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Cosmic radiation cutoff at LOW energies?

The energy spectrum of the cosmic radiation (not CMB) is limited on both sides.

I know about the GZK-cutoff at high energies. Basically, the interaction probability for photons of energies above 10^20 eV becomes so high that all have interacted before they can reach us.

But why is there a limit at lower energies? Earth's magnetic field, atmosphere, and/or radiation belt? Perhaps someone can explain that to me.

con-f-use
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The low-energy 'cutoff' is, for the most part, an observational effect. Low energy charged particles are deflected (or 'modulated') by magnetic fields---the earth's magnetic field, the sun's, and even the interstellar-medium (ISM) magnetic field will effect the observed distribution of particles. I'd assume the primary cause of the cutoff in the observed spectrum is from the earth's magnetic field (as you suggest).

There are additional factors. For example, interaction with the ISM and atmosphere (again, as you said). Also finite lifetimes will play a roll; neutrons, by themselves, for example, are unstable---and rapidly decay. If they are traveling fast enough, we can still observe them, at least as secondary cosmic rays. Also, some particular sources of cosmic rays will only produce above a certain threshold: for example, cosmic rays from the sun will only be at velocities larger than the escape velocity.