Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks

TL;DR

This study investigates the long-term behavior of magnetic turbulence generated by relativistic collisionless shocks, revealing that magnetic fields decay over time and are unlikely to persist downstream, impacting models of gamma-ray burst emissions.

Contribution

The paper provides the first detailed analysis of the decay of magnetic turbulence in relativistic shocks using simulations and kinetic theory, showing magnetic fields do not sustain downstream.

Findings

Magnetic turbulence is highly intermittent and nonpropagating.

Magnetic energy decays approximately as $( ext{frequency} imes t)^{-1}$ over time.

Persistent downstream magnetic fields are unlikely in unmagnetized relativistic shocks.

Abstract

We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic $e^+e^-$ shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, nonpropagating, and decaying. Using linear kinetic theory, we find a simple analytic form for these damping rates. Our theory predicts that overall magnetic energy decays like $(\omega_p t)^{-q}$ with $q \sim 1$, which compares favorably with simulations, but predicts overly rapid damping of short wavelength modes. Magnetic trapping of particles within the magnetic structures may be the origin of this discrepancy. We conclude that initially unmagnetized relativistic shocks in electron-positron plasmas are unable to form persistent downstream magnetic fields. These results put interesting constraints on synchrotron models for the prompt and afterglow emission from GRBs.