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Reading about trapped protons and eletrons in van Allen belts, I get the understanding that the number of trapped electrons increase during a solar maximum (which I find logical because we have more solar flares etc.), but that the number of trapped protons increase during a solar minimum. What is the explanation?

Also: what is "atmospheric cut-off"?

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Without the influence of an external force, the protons will happily gyrate around the magnetic field while bouncing from pole-to-pole as they drift around the Earth in the radiation belts. During a geomagnetic storm, the Earth's field changes rapidly causing protons in the radiation belts to either precipitate into the atmosphere or hit the magnetopause. In both cases, they are generally considered lost and no longer trapped.

Geomagnetic storms are caused by solar eruptions called coronal mass ejections or CMEs (and high speed streams). CMEs are produced by enhanced magnetic activity on the sun, which occurs more frequently during solar maximum.

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