Everything has a tiny nuclear reactor in it. How much of a concern are illegal nuclear bombs?

It is a huge step to go from nuclear powered electrical generation to nuclear bombs. Uranium has two forms, one fairly inert (half-life of 4.5 billion years) and one that is radioactive. The radioactive form is less than 1% of the ore.

It is possible to have power plants that use natural uranium without any concentration.

To build a bomb with uranium, you have to concentrate the U235 to 90%. Iran had to acquire a vast number of centrifuges in order to do the concentrating. In WWII, the Manhattan Project used "electromagnetic separation, gaseous diffusion, and thermal diffusion technologies were all successful and contributed to the project." Centrifuge technology was improved after the war. https://en.wikipedia.org/wiki/Manhattan_Project

Note that of the high cost of the Manhattan Project, most of that was spent in getting the concentrated fissionable material. They needed to build multiple large plants to get the job done.

Look at how it has been possible to identify and disrupt Iran's attempts to get concentrated material. Police in a more open society will have an easier time.

Leaving aside the question of how to actually acquire weapon-grade uranium, which David R elaborated on, there's also the difficulty of actually constructing a functional device.

The most common variant used are implosion weapons, which are extremely difficult to engineer. You would need to first calculate a suitable explosive lens to effectively trigger fission, before actually building a device with these extremely exact tolerances, all while ensuring micro/nanosecond synchronization with the actual explosives.

However, there's another type of nuclear device, which is the gun-type. This is what was used to build Little Boy. Here a piece of uranium is fired through a barrel at a second piece, using the collision force to trigger the fission reaction. The downside here is that you'll end up with a far less efficient and bulkier device, but, well, the USA did manage to get something with the force to destroy a city compact enough to load under a heavy bomber, so it's still feasible.

That said, the question is also to which extent a proper nuclear explosion is necessary. Sure, a failed implosion device will have only a fraction of the normal power, but in return you will be spreading a fair bit of radioactive material through the area, basically creating a low-grade dirty bomb. It's not great for military purposes, and I doubt the actual damage, whether through the explosion or radioactive spread will amount to much in the larger scope of things, but for things like terror attacks it would likely be sufficient.

NASA is working on small nuclear reactors for use in human rated spacecraft and for habitats on Mars. This project is called KRUSTY or Kilopower depending on the specific application, with the "S" in "KRUSTY" standing for "Stirling" than "steam" so it's not likely using water vapor as a working fluid. If you want steam power in your world then I see no problem with that, so long as it's not going into space.

The Kilopower reactors produce about 40 kW of thermal power or about 10 kW of electrical power. A bit of searching the web for how much power a typical house in the USA uses and I see it's about 1 kW averaged through the year. A typical household oven is rated for 10 kW, but those are used at that kind of power for no more than a few hours per year so a bit of planning out the Thanksgiving feast and/or a battery pack could avoid any issues of needing a larger reactor. If heat can be drawn more directly from the reactor, like there's a constantly hot oven available on the side of this reactor structure, then that lowers household electrical needs considerably. That goes double for other heating like hot water, clothes drying, and HVAC.

The size of a Kilopower reactor was described as "about 6 feet tall", which is pretty vague. If we assume a that's a cube, and we'd need a couple feet of concrete shielding all around then this could be something the size of a one car garage. Just kind of have the wall of this structure meet the wall of the kitchen and you can have all kinds of heat for baking food in easy reach. If this is a warm climate then the kitchen might be separated somehow from the rest of the building to keep people comfortable and cooling demands reasonable. While reasonable in size for a house, or a large vehicle like a ship or mining truck, it's not exactly practical for a car. There's going to be diminishing returns on power for getting smaller since there's going to be heavy shielding to keep people safe.

What makes Kilopower so small is use of what might be considered weapon grade material as fuel. If the fuel isn't as enriched then the size of the reactor grows for the same power output. To prevent the use of the core to make weapons the uranium could be mixed with something that is a neutron emitter and difficult to separate. The neutron emissions will cause premature fission in a weapon and so it will tear itself apart before it can reach the density required for full yield, that way it can't produce an explosion bigger than a similar size of conventional explosives. To make it difficult to separate out would be to choose a material with highly similar properties so chemical or mechanical separation would be expensive, more expensive than just digging up raw uranium ore and using that to make a weapon. Uranium-232 is such a material. U-232 undergoes random spontaneous fission which produces a small amount of neutrons that will cause a nuclear bomb to "fizzle out" and therefore be worthless. In a power plant the U-232 has little detrimental effects, and may even be helpful.

Heavy water reactors like CANDU can use natural (unenriched) uranium fuel but they'd be quite large, far too big for a single family home. I don't know how small they can be practically made but the smallest that's been designed is 600 MW electric. Natural uranium is obviously no more dangerous than the uranium people can dig out of the ground because it is, by definition, the kind of uranium people can dig out of the ground. Between the two extremes of weapon grade uranium (for Kilopower) and natural uranium (for CANDU) are many levels of enrichment, and with that many practical sizes of reactors.

For an extra measure of deterring diverting uranium meant for fuel as weapons any new fuel can be mixed with recycled old fuel. The old fuel will have some U-232, Pu-240, and other difficult to separate out neutron emitters. The old fuel never has all the useful uranium burned up and so it would be quite valuable to recycle old cores into making new cores. In a short amount of time it would be difficult to find uranium that's not tainted with these isotopes.

Of course if someone is truly determined to make a nuclear bomb then they'd find a way. With tainted uranium fuel in every household reactor it would be easier to mine, refine, and enrich uranium from the ground than bother cracking open a reactor for its core. People mining and refining uranium in any meaningful quantity would be quite obvious and so not terribly difficult to regulate.

Oh, then there's the issue that making a nuclear bomb takes very precise construction to make it work. The Little Boy bomb may have been a simple design but it took highly refined "virgin" uranium, and precision machined pieces. It wasn't exactly "little" as it weighed over 4 tons. There were "suitcase" nuclear weapons made but that's again getting to requiring even greater precision and highly refined material for the core.

Use Thorium instead of Uranium.

The uranium-based reactor power program grew out of the nuclear weapons research. There is an alternative process that does not seem to produce fuel for weapons, or carry the same risks of meltdown. There are not many Thorium reactors, so there may be some other downside we haven't discovered yet, but it seems hopeful.

DT Fusion, if we could get it to work, produces a highly penetrating neutron and gamma ray. Even if the result of the reaction (Helium) is inert, but the radiation will in time make the whole reactor plant radioactive. Or you could use a thin layer of depleted uranium to stop the radiation and also generate more energy in the process. However, we can make a fast breeder reactor without the fancy fusion bit.

If you stick with Uranium, there is a safer option: the Travelling Wave Reactor. The idea is to have a conventional reactor, or a combination of conventional and Fast Breeder reactor in the same box, with a power-generating wave that travels through the fuel. The reactor does not need to be opened to take out fuel for reprocessing, and it can be disposed of as a unit while still being sealed.

The effect you describe could be a small reactor, or an implausibly efficient radioisotope battery. The difference is that the former uses heat from fission through an artificially induced chain reaction, while the latter uses heat from fission without a chain reaction -- safer and much less efficient.

If it is a small reactor, it may need enriched uranium. The smaller the reactor, the more enrichment is required, until you come close to weapons grade. Depending on the reactor design, you might also get a breeder reactor, which produces plutonium. So there is lots and lots of fissile materials going around.

That leaves the problem of the design of the weapon and the manufacture of the pit and the non-nuclear parts.

• The design requires some understanding of nuclear physics, but without it, how would the reactor industry function?
• Shaping the uranium or plutonium parts with acceptable precision and purity, without poisoning oneself, is a challenge. But the reactor industry must have resolved that, too.
• If you are in a steampunkish setting, you may decide that the electronics for an implosion-type weapon are simply not available. Pneumatics, clockwork, and babbage engines are just not good enough.
• That leaves a gun-type weapon, which is easier to manufacture.

So if you are prepared to accept Jules-Verne-like levels of scientific accuracy, go with radioisotope batteries. Do not specify which isotopes are used.

I already provided an answer but given the comments I thought I'd add another that answer some concerns raised of a world that runs on steam from nuclear fission. Or...

What new vectors of attack would terrorists have in a world with tiny nuclear reactors?

What is a "tiny" nuclear reactor in the first place? I'll put a number out of my ear and call it 10 kW. To put that in perspective my kitchen oven is rated for 10 kW. The typical electrical service to a home (at least around here) is 240 volts at either 150 or 200 amps, approximate that as 40 kW. EV chargers are grouped roughly as level 1, 2, or 3, with level 1 being 1 to 3 kW, level 2 being 5 to 15 kw, level 3 being up to 400 kW.

How big would this be? Looking at a prototype 10 kW nuclear reactor from NASA It looks to be no more than 3 feet by 3 feet with the height difficult to judge but I'm guessing about 6 feet. What would it weigh? If we assume a density on par with a block of concrete then about 10 tons.

A standard 20 foot shipping container is about 8 feet by 8 feet by (you guessed it) 20 feet. The maximum allowed weight is 24 tons. We could likely fit a 10 kW nuclear reactor into one of these containers, and still have enough margin on size and mass for all kinds of safety measures and radiation shielding. A bog standard Kenworth W900 semi moves things like these all day. That W900 semi tractor weighs about 10 tons and produces 400 kW of power.

A 10 kW nuclear reactor isn't going to be some meltdown hazard, my kitchen oven produces that kind of heat. If we assume more like 40 kW of heat, or 400 kW of heat to account for conversion losses, a loss of coolant event, or something then consider that a Kenworth truck doesn't turn to lava and burn through the concrete if it's radiator runs dry. Put in some thermal fuses that will drop in control rods and open up some air vents to bring the power under control and vent the heat until someone can pump it full of borated water (for more cooling, radiation control, and neutron absorption) and haul it away. Full of water the weight would go up a few more tons, so just get a slightly bigger crane and truck.

Could someone blow one of these things up to make a dirty bomb? I guess but there's not a lot of radioactive material in these things to cause much of a hazard. Dirty bombs are overrated. The reactor would have a pretty thick skin, or should if we assume people in this steampunk world understand what they are dealing with.

Could people crack a tiny nuclear reactor open for material to make a nuclear bomb? Unlikely if the people are wise enough to mix in materials that would "poison" the fuel for such use.

If this is a world with a nuclear steam engine in every home then I expect there would not be a lack of water to where people need to worry about heat, fires, radiation shielding, or anything else that water would be useful to mitigate. Last I checked water is so prevalent on Earth that in most places it falls from the sky. People using steam power would likely collect as much of this water as they can than allow it all to run into the ocean. Once boiled off for a steam engine the water is back in the air for it to fall out of the sky again. Rainwater that's collected in open tanks, or even ground water if people dig wells, might not be fit to drink but the steam engines aren't likely to mind. Perhaps terrorists try to contaminate the water supply if they can't attack the electric supply. If people need drinking water then condensers that use food grade material and are periodically cleaned would produce water fit to drink. This removes much of the potential for a terror attack on the water supply.

The original question made a comparison to a nuclear submarine. In a nuclear submarine they can produce their own energy, water, and air. We know they pack enough food to not have to see daylight for months so if people live in a world where terrorists are driving people to live in what are effectively beached submarines then that's a rather crapsack world, but once they got to having these tiny nuclear reactors the terrorists would have to come right up to each reactor to deny that household (or whatever) of their means to live, and at that point the concern isn't about radiation or lack of water, it's who is the better shot with a rifle.

In a densely packed city a 10 kW reactor would likely be too small to bother with. Something more like 10 MW reactors might be more appropriate to have scattered about in easily defended locations in the city. Because the power of a nuclear reactor isn't exactly linear with weight and volume such a reactor could possibly still be moved by trucks, though perhaps not as a single unit but as pieces to be welded together in place. That size of reactor might still be able to be air cooled to prevent a meltdown if somehow cooling water was lost suddenly. There's certainly bigger reactors than that designed to avoid a meltdown if cooling water is lost but those aren't likely driving steam engines but rather CO2 turbines or something.

This could still leave people open to an attack by chemicals, biological weapons, an attack on food being shipped in, or maybe something else I'm missing as a vital commodity or infrastructure. None of that would be new because of using tiny nuclear reactors. Once at the point of having steam engines from nuclear fission scattered through your cities then you can produce clean air, water, and perhaps even enough light, for greenhouses to grow stuff. This is beyond a submarine now, it's more like a generation ship. Presumably these terrorists lack the resources for weapons like field artillery, bomber aircraft, or other equipment we equate with a conventional modern military. That's why they resort to attacking infrastructure, dirty bombs, trying to steal (as opposed to mine) uranium, than go face to face with whatever militia this city has for defense.

There is no way to do that. We can extract nuclear energy only as heat, and then we convert this heat to energy. There is no known way to change this ever, although it is theoretically not impossible.

If we have a heat-power machine, that will make everything large. You can not have a mobil phone driven with such a machine, it will be at least kilos or more. That is because as you decrease the heat-power converter, so will it be lesser effective, due to the heat conduction loss.

Thus, either we have everything embedded with a turbine generator, or we have some wizardry which can generate directly electric current from decaying uranium.

Now case is that there is no way to create a nuclear bomb from nuclear fuel. Either you need fuel refined, reprocessed exactly for that, or you need to essentially mis-use power producing nuclear reactor. Some facts:

• Ordinary uranium has 0.7% fissile isotope, for bomb-grade Uranium it must be enriched above 90%, but for reactors only 3% is enough.
• Plutonium bomb needs Pu-239 isotope. That is not available in the nature, but is produced in nuclear reactors. However, in nuclear reactors, also Pu-240 and Pu-241 is being produced, which poisons the bomb. There is no economical way to separate Pu isotopes. Thus, the only way to create Pu-239 if you turn off the power producing reactor before too much higher Pu isotope would be created. That needs a power producing nuclear reactor where the fuel can be replaced while work, most of them are not. It also needs a nuclear fuel reprocessing plant which is more costly as the reactor itself.

Thus, I believe, proliferation would not be threatened.

Dirty bomb could be easy to create. And probably not what you want to have, if your car leaks and the molten fuel pours to the asphalt. There are many ways to prevent also that, though.

This is a Frame Challenge

The answer is "it would be very unlikely that someone could create a nuclear bomb" because:

• Nuclear reactors don't use the kind of radioactive material nuclear weapons do. Nuclear reactors don't like operating on weapon-grade uranium or plutonium.

• The government would very likely prohibit access to weapon-grade radioactives, meaning that despite the ubiquity of reactors, there isn't a ubiquity of weapon-grade radioactives.

• The average person wouldn't know how to do it.

• The average person who did know how to do it wouldn't have causual access to the equipment needed to purify the radioactives.

• The average person who both knew how to do it and had access to the equipment would, I expect, be very well known (even registered) in a society that permitted ubuiquitous reactors.

In other words, it would be (in my opinion) harder to make an illegal nuclear bomb in your society than it is an illegal truck-bomb from fertilizer in today's societies.

On the other hand...

Maybe what you could do is change the nature of your crisis. Rather than a bunch of mushroom clouds, let's hack the software operating all those nuclear reactors and cause thousands, even millions of them to melt down. That would be an instant nuclear catastrophe that would be more damaging than bombs since one would need to harvest a large number of household nuclear reactors (assuming a linear scale, which wouldn't be true, but roll with it please) to get enough radioactive material to purify to weapon-grade stuff. That would be noticed.

A software hack, on the other hand...

Not a problem with fission bombs, BUT

To make a fission bomb you need bomb-grade Uranium, or Plutonium plus the knowledge to make an implosion-type Plutonium bomb.

The technology for enriching Uranium (gas centrifuge cascades) is out of reach of all but the very largest organisations and could easily be regulated by the state. It's simply not something someone can do in a garage, even given unlimited access to clean unused reactor-grade Uranium.

Plutonium might be separated chemically from used reactor fuel on a small scale, but the amount of radioactive contamination would be huge and would probably kill the person attempting it. There's also the possibility (likelyhood) of an accidental criticality event, or nuclear fizzle. This would kill anybody in the immediate vicinity through irradiation, and spread radioactive contamination more widely.

Separating pure Plutonium is only the start of the problems involved in making a Plutonium fission bomb which actually works.

The real problem is that in this world any wannabe-terrorist could easily get hold of highly radioactive used reactor fuel, add conventional explosives, and make a radiological bomb. Basically, make a mini-Chernobyl that would render the area contaminated unusable for tens to hundreds of years. Or just blow up the operating mini nuclear power plant in, say, a car, with the same outcome.

There should be a LOT of nuclear accidents

In fact, the thing behind all that weapon regulation is the desire to limit high energy production equipment in hands of, umm, civilians, because it's energy influx that kills, as a principle, also such energy producing things could be employed to do various criminal actions, like breaking into or out of somewhere, like a bank for example. So, with average user being able to land their hands on a nuclear reactor, or at least a set of fuel replacement, there will certainly be groups that would either threaten or employ nukes as a means of doing their own business, starting from assassinations and ending with revolutions.

So, you might compare wielding a bit of uranium to wielding a weapon, but a really unreliable weapon that can not just shoot down a certain target, but also eliminate its vicinity together with the wielder (at times). That said, assembling a nuke in one's garage is not an easy task, you need quite a lot of ordinary explosive to even have a chance to not get a "nuclear fizzle" or a meltdown of your valuable uranium storage into a pool of radioactive magma, and you need to actually align that explosive so that the uranium gets correctly imploded to shift phase (assuming they know what is a phase of uranium) and go supercritical. But with the abundance of uranium across the society its accessibility will be high enough for some people to try and get obliterated in the process, resulting in a nuclear accident.

The reactors are also not completely accident-proof

Let's say your house reactors are controlled by a PIC of sorts that's powerful enough and programmed so that it can shut the reactor down in case of something really weird happening in the active zone. It's been tested for safety and has a secondary or tertiary system to prevent the meltdown. It does NOT accept external interference, and might only have some maintenance access for whoever changes its fuel, which should happen pretty often (and I really wonder what do they do with the nuclear waste - it'll grow to extreme amounts over that many reactors!). But now let's assume that some ISIS-like organization has learned about a weakness in its algorithms or some human-originated weakness in maintenance of a certain one, and was able to reach it and initiate the meltdown. With our current stance, reactors are protected by military, but in your world there will never be enough military to protect the entire set of reactors, so there will be some vulnerable objects that could be melted down. Aaaaand you've got a whole Chernobyl or Fukushima-level disaster in a certain house, that destroyed that one and damaged several other houses nearby - potentially initialing a meta-chain reaction in form of one or more of affected reactors to also go meltdown, which is quite likely because if a reactor would be in a center of a radioactive zone where a human can't stand without dying, it'll become out of maintenance and any single malfunction would be enough for it to go down too (at least it'll just shut down, but who knows what would happen next).

There's more - a nuclear accident is a something that regularly happens at various nuclear power plants, even while operated normally, even venting off some of the second ring steam due to a pipe/valve breach that happens over time counts as one, as that steam would be slightly radioactive due to being closer to actually radioactive media that was in contact with the active zone. You might check INES scale with examples of what can happen on a nuclear power plant that's counted as a severe accident, together with their average frequency per reactor, then multiply over your numbers that heat up literally every single building. This alone would number at least several dozen per day with expected number of reactors in your society.

Intel/cops will not be able to stop everyone

As in real life, even with some of the modern systems of crowd control (hey China!), there will always be people who are able to plot crime and succeed in its execution, no matter if they get caught afterwards, a crime related to a nuclear accident, if succeeds, leaves an accident up to actual Chernobyl, depending on what had really happened. Safety concern should quickly rise over several first accidents involving house reactors, to the point of abandoning the entire idea, after all, no one wants to go to sleep in total safety only to find out that they've got irradiated to fifth degree cancer over the night because someone did a boo boo. And the citizens won't really care that those who obliterated that neighboring building were terrorists, burglars or incompetent plumbers; the rage will eventually focus on those who planted those nukes first and foremost.

On top of that: nuclear-powered cars ended up ridiculously superfluous

A nuclear reactor of modern design is a VERY slowly alterable power generator, that is, you can't stop and start it at will, you can throttle it but it'll take hours, and while it's in your garage it still consumes fuel at about the same rate as while driving 300mph. Cars are designed to run part of the time and stand still the rest, while also having relatively low power demand (100 horsepower is just 75 kW, rarely a truck has 1000HP, let alone personal cars), and the reactors were producing about an order of magnitude more. This is actually one of the reasons (aside safety) that made reactors be viable only on large installations like icebreaker ships, military subs, airplane carriers and the like, even in military - like, no nuclear engine on tanks or airplanes. Building a reactor for a large house (say a skyscraper) looks feasible by power demand, but with it being slow to change its output it became easier to build a power grid to transfer electricity to places with high demand, reducing wear load on nuclear plants, reducing start-stop load on coal or gas plants, etc.

Nuclear waste adds to number of accidents by means of polluting environment

Even if everything went well for long enough for the govt to actually start building autonomous houses, there is a problem unsolved here, in nuclear waste disposal. The isotopes produced by uranium fission have a half-life of over 60 years (Cobalt-60, Cesium-137), are aggressive enough to damage facilities designed to separate the spent nuclear fuel, also any structures that contained the fuel (steel, zirconium, whatever else they use) become irradiated over time and infused with radioactive isotopes with highly various half-life, and all this should be somehow put away from the living, or else they would soon turn dead. With each modern water-based reactor requiring refuelling about once per 2 years, and your world's reactors being about the same internally, your society would generate so much nuclear waste that will not be able to be contained anywhere, and even recycling facilities that could retrieve leftover uranium out of spent fuel will be overloaded, as the process is literally nano-tech thus very energy consuming and very slow as well. Note that spent fuel still generates heat and radiation over years required to reduce their initial radioactivity to levels that allow its transfer, demanding special areas near each NPP to store their own spent fuel, and if something happened there, it also counts as an accident and usually requires HazMat interference to clean up.

In total, nuclear fuel in this amount is too unsafe to calculate

Even without destructive human interference, your world is about to blow up with this input data, either from the amount of "normal wear and tear" that the reactor system undergoes, or from the accumulating amount of radiation coming from spent nuclear fuel.