Electron heating in a relativistic, weibel-unstable plasma

The dynamics of two initially unmagnetized relativistic counter-streaming homogeneous ionelectron plasma beams are simulated in two dimensions using the particle-in-cell (PIC) method. It is shown that current filaments, which form due to the Weibel instability, develop a large scale longitudinal electric field in the direction opposite to the current carried by the filaments as predicted by theory. This field, which is partially inductive and partially electrostatic, is identified as the main source of net electron acceleration, greatly exceeding that due to magnetic field decay at later stages. The transverse electric field, though larger than the longitudinal one, is shown to play a smaller role in heating electrons, contrary to previous claims.