How would I determine the radiation fields, if any, of a gas giant planet? What effect would this have on its moons if they have magnetic fields like the Earth does, and are inhabited?
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Not every gas giant or planetary body has same radiation belts. What is important is that it will most definitely be much more deadly than https://en.wikipedia.org/wiki/Van_Allen_radiation_belt. If you want to imagine gas giant with earth like moon in safe zone (like between inner and outer radiation belts) you just can but on Jupiter all galilean moons are inside the dead zone. Basically further you go less likely you get to still be inside radiation belt of theoretic gas giant but no orbit is impossible just less likely. So having 2 moons like that you go into incredibly unlikely unless they are far away from planet. Yes their own magnetosphere natural or artificial would make it better but gas giant radiation zone is pretty hellish. Ice and sea would provide some help as well so deep underwater life through panspermia in nearby moons is a possibility. As special case radiation in for example Europa hits mostly trailing side of the moon due to orbiting speed difference between Europa and radiation belt so your moon can have one side sterilized and one lush.
As for results of such radiation in say less that deadly doses? We will have electrons, ions, high energy protons... you name it. Macro life living in higher than earth environment will most likely have higher mutation rate and natural radiation resistance with possibility of life using elements like lead for insulation and simply reflecting some of it. Possibly magnetic properties either natural of acquired by say eating magnetic ore. Life would also seem shelter in caves, woods, any shade and waters not to shallow but not to deep. Another possibility is for some life to evolve into utilizing this energy in some way.
Sorry for long rant.