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What conditions could create a planet that has higher amounts of antimatter in its radiation belt?

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In the science fiction setting I'm working on, one of the factions are supposed to be using naturally occurring antimatter because the systems they reside in have sufficient natural sources of it.

I've explored the idea of chasing positrons in gas giant storms, but found that antiprotons can be found in the radiation belts of worlds. Antiprotons have more mass and are not trapped in the hostile environment of a gas giant's atmosphere.

Unfortunately, they do not seem to be in sufficient quantities to power a fleet. From what I've read, the Van Allen radiation belt of our planet have somewhere between 100-200 nanograms of antimatter to work with. I think it came out to less energy than a quarter gallon of gasoline.

The concept seemed sound enough that I wanted to see if there were conditions that could affect the abundance of antimatter in the radiation belts of a planet. While this planet does not have to be habitable, it at least has to exist in the same star system as a habitable world.

So, I'm curious to what conditions could create a radiation belt that would produce/contain an abundance of antimatter sufficient to power starships and what properties the planet with such a belt would have, particularly its atmosphere and size.

Since this antimatter is formed during interactions with a planet's atmosphere and cosmic rays, I imagine the star(s) of a system also being a factor which could potentially make a habitable world in that system a little more difficult to have.


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