Magnetic field generation and amplification in an expanding plasma

TL;DR

This paper uses particle-in-cell simulations to explore magnetic field generation in expanding plasmas, revealing a transition from Biermann battery to Weibel instability dominance as system size increases, with detailed spectral analysis.

Contribution

It demonstrates that the Weibel instability becomes the primary magnetic field generator in large plasmas, surpassing the Biermann battery effect, and characterizes the spectral properties of the resulting magnetic fields.

Findings

B ~ d_i/L for system sizes comparable to ion skin depth

Weibel instability dominates for large L/d_i

Magnetic energy spectra follow a -16/3 power law below the electron Larmor radius

Abstract

Particle-in-cell simulations are used to investigate the formation of magnetic fields, B, in plasmas with perpendicular electron density and temperature gradients. For system sizes, L, comparable to the ion skin depth, d_i, it is shown that B ~ d_i/L, consistent with the Biermann battery effect. However, for large L/d_i, it is found that the Weibel instability (due to electron temperature anisotropy) supersedes the Biermann battery as the main producer of B. The Weibel-produced fields saturate at a finite amplitude (plasma \beta \approx 100), independent of L. The magnetic energy spectra below the electron Larmor radius scale is well fitted by power law with slope -16/3, as predicted in Schekochihin et al., Astrophys. J. Suppl. Ser 182, 310 (2009).