Cosmic Rays

Cosmic rays consist of atomic nuclei (mostly H nuclei) and electrons. Positrons and antiproton may also be present. The existence of cosmic rays has been known since the beginning of XX century. Despite the long period since they have been known, many "open questions" on their origin are still without answer.
Cosmic rays may get their energy through the mechanism called "Fermi acceleration", a process in which the particles gain energy by a compressing medium. Shocks in the interstellar medium can generate such a situation. The matter in the pre-shock region and in the post-shock regions acts as magnetic walls. A charged particle on the shock edge sees the two regions of the shock as a compressing system which accelerate the particle.
The gas density jump, in the case of shock, is

$$r = \frac{\gamma + 1}{\gamma - 1 + \frac{2}{M^{2}}}$$ (1.1)

where $\gamma$ is the adiabatic index and $M$ is the Mach number. For relativistic particles the energy distribution generated by shock acceleration follows a power law $f(E) = kE^{-p}$ where $p$ is:

$$p={\frac{r+2}{r-1}}$$ (1.2)

For very large $M$ and the usual $\gamma = 5/3$, $p$ is equal to 2, while for $\gamma = 4/3$ (typical value for relativistic gas) $p$ is 3/2.
Radio observations have shown the presence of accelerated electrons inside supernova remnants (SNR), which are therefore identified as the most probable birthplace for the cosmic-ray electronic component. SNR are also supposed to allow for proton and nuclei acceleration, but no evidence has been found until now.
Regardless to their origin, the features of the spatial and spectral distribution of cosmic rays results to depend also on the interaction with the interstellar medium in which they propagate. The interaction with the Galactic magnetic field cause the cosmic ray diffusion to depend on both the particles energy and the magnetic field irregularities spectrum. Considering a Kolmogorov irregularities spectrum, the particle diffusion outside the Galaxy disk is proportional to $E^{1/3}$, which makes cosmic ray spectrum steeper by a factor $1/3$.
Cosmic ray interaction with the interstellar medium also causes energy losses, which in turn modify in different way the initial spectrum for electron and proton.