Can supernova remnants accelerate protons up to PeV energies?

Supernova remnants are believed to be the sources of galactic cosmic rays. Within this framework, diffusive shock acceleration must operate in these objects and accelerate protons all the way up to PeV energies. To do so, significant amplification of the magnetic field at the shock is required. The goal of this paper is to investigate the capability of supernova remnants to accelerate PeV protons. We present analytic estimates of the maximum energy of accelerated protons under various assumptions about the field amplification at supernova remnant shocks. We show that acceleration up to PeV energies is problematic in all the scenarios considered. This implies that either a different (more efficient) mechanism of field amplification operates at supernova remnant shocks, or that the sources of galactic cosmic rays in the PeV energy range should be searched somewhere else.