Impact of continuous particle injection on generation and decay of the magnetic field in collisionless shocks

We present numerical simulations of the magnetic field turbulence in a collisionless electron–positron plasma with continuous injection of new pairs, which maintains the anisotropy in the particle distribution over a long time. With these simulations, we follow the evolution of a small (and, therefore, uniform) region in the fluid comoving frame to model the generation and decay of the magnetic field in shocks. The upstream is modified by two-photon pair production due to self-absorption of the shock's high-energy radiation. We find that the overall picture of the magnetic field build-up is consistent with the development of Weibel instability. However, the long-term injection of anisotropic pairs in the upstream leads to the formation of large-scale structures in the magnetic field, while small-scale structures are almost absent. We find that being amplified at the shock front, this magnetic field mostly preserves its large spatial scale and then slowly decays in the downstream on a time-scale approximately equal to the duration of the injection phase. The observed decay of the magnetic field is in exceptionally good agreement with predictions of the so-called phase mixing model. The generation of a long-lived magnetic field in relativistic collisionless shocks with an injection-modified upstream explains how they can efficiently produce the synchrotron radiation in gamma-ray bursts.