Self-consistent studies of electron acceleration to ultrarelativistic energies by upper hybrid waves

When electrons that are trapped by strong electrostatic waves are carried across a magnetic field, the Lorentz force can in principle accelerate them to ultrahigh energies. This wave accelerator known as the electron surfing acceleration is thus a potential generation mechanism for ultrarelativistic electrons at astrophysical shocks. Here, we present for the first time a self-consistent simulation that follows the growth and saturation of strong electrostatic waves that are triggered by proton beams moving at relativistic speeds relative to a background plasma. We find in our simulation that proton beams moving at a Lorentz factor of 7 can accelerate electrons to 1 GeV by means of electron surfing acceleration. Thereafter the wave collapses, and it scatters some electrons to energies in excess of 10 GeV. The plasma charge density modulations give rise to a strong growth of the fast extraordinary ( X) wave in frequency intervals for which its group velocity is comparable to the beam speed.