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The idea is to build a cybernetic body for a human. Only the brain and a few glands related to emotions, like adrenal glands, will be kept. The brain and the glands will be in a closed, plug-and-play, container, that can be connected to compatible bodies, to turn humans into cybernetic space elves capable of living long enough to cross the void between the stars without relying on relativistic ships (assume for now that it is possible to keep the brain healthy for thousands of years with the correct chemistry).

But these bodies need power sources. Compact, energetic power sources. I'm thinking fission reactors.

Is it possible to build a fission reactor so small that can be possible to fit it in a human chest cavity? Would such a miniaturized reactor be better, in terms of power output and autonomy, then a combustion engine or batteries?

Fission reactions (as opposed to reactors) is already how we power deep space probes, it should work for cyborgs in space.

A type of radioisotopic power system known as radioisotope thermoelectric generators employ radioactive materials such as plutonium-238 to produce heat and make use of a principle of electrics known as the Seebeck effect to produce power.
Put simply, the Seebeck effect is when two different semi-conductive metals are connected. With one end heated, electrons will move from the hotter metal to the colder one.

https://cosmosmagazine.com/technology/where-do-deep-space-probes-get-their-power-from

Advantages: It works, basically forever. If it's not enough power then just have more of them.

Disadvantages: You're producing heat and then harvesting it, so it's bigger than "fitting inside of a human chest".

However for cyborgs in space there's no need to keep your power source next to your brain. The ship has a power source, we can ship electricity to various places real easy, a cyborg can have a power cable for most situations and batteries for when it has to be disconnected.

Fission power requires critical mass to work, making it difficult to miniaturize power plants, even ignoring problems with radiation and radioactive waste. Californium-252 has the smallest critical mass of 2.73 kg, but it is expensive to synthesize. In addition, fission doesn't produce electricity directly, but instead evaporate water that produces electricity in turbines, adding to the weight of the power plant. Did I mention shielding? Cutting gamma radiation in half requires 1 cm of lead, and reducing it to (say) less than two percent will thus require 6 cm lead shielding, which quickly becomes very heavy.



An alternative might be fusion power, which has no critical mass. In return, however, fusion requires very high pressure and temperature, which might be difficult to contain in a small reactor. The smallest experimental reactors being build are the size of small houses. You would probably need fusion processes that don't emit free neutrons, which make stuff radioactive and are difficult to shield. Examples are deuterium-lithium and proton-boron processes, but these typically require greater pressure and temperature than neutronic processes. They also tend to require steam turbines to produce electricity. A theoretical exception is 'focus fusion', which produces electricity directly. This might be your best bet.

If you want to keep the fleshy bits of your space elves, steer well clear of pretty much any kind of nuclear power supply, fission, fusion or annihilation. Highly penetrating x-rays and gamma rays you may be able to shield against (though I wouldn't bet on it) but the spray of fast neutrons you can expect to find flying out of any fission reaction and many fusion reactions (yes, even proton-boron fusion, where about 0.1% of the reactions will shoot out nice, fast, highly-penetrating and highly destructive neutrons) will be basically unstoppable and everyone will die of cancer before arriving at the new world. Even if you have super space medicine to fix cancer, those brains are gonna be pretty fried a lot of cells are gonna die. Not good news.

But to flip it around, how much power do you think you really need? "nuclear reactor" sounds like the sort of thing you'd want to power a rocket engine, or an energy weapon, not a person. A human body has an average power use of about 100W. An efficient robotic chassis with similar performance could be driven with modern batteries and recharged from time to time (daily, probably). On a spacecraft designed for such things, you might have charging points pretty much anywhere and everywhere people might congregate or rest. Super future batteries or fuel cells could either be recharged much less frequently, or provide much more power, if you can think of something to do with it all.

Remember also that a lot of the power draw will be moving around, but on a non-relativistic spacecraft (or even a plausible relativistic one, to be honest) there will be little to no acceleration from thrust so the only gravity forces you have to work against are artificial ones that you can dial up or down to your heart's content. Just turn the spin decks down and relax in microgravity.

(also if you really, really want fission power, be aware that fancy isotopes with small critical masses tend to have half-lives much, much shorter than your projected thousand year flight time. bring a big breeder reactor and a good supply of parent isotopes to work from)

Stick with chemical engines.

In a cyborg you have a whole body cavity to work with. The fact that is is a cyborg means to me that it will be in human-type circumstances; the only reason I can think of for a robot to emulate the human form. Human circumstances means there will probably be opportunities to eat and to breathe.

I propose that you put an internal combustion engine in there at the site of the heart. "Breathing" will provide the oxygen and also a mechanism to vent heat. The cyborg can eat fuel. Cyborg fuel might be kerosene or even rocket fuel; a cyborg in circumstances where it is unable to breathe might eat rocket fuel with oxidizer included. Other combustibles might include butter, chicken, or rum (carried in a hip flask for emergencies). RPMs of the engine will increase as dictated by caloric value of food and energy needs.

The exhalations of the cyborg will depend on what fuel it is currently running on. There might be a lot of smoke, or sometimes even flames.

It is worth noting that the varying heat of exhalations will correspond to varying gas density and so variation in vocal pitch, assuming the cyborgs use vibrations and the exhaled airstream to make sounds. A cold cyborg at rest will have a low voice; possibly quite low depending how cool they get. A hot cyborg exhaling flames will have a very high squeaky voice.