PIC simulation of a strong double layer in a nonrelativistic plasma   flow: Electron acceleration to ultrarelativistic speeds
  Two charge- and current neutral plasma beams are modelled with a one-dimensional PIC simulation. The beams are uniform and unbounded. The relative speed between both beams is 0.4c. One beam is composed of electrons and protons and one out of protons and negatively charged oxygen (dust). All species have the temperature 9 keV. A Buneman instability develops between the electrons of the first beam and the protons of the second beam. The wave traps the electrons, which form plasmons. The plasmons couple energy into the ion acoustic waves, which trap the protons of the second beam. A proton phase space hole grows, which develops through its interaction with the oxygen and the heated electrons into a rarefaction pulse. This pulse drives a strong ion acoustic double layer, which accelerates a beam of electrons to about 50 MeV, which is comparable to the proton kinetic energy. The proton distribution eventually evolves into an electrostatic shock. Beams of charged particles moving at such speeds may occur in the foreshock of supernova remnant shocks. This double layer is thus potentially relevant for the electron acceleration (injection) into the diffusive shock acceleration by supernova remnants shocks. 
M E Dieckmann and A Bret