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.

Context. Recent observations of hard X-rays and very high energy gamma-rays from a number of young shell type supernova remnants indicate the importance of detailed quantitative studies of energy spectra of relativistic electrons formed via diffusive shock acceleration accompanied by intense nonthermal emission through synchrotron radiation and inverse Compton scattering. Aims. The aim of this work was derivation of exact asymptotic solutions of the kinetic equation which describes the energy distribution of shock-accelerated electrons for an arbitrary energy-dependence of the diffusion coefficient. Methods. The asymptotic solutions at low and very high energy domains coupled with numerical calculations in the intermediate energy range allow analytical presentations of energy spectra of electrons for the entire energy region. Results. Under the assumption that the energy losses of electrons are dominated by synchrotron cooling, we derived the exact asymptotic spectra of electrons without any restriction on the diffusion coefficient. We also obtained simple analytical approximations which describe, with accuracy better than ten percent, the energy spectra of nonthermal emission of shock-accelerated electrons due to the synchrotron radiation and inverse Compton scattering. Conclusions. The results can be applied for interpretation of X-ray and gamma-ray observations of shell type supernova remnants, as well as other nonthermal high energy source populations like microquasars and large scale synchrotron jets of active galactic nuclei.

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