Magnetic-field generation and amplification in an expanding plasma

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 β ≈ 100), independent of L. The magnetic energy spectra below the electron Larmor radius scale are well fitted by the power law with slope -16/3, as predicted by Schekochihin et al. [Astrophys. J. Suppl. Ser. 182, 310 (2009)].