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Cosmic ray propagation in the interstellar magnetic fields

The propagation of TeV-PeV cosmic rays (CR) in our Galaxy can be described as a diffusive process. We discuss here two effects, with important observational consequences, that cannot be predicted by the diffusion approximation in its usual form. First, we present an explanation for the CR anisotropies observed at small angular scales on the sky. We show that the local magnetic field configuration within a CR mean free path from Earth naturally results in CR flux anisotropies at small and medium scales. Second, we point out that TeV-PeV CRs should be expected to diffuse strongly anisotropically in the interstellar medium on scales smaller than the maximum scale of spatial fluctuations of the field, $\sim 100$ pc. This notably questions the usual assumptions on CR diffusion around sources.