most common was a water boiling explosion. Most modern bleves are tankers, usually carrying petroleum produces (LPG being common.) However, although the fireball after the explosion is both dramatic and causes damage, the explosion is not powered by combustion of the released liquid. It is simply the stored energy in the high pressure boiling liquid being released. Steam locomotive explosions could be devastating for just this reason - with some locos running up to 1500psi under normal conditions there is a lot of energy - especially when conditions are not normal. A reactor vessel failure from internal boiling water would probably level a suburb.
None of us.* I can quickly sketch the outline and basic principles of a fission-fusion-fission weapon (as could anybody who has read the Wiki article), but there are key technical designs and issues that have not, to my knowledge, ever been made public (and some indications that stuff that has been made public has been false-flag). A multi-stage device is an incredibly complex problem in energy management.
How sophisticated are your machining skills? You can get raw materials (minus the fuel), but you’ll have to make most of the device components.
I’d like to see a cite for the “would have worked”. Unless it was an gun type fission device in which case sure. Those are relatively easy to design at very low expected yields (for higher yields you need an implosion sphere with a hollow core and initiator).
No. Fusion (aka “Nuclear”) weapons and “atomic” weapons are two different beasts although the standard fission-fusion-fission device does use an atomic bomb to start the reaction.
So, how was the information in the Progressive Magazine article in 1979 so useful or threatening that the Department of Energy sought an injunction to block its publication?
Reminds me of a bit from the classic Billie Bob Thornton movie “The Astronaut Farmer”, where the main character observes that nobody in the government cared that he was building a rocket capable of putting a person in orbit until he bought 10,000 pounds of rocket fuel (IIRC, it raised a red flag because you can use various types of liquid fuels as components in high explosives)