PIC Simulations of the Temperature Anisotropy-Driven Weibel Instability: Analyzing the perpendicular mode

TL;DR

This paper uses 2D PIC simulations to analyze the temperature anisotropy-driven Weibel instability, revealing nonlinear electric field growth and the importance of magnetic stress tensor effects in a 2D setting.

Contribution

It provides new insights into the nonlinear electric field development and magnetic stress tensor role in the 2D Weibel instability, extending previous 1D analyses.

Findings

Exponential magnetic field growth matches linear theory predictions.

Electric fields grow during saturation, not fully explained by linear theory.

Eddy currents enable the growth of a third magnetic field component.

Abstract

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.