Reinterpretation of Fermi Acceleration of Cosmic Rays in Terms of Ballistic Surfing Acceleration in Supernova Shocks

The applicability of the first-order Fermi mechanism—a cornerstone of the diffusive shock acceleration (DSA) model—in explaining the cosmic ray spectrum is reexamined in light of recent observations from the Magnetospheric Multiscale (MMS) mission at Earth’s bow shock. It is demonstrated that the Fermi and DSA mechanisms lack physical justification and should be replaced by the physically correct ballistic surfing acceleration (BSA) mechanism. The results show that cosmic rays are energized by the convection electric field during ballistic surfing upstream of quasi-perpendicular shocks, independently of internal shock processes. The spectral index of cosmic rays is determined by the magnetic field compression and shock geometry: the acceleration is strongest in perpendicular shocks and vanishes in parallel shocks. The BSA mechanism reproduces the observed spectral indices, with s=−2.7 below the knee at 1016 eV and s=−3 above it. It is suggested that the spectral knee may correspond to particles whose gyroradii are comparable to the characteristic size of shocks in supernova remnants. The acceleration time to reach the knee energy, as predicted by the BSA, is in the order of 500 years.