  An instability driven by the thermal anisotropy of a single electron species
is investigated in a 2D particle-in-cell (PIC) simulation. This instability is
the one considered by Weibel and it differs from the beam driven filamentation
instability. A comparison of the simulation results with analytic theory
provides similar exponential growth rates of the magnetic field during the
linear growth phase of the instability. We observe in accordance with previous
works the growth of electric fields during the saturation phase of the
instability. Some components of this electric field are not accounted for by
the linearized theory. A single-fluid-based theory is used to determine the
source of this nonlinear electric field. It is demonstrated that the magnetic
stress tensor, which vanishes in a 1D geometry, is more important in this
2-dimensional model used here. The electric field grows to an amplitude, which
yields a force on the electrons that is comparable to the magnetic one. The
peak energy density of each magnetic field component in the simulation plane
agrees with previous estimates. Eddy currents develop, which let the amplitude
of the third magnetic field component grow, which is not observed in a 1D
simulation.
