ELECTRON HEATING IN A RELATIVISTIC, WEIBEL-UNSTABLE PLASMA
The dynamics of two initially unmagnetized relativistic counter-streaming homogeneous ion–electron plasma beams are simulated in two dimensions (2D) 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, although larger than the longitudinal field, is shown to play a smaller role in heating electrons, contrary to previous claims. It is found that in one dimension, the electrons become strongly magnetized and are not accelerated beyond their initial kinetic energy. Rather, the heating of the electrons is enhanced by the bending and break up of the filaments, which releases electrons that would otherwise be trapped within a single filament and slow the development of the Weibel instability (i.e., the magnetic field growth) via induction as per Lenz’s law. In 2D simulations, electrons are heated to about one quarter of the initial kinetic energy of ions. The magnetic energy at maximum is about 4%, decaying to less than 1% by the end of the simulation. The ions are found to gradually decelerate until the end of the simulation, by which time they retain a residual anisotropy of less than 10%.