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I am looking for a good reference on cosmic ray, both galactic and solar. Does anyone have any suggestion?

I'm looking for a reference that covers the production and propagation of cosmic rays in a rigorous way. It should target people that know about particle physics, but are ignorant about cosmic rays.

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Reinhard Schlickeiser's Cosmic Ray Astrophysics (Springer publisher link) is probably a good starting point for you. From the "about this textbook" in the link:

This book provides an exhaustive account of the origin and dynamics of cosmic rays.

It may be a little dated, having been printed in 2002 (pre-Fermi LAT), but it covers exactly what you want: the production & propagation of cosmic rays--it's been a while since I read it (having moved away from academia a few years ago), but I believe it covers galactic CRs (which ought to cover solar as well) and I think it does touch upon extra-galactic CRs.

I don't really recall it being particularly difficult with the maths beyond e.g. vector calculus. A background in astrophysics is probably useful, especially with radiative processes (i.e., having read/worked through Rybicki & Lightman). I don't think particle physics knowledge is needed in the book, but, again, it's been a while since I've needed to look at it.

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A good an updated (2016) reference is Cosmic rays and particle physics, by T. Gaisser, R. Engel and E. Resconi, active researchers in the field. It includes a lot of the recent results in UHECR (Ultra high energy cosmic rays, energies of around $10^{20}\,\mathrm{eV}$) by currently running experiments (like Telescope Array, the Auger Observatory, or the Icecube observatory). It goes through some particle physics, and talks about acceleration and propagation of cosmic rays in the galaxy and outside, although it may not go too far in solar cosmic rays. I would say that the book is rigorous enough, but one can't forget that our knowledge about cosmic ray production is limited. What I like about the book is that it provides a good description about the many parts of physics that come together in cosmic ray physics.

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