Collisionless electron-ion shocks in relativistic unmagnetized   jet-ambient interactions: Non-thermal electron injection by double layer
  The course of non-thermal electron ejection in relativistic unmagnetized electron-ion shocks is investigated by performing self-consistent particle-in-cell simulations. The shocks are excited through the injection of relativistic jet into ambient plasma, leading to two distinct shocks (named as the trailing shock and leading shock) and a contact discontinuity. The Weibel-like instabilities heat the electrons up to approximately half of ion kinetic energy. The double layers formed in the trailing and leading edges then accelerated the electrons by the ion kinetic energy. The electron distribution function in the leading edge shows a clear non-thermal power-law tail which contains $\sim1\%$ of electrons and $\sim8\%$ of electron energy. Its power-law index is -2.6. The acceleration efficiency is $\sim23\%$ by number and $\sim50\%$ by energy and the power-law index is -1.8 for electron distribution function in the trailing edge. The effect of the dimensionality is examined by comparing results of 3D simulation with 2D ones. It exhibits that the electron acceleration is more efficient in 2D. 
Kazem Ardaneh, Dongsheng Cai, Ken-Ichi Nishikawa
astro-ph.HE physics.plasm-ph