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Could a sufficiently advanced civilization feasibly harvest antimatter from the van allen belts of a gas giant and use it for fast interplanetary travel.

The main idea stemmed from this video, among the topics that are discussed there is the possibility of harvesting antimatter from Earth's Van Allen Belts through the use of electromagnetic harvesters.

However, after looking around the net, it seems that the quantity of antimatter in earth's orbit would be far too little to be of any use, something like the equivalent of a liter of gasoline. But then I thought, what if instead the target were the van allen belts of a celestial body comparable with jupiter and with an analogous magnetosphere which would be millions of times more powerful?

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    $\begingroup$ Anti-matter is produced in almost every bolt of lightning here on Earth. Yet I would hardly consider that harvesting lighting bolts for antimatter would be practical. It would take more energy to do it than you harvest. $\endgroup$ May 15 at 17:33

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Feasibility is in the eye of the beholder

Recommended that you refer to the NASA paper (pg 31.) that looked at this topic in more detail than you are likely to find in other places.

In short, expected anti-matter in orbit, is estimated but admits that the actual values could easily be off by an order of magnitude.

Earth 0.25 ng
Jupiter 1.0 µg
Saturn 400 µg

Saturn thus is expected to have about 1600 times as much anti-matter as Earth, primarily due to the increased production associated with its ring system.

I would argue that this is enough to be interesting for some uses in space. You are not remotely close sending payloads to Alpha Centauri at 10% of light-speed (think in terms of kg of anti-matter fuel for a 10 kg probe), but there might be some special applications where it would be worthwhile.

For interplanetary travel even old-fashioned fission though hundreds of times less energy dense is more feasible considering that you can easily get tons of the fuel with local sourcing.

For large anti-matter applications, you are going to have to make your own, and at 160 trillion USD per gram based on the cost of electric power alone, you are going to need a better method.

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    $\begingroup$ Hmm interesting...though I'd like to know, how long would it take for the quantity of antimatter to regenerate? For instance, if one were to harvest all of the 400 micrograms of antimatter around Saturn, how long would it take for 400 more micrograms to come about? $\endgroup$ May 15 at 18:50
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    $\begingroup$ @JuimyTheHyena - This is also addressed in the NASA paper, estimated crudely to take a few years. $\endgroup$ May 15 at 18:52
  • $\begingroup$ If I didn't mess up the math, the electricity cost of making the equivalent of the 400 micrograms from Saturn would cost 64 billion USD which I would interpret as making antimatter is cheaper than harvesting it around Saturn. $\endgroup$
    – quarague
    May 17 at 10:31
  • $\begingroup$ @quarague - The 160 trillion per gram number was taken from the NASA report (pg. 5)- I confused it with the electricity cost. $\endgroup$ May 17 at 12:22
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Assuming that you have the technology to efficiently separate, harvest and contain antimatter, you will have to deal with the deeper gravity well of a gas giant and its related greater energy expenditure for anything wanting to escape it.

Together with the intrinsic low amount of available antimatter (a gas giant doesn't have a preferential route for its production, it has just a more intense magnetic field, so the scaling is linear), I doubt it would worth the effort.

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    $\begingroup$ Given the value of antimatter the energy you need to escape the gravity well seems almost negligible. Where the inner radiation belts of Jupiter are located escape velocity should be around 40-45 km/s. But I also doubt that it would be "worth the effort" $\endgroup$
    – Avun Jahei
    May 16 at 2:03

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