Magnetic diffusion effects on the Ultra-High Energy Cosmic Ray spectrum and composition

Understand

We discuss the effects of diffusion of high energy cosmic rays in turbulent extra-galactic magnetic fields.

• We find an approximate expression for the low energy suppression of the spectrum of the different mass components (with charge $Z$) in the case in which this suppression happens at energies below $\sim Z$ EeV, so that energy losses are dominated by the adiabatic ones.
• The low energy suppression appears when cosmic rays from the closest sources take a time comparable to the age of the Universe to reach the Earth.
• This occurs for energies $E< Z\, {\rm EeV}\,(B/{{\rm G}})\sqrt{l_c/{\rm Mpc}}(d_s/70\ {\rm Mpc})$ in terms of the magnetic field RMS strength $B$, its coherence length $l_c$ and the typical separation between sources $d_s$.