Particle acceleration in supernova remnants, the Bell-Lucek hypothesis and the cosmic ray "knee"

Young supernova remnants are thought to be the sites where cosmic ray acceleration occurs by the mechanism of diffusive shock acceleration. The maximum energy gained in this process is conventionally extimated to have a value close to, but distinctly below, the knee'' ($\sim 10^{15}$ eV) of the cosmic-ray spectrum. Bell & Lucek (2001) have suggested that the generated cosmic rays simultaneously amplify the magnetic field around the supernova remnant shock to many times its pre-shock value. In this case the acceleration rate may be significantly increased and protons can easily reach energies up to $10^{17}$ eV. We use a simplified’’ box model incorporating the magnetic field amplification suggested by Bell & Lucek to investigate the resulting modifications of the cosmic-ray spectrum. The model predicts a spectral break at high energies, close to the ``knee’’ region, and in good accordance with observations.