Proton Acceleration with Relativistic Electromagnetic Shock

Understanding the mechanisms behind the extreme energies of cosmic rays is crucial for unraveling fundamental physical processes in astrophysical environments. This study proposes a novel mechanism for accelerating cosmic-ray protons. By examining a high-velocity collision between an astrophysical object and static magnetic fields, the generation of an intense transverse electric field capable of trapping and accelerating protons are find to relativistic energies. Through Hamiltonian analysis, a scaling law that correlates the proton energy is derived to the minimum longitudinal thickness of the relativistic electromagnetic shock required for acceleration. One-dimensional (1D) Particle-In-Cell (PIC) simulations show that an electromagnetic shock driver with a given intensity can accelerate protons from 4.7 MeV to 13 GeV, driven by the transverse electric field induce by the compressed static magnetic field. These results suggest that this mechanism can be experimentally realized in magnetized laser-plasma systems, offering a novel approach for studying astrophysical phenomena in controlled laboratory experiments.