  The modeling of gamma-ray burst afterglow emission bears witness to strong
electron heating in the precursor of Weibel-mediated, relativistic
collisionless shock waves propagating in unmagnetized electron-ion plasmas. In
this Letter, we propose a theoretical model, which describes electron heating
via a Joule-like process caused by pitch-angle scattering in the decelerating,
self-induced microturbulence and the coherent charge-separation field induced
by the difference in inertia between electrons and ions. The emergence of this
electric field across the precursor of electron-ion shocks is confirmed by
large-scale particle-in-cell (PIC) simulations. Integrating the model using a
Monte Carlo-Poisson method, we compare the main observables to the PIC
simulations to conclude that the above mechanism can indeed account for the
bulk of electron heating.

High Energy Astrophysical Phenomena;Plasma Physics