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I think, it could be a reactor utilizing californium-242 (or, at least, weapon-grade U-235) cooled and moderated by heavy water.

Essentially, it were similar to an atomic bomb, but - of course - it would be optimized for stay around the equilibrial state.

The result were probably a very strong neutron source.

I think, it could be used for various things, mainly in the space applications.

Does any cost/size estimations about this ever created?

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  • $\begingroup$ I believe a google search for implant nuclear battery will provide you with some interesting results. Sub-inch sized batteries depending on natural decay of radioisotopes; they don't depend on forced fission, but you can still classify them as nuclear reactors... $\endgroup$
    – SF.
    Jan 23 '15 at 12:29
  • $\begingroup$ @SF. This question targeted the moderated, chain-reaction based reactors (because only they are controllable, and their power density is also much better). Maybe I wasn't enough clear? I would happily extend/clarify the question. $\endgroup$
    – peterh
    Jan 23 '15 at 12:32
  • $\begingroup$ that's why I submitted that as a comment, not as an answer; Yes, this is not a reactor based on chain-reaction, still, if extreme miniaturization is your goal, this might be a better path to research. $\endgroup$
    – SF.
    Jan 23 '15 at 12:34
  • $\begingroup$ If you count nuclear batteries, the smallest one would be a single unstable atom of the smallest type, so that would be a single atom of tritium. But that won't be very useful. $\endgroup$
    – JanKanis
    Mar 27 '18 at 9:07
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The RM-1 Russian submarine reactor had a core of less than one cubic metre. It had about 100kg fuel load, which was 90% enriched (i.e. 90kg) Uranium 235. This was liquid-metal cooled [specifically a "eutectic lead-bismuth alloy (44.5 wt% lead, 55.5 wt% bismuth)" - source as below, p40], so didn't need a moderator.

Submarine 901 had in its right-board reactor just 30.6 kg of Uranium 235; this was at 20% enrichment, so a total fuel load of 153 kg.

These were controllable chain-reaction based reactors.

Source:

NKS-138 Russian Nuclear Power Plants for Marine Applications
Ole Reistad, Norwegian Radiation Protection Authority, Norway
Povl L. Ølgaard, Risø National Laboratory, Denmark
Published by Nordic Nuclear Safety Research, April 2006
ISBN: 87-7893-200-9
http://www.nks.org/scripts/getdocument.php?file=111010111120029

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  • $\begingroup$ Thank you! Do you know, how are they moderated? With heavy water? $\endgroup$
    – peterh
    Jan 23 '15 at 18:06
  • $\begingroup$ @PeterHorvath hmm, apparently some Russian naval reactors have been water-moderated, but the liquid-metal cooled ones (e.g. RM-1) don't need moderators; they are nevertheless controllable proper grown-up reactors. Is moderation a deal-breaker for you, or are liquid-metal-cooled ones ok too? $\endgroup$
    – 410 gone
    Jan 23 '15 at 18:13
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Radioisotope thermoelectric generators have been used in space for decades, both on the moon missions and on deep-space probes where solar cells would not be practical.

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    $\begingroup$ RTGs are not fission reactors; they utilize heat from the decay of isotopes while not actual fissioning the isotopes themselves. $\endgroup$
    – HDE 226868
    Jan 22 '15 at 19:39
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    $\begingroup$ @HDE226868: Please explain how "decay" is not "fission". Granted, it isn't the uncontrolled chain reaction you use in, say, a bomb, or the carefully-controlled chain reaction you use in a large terrestrial generator. But it's still fission -- some of it spontaneous, and some of it triggered by neutrons. $\endgroup$
    – Dave Tweed
    Jan 22 '15 at 20:01
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    $\begingroup$ @DaveTweed - There is spontaneous fission, you're right at that. But in those radioisotope thermoelectric generators, we have (ideally) mainly alpha decay, which I would not call fission. $\endgroup$
    – John H. K.
    Jan 22 '15 at 21:42
  • $\begingroup$ RTG is not okay, they is not controllable and their power density is bad. But anyways, your answer was informative. $\endgroup$
    – peterh
    Jan 23 '15 at 12:33
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    $\begingroup$ This in in part a terminology issue but "fission reactor" is commonly understood to mean critical fission reactor, i.e. the reactor must attain criticality. $\endgroup$
    – Fizz
    Feb 10 '15 at 20:44
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It largely depends on the critical mass of the fuel - that is, the smallest amount of fuel that is needed for a controlled, sustained reaction to occur. This is often on the order of ten or so kilograms, but can vary with the other aspects of the design (see, for example, this paper on $^{238}\text{Pu}$). The Wikipedia page also has a nice summary from various sources of the size of a sphere containing the critical mass (and the critical mass itself) of quite a few different isotopes. The diameters range from 6.9 centimeters to 30-35 centimeters.

The DOE has a page on the size of fusion reactors; one of the expert responses mentions fission reactors and, while admitting that the critical mass can be very low,

A typical critical mass for a fission reaction would be several kilograms. This would be very portable, if it was not for the shielding needed to keep from frying everybody in the vicinity. Plus, you need cooling and heat exchangers to use the heat that is produced. Both fusion and fission reactors put out heat as their primary method of energy production.

The Depleted Cranium blog notes that the first nuclear reactor, CP-1, was really the smallest ever. It used 40 tons of uranium and 400 tons of graphite to be used as a nuclear moderator. This graphite was made into 45,000 blocks, which created a structure like this drawing: CP-1

You need a material like graphite as a moderator, and you need it to be in substantial quantities. CP-1 used the smallest amount possible and produced only a small amount of energy. So you're not going to get under about 450 tons if you want to actually generate a substantial amount of energy.

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    $\begingroup$ The concept of "critical mass" relates only to self-sustaining chain reactions. This is not the only way in which fissionable materials can be used. $\endgroup$
    – Dave Tweed
    Jan 22 '15 at 20:34
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    $\begingroup$ I'm not sure exactly what you're indicating about CP-1, but I really doubt that it's the smallest ever. I've used a small 10kW research reactor based on the core design of a submarine powerplant. That entire thing was no larger than what is indicated in the picture. Further, much of the size there was devoted to extra water to reduce neutron leakage for safety reasons, not to act as a moderator. $\endgroup$
    – Dan
    Jan 22 '15 at 20:53
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An almost-critical sphere of fissionable material would do. Add some neutron reflecting material that can be rotated to increase or decrease the neutron reflection. Or you could have two halves of a critical sphere that are moved closer together or further apart to control the reactivity.

A moderator is not necessary if the reactor operates on fast neutrons, thermal (slow) neutron reactors are just easier/cheaper to operate and more proliferation resistant.

If you only operate it at low power levels you would not need a lot of cooling (though the reactor would probably not be very useful).

The largest amount of mass would be the shielding. So as long as you don't care about that, you're fine (and in your question you don't mention it). There has been research into nuclear powered cars, aircraft, and trains, but the size and weight of the shielding was the main technical problem for such applications.

The output of nuclear reactions is heat, if you want to convert it to electricity or another more useful form of energy, you will need some kind of heat engine, which (depending on the temperature) needs to dump 75% of the heat input as low temperature waste heat. So you will need some kind of heat sink for that. But again that is not part of the question.

edit: To be more specific, the output of a nuclear reactor is some heat in the reaction products, and most of the energy in the neutron radiation. Reactors usually also capture those neutrons in order to convert their energy to heat, so that is anoher reason why you might want to use neutron reflectors. The most difficult to shield radiation are the gamma rays, which typically require several meters of concrete or a thick slab of lead to block.

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