You don't

Not without handwaving.

Teenage and 8 kW

This is a first issue. I don't know any country that would allow teenagers to operate power plants on their own. High school teenagers usually can't even become licensed electricians. There was a time when you bought electrical appliances without the plug, and installed plug on your own, at home. But these times are gone now, because this was just a bit too difficult for general public. And we are talking about really, really smaller power and much simpler operation.

Nuclear reactor size

Smallest presumably safe I've heard about is Chinese cargo container reactor.

The tiny power plant would fit inside a shipping container and could generate 10 megawatts of heat - enough to power 50,000 households.

Given that you can't get any cheaper or smaller and still have good security against leakage etc. This means it won't be cheaper. If single unit won't be cheaper, then your idea is 50,000 times more expensive. No government will ever fund it, when they could fund something so much cheaper with similar effect.

There are other designs but the problem is the same - with a single unit, you will be able to power up a whole town, and going smaller doesn't make it any cheaper, and not much safer.

Obtaining materials

You need to handwave weapons of mass destruction and dirty bomb terrorism risks from your world. This is a really, really big handwave. Currently, any fission materials are (supposed to be) tracked as national security issues.

Waste disposal

Surprisingly, this one is only a small issue. If you can have a safe cargo container reactor, you can just send it for refueling, and have waste processed the way it is now.

For many technical reasons using nuclear power for individual houses is not a great idea. With nuclear power you either get too few energy to power a house (RTG's), or way too many and it's incredibly wasteful (fission, fusion). And while operating an already built nuclear reactor is not that hard - sailors do in nuclear ships and submarines, and they don't demand a physics grade to work in the navy - building it DIY-style it's not going to end well.

To start with, mining the fissile material is a pain in the ass. Several tonnes of rock are needed for every kilo of uranium, and most of it it's U-238. You'll need to refine it to augment the quantity of U-235 in the mix, or the chain reaction won't be sustainable (how high the percentage of U-235 depends on the type of reactor; it's higher for BWR than PWR, for example). And centrifuging uranium it's not something you can do in your washing-machine.

Building the uranium rods that you need in order to run your reactor is a very long and complex process, and then you have to put them in a reactor carefully designed to fit them at precise positions and geometry. In short, you could buy the reactor and the fuel and run your own nuclear plant with some handwaving here and there - after all, it's all run by computers, nowadays - but for building one with spare parts, I'd say "No".

You can draw inspiration from what Enrico Fermi's team did in the lab of via Panisperna. Assuming you have some fixile material, you would also need:

• a neutron generator
• a neutron moderator (Fermi used paraffine, but also water could do)

if you put the fixile material in water and irradiate it wit a flux of neutrons, you will end up breaking some atomic nucleus and generate energy. That energy will warm up the water.

If you want to scale up and build an atomic pile, like Fermi did in the US with CP-1, the size will grow up and you won't be able to host it in your backyard.

It contained 45,000 graphite blocks weighing 400 short tons (360 t) used as neutron moderators, and was fueled by 6 short tons (5.4 t) of uranium metal and 50 short tons (45 t) of uranium oxide.

and

The pile had run for about 4.5 minutes at about 0.5 watts. On 12 December 1942 CP-1's power output was increased to 200 W, enough to power a light bulb. Lacking shielding of any kind, it was a radiation hazard for everyone in the vicinity, and further testing was continued at 0.5 W.

They could, but they will not be allowed to

Physically, in your world, it would be possible for your high-school to build it. As long as they get access to the material they will be able to pile it together — literally so; the first reactor ever was in fact called Chicago Pile-1 — and get a chain reaction going.

And even today, high-schoolers are doing nuclear reactor experiments, constructing so called fusors.

This is a fusion reactor made by a high-school student

The main problem is that these fusors to not have a $Q > 1$, which is to say they use more energy than they produce. Never the less: high school students are creating nuclear fusion.

The thing that will trip up your intrepid high-school student is not that they will not physically be able to, but that they will not be allowed to.

As hinted in Fight Club, you can make quite destructive things with household items. Sweden's own version of the Radioactive Boy Scout not only managed to call the attention to the Swedish Radiation Safety Authority for trying to make a reactor out of discarded smoke detectors, he also did other things, such as make ricin.

This is — of course — not permitted. When it comes to handling substances that can be dangerous to life and the environment, this is usually regulated. You will need to seek a permit in order to engage in any such enterprise. This applies especially if your enterprise will leave any kind of hazardous waste.

You say "but I will just have him deal with the waste". Well no, this is not acceptable. He could do it, simply by just depositing it 10 meters down in the ground. From a physical point of view this would perfectly safe. But the regulatory authorities would throw a fit about it because this is not allowed. When it comes to waste of this sort, it needs to be dealt with in a professional, monitored and approved manner.

Also fissionable materials — such as uranium — are very highly regulated and cannot be obtained willy nilly at the nearest Nukes'R'Us. Even if you never intend to put the Uranium in a reactor, the it is a toxic heavy metal, and you may not play around with that, at least not legally.

Ken Silverstein: The Radioactive Boy Scout: The Frightening True Story of a Whiz Kid and His Homemade Nuclear Reactor.

This book is the answer in depth to your question. In 1993 David Hahn did just that. The book is his story.

Book was published for the first time in 2004 (and later on the 11th January of 2005 as publisher's 33673rd edition) by Villard with ISBN-10: 0812966600.

1.7 billion years ago, nature assembled a natural fission reactor at a location now called Oklo. Back then, there was more U235 in natural Uranium than there is today, and so creating a high enough concentration of natural Uranium is all that was needed. https://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor

This is Worldbuilding, so you might be an intelligent humanoid alien living on a planet where progress from supernova-dust to solar system to life to people moved faster than here on Earth. In which case, your society is going to have some interesting possibilities and problems. It's also possible that evolution has made you somewhat more radiation-tolerant than us Earthlings, if there are natural nuclear-geothermal heat sources dotted around all over the place, along with shorter-lived fission fragments in your groundwater. (Note: little of Earth's crust today is 1.7 billion years or older, so the Oklo event was probably not the only such instance, just the only one that we have evidence for).

Your biggest issue with building a reactor would be that they've got a minimum output, well in excess of what you could use.

You could build an RTG (https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_generator) instead, though it'd probably be well below what you could use.

You'd just need:

• something to convert heat to electricity, e.g.
  • peliter heat pump
  • turbines, which could be bought pre-assembled
  • a steam engine linked up to drive a generator
• a large lump of radioactive stuff; I'm not sure how critical it'd be what you picked, as long as it got warm, and didn't go critical. A large pile of smoke detector samples might work. Assuming your world where this was legal, you could presumably buy a suitable source.

And then you'd probably need chemo, unless you'd been extremely careful...

The problem with your basic premis: promoting household reactors are two fold.

1. Reactors benefit from economies of scale. It costs almost as much to make a reactor for one house as it does to make one for ten houses. This would be a very inefficient policy.
2. There isn't enough uranium in the world to supply widespread use for any reasonable length of time. You could use thorium which is much more common but it has other issues (that you may be able to hand wave).

That being said, thorium is very easy to get. The US and China have piles of it sitting around as the leftovers from mining rare earth elements (they tend to be found together).

Home made reactors are likely to be "low output" reactors. The more you concentrate the neutrons, the faster the reaction. By having the radioactive sources more spread out, they will decay at a slower rate. They would be bigger for any given output but wouldn't need to be as complex. Current reactors run on a needle point balance. Since the low efficiency reactors wouldn't burn through their fuel source as fast, there would be less radioactive waste and the waste would be easier to handle. Current "spent" rods are still quite hot. They often need to be kept in a water bath of flowing water to keep the water from boiling off (why they don't make a steam generator from that, I've wondered about since I was 10).

If home made reactors are legal there is likely some sort of radioactive waste disposal infrastructure. You would only need a pick up every 10 or so years. Just call 1-800-GLOW-GON.

Starting up a nuclear reactor requires that you have enough fissile material for a critical reaction. This amount is know as the Critical Mass.

Many people are suggesting using the normal Uranium 235 fuel cycle, but the critical mass for low grade uranium ore (i.e. the percentage of the Uranium that is 235 vs 238 or other isotopes) is very high, at 15% it is over 600lbs, and that requires a lot of enrichment, natural 235 is only around 0.75%. This is why nuclear reactors are not usually built in small power outputs, there are fundamental limits on how small you can make them.

As far as the waste disposal portion of the question, the standard method of nuclear waste disposal is essentially to contain the material and put it somewhere isolated until it isn't radioactive anymore, for longer lived wastes this is still an unsolved problem requiring tens of thousands of years of isolation, this isn't likely to work well in your backyard either.

There are several simple (loosely defined) ways to accomplish this without a bulky reactor plant. Use the heat from radioactive decay to create power. It eliminates the need for the reactor vessel and a cooling structure. I understand this is not a nuclear reactor, but it is a way a home consumer could access nuclear power.

Advanced Stirling Radioisotope Generator

An Advanced Stirling Radioisotope Generator (ASRG) is a radioisotope power system developed at NASA's Glenn Research Center. It's based on an idea of creating power from the heat of radioactive decay from plutonium.

It uses a Stirling power conversion technology to convert the radioactive-decay heat into electricity for use on spacecraft.

A Stirling engine is a closed-cycle regenerative heat engine with a permanently gaseous working fluid. Closed-cycle, in this context, means a thermodynamic system in which the working fluid is permanently contained within the system, and regenerative describes the use of a specific type of internal heat exchanger and thermal store, known as the regenerator. The inclusion of a regenerator differentiates the Stirling engine from other closed cycle hot air engines.

The positive is this a pretty simple mechanical system. The drawback is that this unit will produce 130 watts of power from 1.2 kilos of plutonium-238-dioxide. To meet your power goals, you would need to run several in series, or perhaps in your world, the technical limitations were overcome and one unit will produce the required power.

For more information, check out: https://en.wikipedia.org/wiki/Advanced_Stirling_radioisotope_generator

Radioisotope thermoelectric generator

Another existing power source is the Radioisotope thermoelectric generator. The positives are this can be created with no moving parts. The drawback is a low power yield.

https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_generator

Thermovoltaic

A Thermovoltaic generator captures the light given off the thermal source and translates that into power. The positives are that thermovoltaics provide consistent and reliable power without large amounts of fuel. The drawback is that they are not very efficient. If your power source was in a sphere of thermal-voltaic cells, you could run them in series to produce the energy you need. Perhaps in your world, there's a more efficient source of thermovoltaic cells, which could produce the 8,000 watts of desired power.

https://en.wikipedia.org/wiki/Thermophotovoltaic

First, what do you mean by "efficient enough" ? The meaning of efficiency is getting high yield out of less amount of fuel. This will require a highly refined system, which is...unlikely for anyone below specialised company to achieve.

As for building a reactor: you need four basic components. A reactor proper - meaning container of fissile material, is the first one. Second one is cooling system, both to help carry off energy to convert into electicity, and for your reactor proper not melting down within minutes to seconds from putting together enough fissile mass for it to achieve criticality. Third is a power generator. This one is easy - any steam turbine will do the trick. Fourth one is shielding.

For a teenager, only the generator component would be understandable, and somewhat possible to construct. Most problematic ones are the ones that are most crucial - the reactor itself (if only due to, really, insane level of metalurgy required. Just a steel tube will not do the trick. Correct materials used are also a must, because radiation-material interaction can be very damaging to both reactor, and anyone around it, esp. in the long run). Radiation protection is even more tricky, not to mention work and knowledge required to be able to run the system in a stable configuration (for reference, if you get an unstable configuration, Chernobyl happens...rapidly).

This might be doable on a college level, MAYBE. And thats stretching it.

Iff you can handwave the fuel problem, particularly the fuel problem for a relatively highly enriched fuel (U235 or Pu239 or a mix would do) then the actual machine is not particularly complicated, but you will want to be able to pour significant concrete for a biological shield.

A single fuel element, (Heavy) water cooled with a surrounding neutron reflector close enough that the thing is slightly under moderated (Important to have a negative void coefficient), in a sealed stainless steel tube maybe 10M long with the water level extending to maybe 5M above the fuel could I suspect be made to run in equilibrium between the steam (subtracting reactivity due to the negative void coefficient) and the slightly above delayed criticality of the system. The steam generator for the secondary loop would wrap around the top few meters of the thing (Doubles as biological shield for the gamma from the nitrogen decay chain). Add some boron compound to the heavy water to allow the thing to be throttled by tweaking the water chemistry and to extend fuel life by reducing the poisoning as the burn up increases?

There might also be some tricks you can play with doppler broadening to make the thing more reliably self regulating.

@10kW thermal, you would have to REALLY work to get a meltdown and could probably design in sufficient thermal mass to deal with the short term decay heat long enough for the decay heat to drop to the point that convection and conduction would keep the fuel from melting.

IIRC there was a (Soviet?) criticality accident that left them with a PU bomb core running as a reactor for some time with the control being the equalibrium between the core expanding as it heated and the increased neutron losses from the surface area, I suspect they eventually sent someone in to knock the thing apart with a stick!

Iff you can handwave a low energy cost efficient muon source then a muon catalyzed fusion machine may just be possible, not sure that Hirch/Farnsworth does it even then, but Bussard polywell just might.

Not sure most 14 year olds have the combination of maths, physics and mechanical skills to put a reactor together (I certainly would not have been able to do it back then).

There are two massive problems that make this completely non-viable and a third that's going to limit you.

1) Uranium-based reactors require a critical mass of uranium to work. This sets a minimum size for the reactor and from a practical standpoint a minimum power. Trying to power a house from a uranium reactor is like trying to power your toy boat with the engine out of a yacht.

This can be avoided with a neutron-induced thorium reaction. No critical mass is necessary and thus it can run at lower power levels.

2) Shielding. It matters not whether you're producing a 8kw or 8gw, your shielding thickness is almost the same. Your containment is the same. If you want something safe to be around it's simply going to be too big for home use.

3) Cooling pools. Again, a shielding issue. They're big to put enough water between you and the hot stuff. Once again, something that won't fit in a home.

The key problem with building a backyard nuclear power plant is getting sufficient quantities of fissile material of sufficient purity to easily achieve criticality with a crude reactor design. Naturally occurring deposits of fissile materials burn themselves out fairly early in a planet's lifetime, so by the time 4+ billion years has passed, all that is left is the stuff that takes quite a bit of processing to burn, and it is safe to say that processing of natural ores in their current state into nuclear fuel is something that is well outside the capabilities of even the most industrious and precocious teen.

But OP did not specify that this planet was Earth. If we assume his world is a geologically much younger planet (about 2 billion years old, give or take a few hundred million), then it is conceivable that naturally occurring deposits of fissionables are still lying about that can be purified by simple chemical processes that any child can accomplish. For example, she could crush the ores with a hammer or some other means, wash the crushed ore in acid to put the fissionables into solution, filter out the crud from her solution, and then raise the pH of the solution with lye to make the fissionables precipitate out. If she is starting with high enough grade ores to begin with, then this should be all that is needed to get nuclear fuel that can achieve criticality.

Then our young atomic engineer needs an atomic pile, and that can just be a pile... as in a pile of dirt. Run some plumbing through the pile to extract heat to drive whatever heat engine she chooses, and some other plumbing through which she can maneuver moderators/neutron sinks to regulate the power output by pushing them through the pile to where her fuel is buried. She might also want to bury some thermocouples and maybe other detectors in near the fuel to get an idea what is going on while she is shuffling her makeshift control rods about.

The resulting nuclear power plant would be crude, and the chances of prompt criticality accidents sterilizing the entire neighborhood would be ludicrously high, but this is a young planet, which means the inhabitants are colonists from someplace else as the only things which would have had a chance to evolve there yet would be things like algae and bacteria. This leaves open the possibility of a fairly low population density (very, VERY large backyards), and thus relatively limited concern over what the neighbor does on their side of the hedge. If your nearest neighbor is a few miles away and they are not downwind, then what do they care if you mess up and make a glowing crater behind your house?

Buy an old ship diesel engine (2 stroke as they are) with a generator attached to it. Drill the bottom of the cylinders with reduced diameter. Thread the extra centimeters. Buy a bunch of thin pure plutonium screws with 100g weight each with the same diameter. Screw some of them in each cylinder from the bottom - on top of each other using a long tool and a horizontal bar; I guess it will be about 40 of them per cylinder needed. 12 cylinders, 4 kg plutonium each. When your "screwdriver" comes out of the cylinder glowing hot, you put enough plutonium in that cylinder. Over to the next one. Use water as fuel (use the fuel pump to pump it from your well or lake) and start the "engine" using its original starter. If it's not running fast enough, put some more plutonium "screws" in.

The plutonium will last for long enough that you don't have to worry about its disposal.

You Can Do This

First get hold of some fissile material. Uranium-235 can be dug up.

Make sure it's quite pure, and ideally buy it in rods.

Now stick those rods into a boiler attached to a steam engine.

Use the engine to drive your electricity generator.

Extra marks for re-using the water by condensing it from the steam outlet. You can use waste heat to warm the house, or for heating the swimming pool, as you like.

By far the easiest way would be to buy up a power company that is already planning to build a nuclear power station. When the security fence goes up, build an actual dwellinghouse for yourself at the entry instead of the usual prefab security hut. Have the back door open inside the fence.

Now you can build the nuclear reactor in your backyard.