Survival of Weibel-generated magnetic fields downstream of relativistic shocks
In plain words
Shocks in nearly unmagnetized relativistic plasma, as in gamma-ray burst afterglows, create magnetic fields through an instability that bunches the plasma current into filaments. Simulations show these fields fade quickly, yet the observed emission needs them to persist far behind the shock.
Precise statement
In relativistic unmagnetized or weakly magnetized ($\sigma$ below about 1e-3) electron-positron and electron-ion shocks, the Weibel (current-filamentation) instability generates fields with energy fraction $\epsilon_B\sim0.01\ \text{to}\ 0.1$ near the shock, which decay within about 1e2 to 1e3 skin depths $c/\omega_p$ in particle-in-cell simulations. Determine whether self-consistent particle acceleration and upstream precursor fields sustain $\epsilon_B$ of 1e-5 to 1e-2 over distances many orders of magnitude larger, as afterglow modeling infers, and give $\epsilon_B$ versus distance downstream. An answer is a derived decay law validated by long particle-in-cell runs.
What would settle it
Particle-in-cell simulations long enough to include high-energy particle feedback, matched by an analytic decay law that can be extrapolated to emission-region scales.
Status in the literature
Field decay downstream of relativistic Weibel-mediated pair shocks was quantified by Chang, Spitkovsky and Arons (2008, https://doi.org/10.1086/524764); the far-downstream field level is still unresolved.