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.