Long-term Evolution of Relativistic Unmagnetized Collisionless Shocks

We study a relativistic collisionless electron-positron shock propagating into an unmagnetized ambient medium using 2D particle-in-cell simulations of unprecedented duration and size. The shock generates intermittent magnetic structures of increasingly larger size as the simulation progresses. Toward the end of our simulation, at around 26,000 plasma times, the magnetic coherence scale approaches $\lambda\sim 100$ plasma skin depths, both ahead and behind the shock front. We anticipate a continued growth of $\lambda$ beyond the time span of our simulation, as long as the shock accelerates particles to increasingly higher energies. The post-shock field is concentrated in localized patches, which maintain a local magnetic energy fraction $\varepsilon_B\sim 0.1$. Particles randomly sampling the downstream fields spend most of their time in low field regions ($\varepsilon_B\ll 0.1$), but emit a large fraction of the synchrotron power in the localized patches with strong fields ($\varepsilon_B\sim 0.1$). Our results have important implications for models of gamma-ray burst afterglows.