# Nonlinear saturation of the Weibel instability

## TL;DR

This paper investigates the nonlinear saturation mechanisms of the Weibel instability in plasmas, revealing the significant role of electrostatic potentials in colder electron populations, which was previously underexplored.

## Contribution

It demonstrates that electrostatic potentials significantly influence Weibel instability saturation in colder plasmas, expanding understanding beyond magnetic trapping and skin depth effects.

## Key findings

- Electrostatic potential develops in colder electron populations during WI saturation.
- Electrostatic fields can create potential wells that influence saturation dynamics.
- Secondary instabilities can strengthen electrostatic fields affecting WI saturation.

## Abstract

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.