How does this fit in with the other types of radiation?

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From my high school physics, I remember learning about alpha, beta, and gamma radiation. Today I was reading about galactic cosmic radiation and specifically, how it’s primarily made up of alpha particles, but also consists of other fast travelling heavy nuclei which can be very dangerous.

My question is, how do these heavy ions fit in with the three radiations I learned about? They’re not helium nuclei, electrons, or EM radiation... are they some fourth type of ‘radiation‘? Or do we just not call fast travelling heavy elements a specific radiation?

My initial thought was that such an ion could be a gamma radiation emitter. Such that it would enter the body and then emit one of the three radiations which as far as my understanding goes are the only three ionising radiations. But then I read that it is the actual nuclei itself which is responsible for DNA damage... so I guess my thinking was wrong.

Anyway... some clarification about where these fit in with the other radiations, or if indeed I’ve missed how they are simply one of these already, would be much appreciated!