Cosmic rays scatter off magnetic irregularities (Alfvén waves) with which they are resonant, that is waves of wavelength comparable to their gyroradii. These waves may be generated either by the cosmic rays themselves, if they stream faster than the Alfvén speed, or by sources of MHD turbulence. Waves excited by streaming cosmic rays are ideally shaped for scattering, whereas the scattering eff...

We discuss the relation between the acceleration spectra of extragalactic cosmic ray protons and the luminosity and cosmological evolution of their sources and the production of ultra high energy cosmogenic neutrinos in their propagation from the sources to us.

The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference magnetohydrodynamic code is discussed. It is shown that the standard implementation fails near singular X-points of the magnetic field, which are common if the field i...

Cosmic rays scatter off magnetic irregularities (Alfvén waves) with which they are resonant, that is, waves of wavelength comparable to their gyroradii. These waves may be generated either by the cosmic rays themselves, if they stream faster than the Alfvén speed, or by sources of MHD turbulence. Waves excited by streaming cosmic rays are ideally shaped for scattering, whereas the scattering ef...

This paper summarizes recent developments in the study of the propagation of ultra-high energy cosmic ray protons or nuclei in the Universe, with emphasis on the consequences of energy losses and on the influence of extra-galactic magnetic fields.

We introduce a static toy model of the cosmic ray (CR) universe in which cosmic ray propagation is taken to be diffusive and cosmic ray sources are distributed randomly with a density the same as that of local L∗ galaxies, 5 × 10 −3 Mpc. These sources “fire” at random times through the history of the universe but with a set expectation time for the period between bursts. Our toy model model cap...

Diffusive shock acceleration operating at expanding supernova remnant shells is by far the most popular model for the origin of galactic cosmic rays. Despite the general consensus received by this model, an unambiguous and conclusive proof of the supernova remnant hypothesis is still missing. In this context, the recent developments in gamma ray astronomy provide us with precious insights into ...