Long-Term Evolution of Relativistic Unmagnetized Collisionless Shocks

We study a relativistic collisionless electron-positron shock propagatinginto an unmagnetized ambient medium using 2D particle-in-cell simulations ofunprecedented duration and size. The shock generates intermittent magneticstructures of increasingly larger size as the simulation progresses. Toward theend of our simulation, at around 26,000 plasma times, the magnetic coherencescale approaches $\lambda\sim 100$ plasma skin depths, both ahead and behindthe shock front. We anticipate a continued growth of $\lambda$ beyond the timespan of our simulation, as long as the shock accelerates particles toincreasingly higher energies. The post-shock field is concentrated in localizedpatches, which maintain a local magnetic energy fraction $\varepsilon_B\sim0.1$. Particles randomly sampling the downstream fields spend most of theirtime in low field regions ($\varepsilon_B\ll 0.1$), but emit a large fractionof the synchrotron power in the localized patches with strong fields($\varepsilon_B\sim 0.1$). Our results have important implications for modelsof gamma-ray burst afterglows.