Electron Energization in Quasi-Parallel Shocks: Test-Particle-Electrons in a Proton Driven Turbulence

In situ observations of energetic particles at the Earth's bow-shock attainable by the satellite missions have long created an opinion that electrons are most efficiently accelerated in a quasi-perpendicular shock geometry. However, shocks that deemed responsible for the production of cosmic ray electrons and their radiation from sources such as supernova remnants are much more powerful and larger than the Earth's bow-shock. Their remote observations suggest that electrons are accelerated very efficiently in the quasi-parallel shocks as well. In this paper we investigate the possibility that protons accelerated to high energies create sufficient wave turbulence necessary for the electron preheating and subsequent injection into the diffusive shock acceleration in a quasi-parallel shock geometry. An additional test-particle-electron population, meant as a low-density addition to the electron core-distribution the hybrid simulation operates on, is introduced. Its purpose is to investigate how these electrons are energized by the "hybrid" electromagnetic field. The reduced spatial dimensionality allowed us to dramatically increase the number of macro-ions per numerical cell and achieve the converged results for the velocity distributions of test-electrons. We discuss the electron preheating mechanisms which can make a significant part of thermal electrons accessible to the ion-driven waves observed in hybrid simulations. We find that the precursor wave field supplied by ions has considerable potential to preheat the electrons before they are shocked at the subshock. Our results indicate that a downstream thermal equilibration of the hot test-electrons and protons does not occur. Instead, the resulting electron-to-proton temperature ratio is a decreasing function of the shock Mach number, $M_\mathrm{A},$ tending to a saturation at high $M_\mathrm{A}.$