Spectral hardening of cosmic ray protons and helium nuclei in supernova remnant shocks

The observed hardening of the spectra of cosmic ray protons and helium nuclei is studied within the model of nonlinear diffusive shock acceleration of supernova remnants (SNRs). In this model, the injected particles with energies below the spectral "knee" are assumed to be described by two populations with different spectral indexes around 200 GeV. The high-energy population is dominated by the particles with energies above 200 GeV released upstream of the shock of SNR, and the low-energy population is attributed to the particles with energies below 200 GeV released downstream of the shock of SNR. In this scenario, the spectral hardening of cosmic ray protons and helium nuclei observed by PAMELA, AMS-02, and CREAM experiments can be reproduced.