Magnetic field production in an expanding plasma: Biermann or Weibel?

Recent laboratory experiments focusing intense lasers ($\sim kJ$) at solid targets show the production of strong magnetic fields (of order a megaGauss). It is conjectured that these fields arise via the Biermann battery mechanism, due to non-aligned electron density and temperature gradients. We investigate the generation and amplification of such magnetic fields in a kinetic particle-in-cell model, and its dependence on system size, $L$. For moderate system sizes ($L$ $\ga$ $d_i$), we find that the strength of the magnetic fields scales as $1/L$, consistent with their origin being due to the Biermann effect. However, for large $L/d_i$, we discover that the Weibel instability (due to electron temperature anisotropy) supersedes the Biermann battery effect as the main mechanism behind the production of magnetic fields. The Weibel-produced fields, unlike the ones due to Biermann, saturate at a finite amplitude (plasma $\beta\sim 1$) for large $L/d_i$. These results have strong implications for the interpretation of laser-solid interaction experiments. They may also be important to the understanding of the origin of the observed magnetic fields in the universe.