  The growth and saturation of magnetic fields due to the Weibel instability
(WI) have important implications for laboratory and astrophysical plasmas, and
this has drawn significant interest recently. Since the WI can generate a large
magnetic field from no initial field, the maximum magnitudes achieved can have
significant consequences for a number of applications. Hence, an understanding
of the detailed dynamics driving the nonlinear saturation of the WI is
important. This work considers the nonlinear saturation of the WI when
counter-streaming populations of initially unmagnetized electrons are perturbed
by a magnetic field oriented perpendicular to the direction of streaming.
Previous works have found magnetic trapping to be important and connected
electron skin depth spatial scales to the nonlinear saturation of the WI. 2
Results presented in this work are consistent with these findings for a
high-temperature case. However, using a high-order continuum kinetic simulation
tool, this work demonstrates that, when the electron populations are colder, a
significant electrostatic potential develops that works with the magnetic field
to create potential wells. The electrostatic field develops due to transverse
flows induced by the WI, and in some cases is strengthened by a secondary
instability. This field plays a key role in saturation of the WI for colder
populations. The role of the electrostatic potential in Weibel instability
saturation has not been studied in detail previously.
