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Precise measurements of galactic cosmic rays revealed a significantdifference between the rigidity spectral indices of protons and helium ions.This finding is a notable contrast to the commonly accepted theoreticalprediction that supernova remnant (SNR) shocks accelerate protons and heliumions with the same rigidity alike. Most of the earlier explanations for the"paradox" appealed to SNR environmental factors, such as inhomogeneous $p$/Hemixes in the shock upstream medium, variable ionization states of He, or amulti-SNR origin of the observed spectra. The newest observations, however, arein tension with most of them. In this paper, we show by self-consistent hybridsimulations that such special conditions are not vital for the explanation ofthe cosmic ray rigidity spectra. In particular, our simulations prove that anSNR shock can modify the chemical composition of accelerated cosmic rays bypreferentially extracting them from a homogeneous background plasma withoutadditional, largely untestable assumptions. Our results confirm the earliertheoretical predictions of how the efficiency of injection depends on the shockMach number $M.$ Its increase with the charge-to-mass ratio saturates at alevel that grows with $M.$ We have convolved the time-dependent injection ratesof protons and helium ions, obtained from the simulations, with a decreasingshock strength over the active life of SNRs. The integrated SNR rigidityspectrum for $p$/He ratio compares well with the AMS-02 and PAMELA data.

Acceleration of Cosmic Rays in Supernova Shocks: elemental selectivity of the injection mechanism