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Let’s say people (humans) arrive on a planet. Oh no, it’s too hot! Okay, we live underground in lava tubes. Oh no, it’s too dark! Okay, so illuminate the tubes with self-repairing fusion-reactors that function like miniature suns. We’ll call them pseudo-suns.

Let’s say the typical pseudo-sun emits a similar amount of light as a football-stadium light (about 1,000 watts), and triggers the reaction by subjecting the gas to immense pressure. How much hydrogen would these reactors need to keep running on a timespan of hundreds/thousands of years?

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  • $\begingroup$ Might be unfeasible: creating and sustaining conditions for fusion to start and go on for a long time might need so much energy that if the output is some 1 kW, it would be barely doing anything useful compared to what aforementioned things need. An incandescent lamp produces lot of heat and only little light (3 - 5 %), so it is very inefficient but it would beat this setup. Merely maintaining the pressure and containing the fusion takes megawatts. $\endgroup$
    – Jani Miettinen
    Commented Dec 30, 2022 at 16:07
  • $\begingroup$ This is an incredibly strange question given that the practicalities of miniaturising fusion power generation to this extent would be infinitely more difficult and relevant than the amount of hydrogen such a system would consume... $\endgroup$
    – Ian Kemp
    Commented Dec 31, 2022 at 17:17

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Basic numbers

A watt is one joule per second. There are 31.536 million seconds per year. Something generating one kilowatt of power yields about 3.15 x 10^10 joules if it runs for a whole year.

The fusion reaction the Sun uses is proton-proton fusion, which the Power of Sci-Fi says we'll be able to use as fuel in a reactor by the time we can colonize other planets anyway. This produces ~ 25 MeV per 4 hydrogen atoms. 25 MeV is 4.01 x 10^-12 joules.

To produce 3.15 x 10^10 joules, we need to run that reaction 7.86 x 10^21 times. That uses twice as many molecules of hydrogen gas (H2). Chemists find it easy to measure chemical weights using the mole. We have here about .0261 moles of hydrogen gas (H2) which is about .0522 grams.

Efficiency

No reaction is a hundred percent efficient. There ain't no such thing as a free lunch. I am assuming Futurium power, that is, much more advanced fusion technology that can achieve an implausible-by-today's-standards degree of efficiency. Futurium powered fusion can plausibly have just about any level of efficiency you want. Pessimistically, let's suppose 10% of the reactor's total energy (and thus, reaction mass) consumed is converted into usable output (light, in this case). This means we're using roughly ten times as much hydrogen gas as the theoretical limit, or about .522 grams to operate one of these for one year.

Ramifications

So, first of all: the total mass these reactors consume is miniscule. A one-kilowatt reactor burns .522 grams of hydrogen gas per year to provide the desired illumination. A reactor that generates more than 1 kilowatt of power will use proportionally more fuel, but still hardly anything.

One of these things running for a thousand years will use 520 grams of fuel. Ten thousand will use 5200 kilograms over that same timeframe. That might sound like a lot, but a person is about ten percent hydrogen by weight, which is somewhere around 6-7 kilograms.

In other words, the amount of hydrogen found in the organic material you're using to feed this population almost certainly dwarfs, by several orders of magnitude, the amount you would ever need for fuel. A small settlement is probably a military outpost or research base or something that regularly gets resupplied, and a large settlement is large enough this is a drop in the bucket.

This is why I used proton-proton fusion; other hydrogen fusion recipes, like the ones we're trying in our reactors in reality, require uncommon isotopes of hydrogen, which means they need a special fuel supply. Proton-proton fusion can use anything.

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    $\begingroup$ Hm, is that accounting for whatever we lose in the conversion? My understanding is that fusion reactors -- like fission reactors -- don't convert much of the energy into electricity. They are fancy heaters, and we convert the heat into electricity. The bulk of the energy is lost, I think? $\endgroup$
    – JamieB
    Commented Dec 31, 2022 at 0:57
  • $\begingroup$ It is not. I should clarify that. I don't think it meaningfully changes the answer, but it is worth noting, $\endgroup$
    – Ton Day
    Commented Dec 31, 2022 at 1:09
  • $\begingroup$ The numbers are unbelievable. 0.0522 g per year? A kilowatt is 1000 Joules per second. There are about 31.5 M seconds in a year, amounting to 31.5 gigajoules per year that this reactor outputs. $E=mc^{2}$ -> 4.7 trillion Joules of mass-energy content in 0.0522 grams. Your reactor captures almost 10% of the mass-energy content of the fuel. Not even some of the best hypothetical matter-antimatter reactors can get that kind of efficiency! $\endgroup$
    – BMF
    Commented Dec 31, 2022 at 1:16
  • $\begingroup$ I walked through the same math you just cited in my answer. Yes, it turns about 10% of the mass of the hydrogen gas into energy. I did use Google-sensei to look up (and linked to it to show my work) the reaction equation for proton-proton fusion, because I'm not a nuclear physicist. $\endgroup$
    – Ton Day
    Commented Dec 31, 2022 at 1:22
  • $\begingroup$ Except that protium fusion is energetic but generates little power. The Sun's core generates about as much power as a compost pile per cubic meter, about 300 Watts to be exact. $\endgroup$
    – Arcturus
    Commented Dec 31, 2022 at 4:42

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