We survey the theory and experimental tests for the propagation of cosmic rays in the Galaxy up to energies of 10 15 eV. A guide to the previous reviews and essential literature is given, followed by an exposition of basic principles. The basic ideas of cosmic-ray propagation are described, and the physical origin of its processes are explained. The various techniques for computing the observational consequences of the theory are described and contrasted. These include analytical and numerical techniques. We present the comparison of models with data including direct and indirect -especially gamma-ray -observations, and indicate what we can learn about cosmic-ray propagation. Some particular important topics including electrons and antiparticles are chosen for discussion.

It is demonstrated that clusters of galaxies are able to keep cosmic rays for a time exceeding the age of the universe. This phenomenon reveals itself by the production of the di †use Ñux of high-energy gamma and neutrino radiation due to the interaction of the cosmic rays with the intracluster gas. The produced Ñux is determined by the cosmological density of baryons, if a large part of this density is provided ) b , by the intracluster gas. The signal from relic cosmic rays has to be compared with the Ñux produced by the late sources, which can be considered as a background in the search for cosmic-ray production in the past. We calculate this Ñux considering the normal galaxies and active galactic nuclei (AGNs) in the clusters as the sources of cosmic rays. Another potential cosmic-ray source is the shock in the gas accreting to a cluster. We found that this background is relatively high : the di †use Ñuxes produced by relic cosmic rays are of the same order of magnitude that can be expected from AGNs in the clusters. In all cases the predicted di †use gamma-ray Ñux is smaller than the observed one, and the di †use neutrino Ñux can be seen as the small bump at E D 106 GeV over the atmospheric neutrino Ñux. A bright phase in the galaxy evolution can be a source of the relic cosmic rays in clusters, revealing itself by di †use gamma and neutrino radiation. We found that the observation of a signal from the bright phase is better for an individual cluster.

The physical processes involved in diffusion of Galactic cosmic rays in the interstellar medium are addressed. We study the possibility that the nonlinear MHD cascade sets the power-law spectrum of turbulence which scatters charged energetic particles. We find that the dissipation of waves due to the resonant interaction with cosmic ray particles may terminate the Kraichnan-type cascade below wavelengths 10 13 cm. The effect of this wave dissipation has been incorporated in the GALPROP numerical propagation code in order to asses the impact on measurable astrophysical data. The energy-dependence of the cosmic-ray diffusion coefficient found in the resulting self-consistent model may explain the peaks in the secondary to primary nuclei ratios observed at about 1 GeV/nucleon.

Abstract. The cosmic-ray streaming instability creates strong magnetohydrodynamic turbulence in the precursor of a SN shock. The level of turbulence determines the maximum energy of cosmic-ray particles accelerated by the diffusive shock acceleration mechanism. In this paper we present the continuation of previous work . We assume that Kolmogorov type nonlinear wave interactions together with ion-neutral collisions restrict the amplitude of the random magnetic field. As a result, the maximum energy of the accelerated particles strongly depends on the age of a SNR. The average spectrum of cosmic rays injected in the interstellar medium in the course of the adiabatic SNR evolution (the Sedov stage) is approximately Q(p)p 2 ∝ p −2 at energies larger than 10−30 GeV/nucleon and with a maximum particle energy that is close to the position of the knee in the cosmic-ray spectrum observed at ∼4 × 10 15 eV. At an earlier stage of SNR evolution -the ejecta-dominated stage described by the Chevalier-Nadyozhin solution, the particles are accelerated to higher energies and have a rather steep power-law distribution. These results suggest that the knee may mark the transition from the ejecta-dominated to the adiabatic evolution of SNR shocks which accelerate cosmic rays.