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We present numerical simulations of the magnetic field turbulence in collisionless electron-positron plasma with continuous injection of new pairs, which maintains anisotropy in the particle distribution over long time. With these simulations we follow evolution of a small (and therefore uniform) region in the fluid comoving frame modelling generation and decay of the magnetic field in shocks, where 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 magnetic field build-up is consistent with development of Weibel instability. However, the long-term injection of anisotropic pairs in the upstream leads to formation of large-scale structures in the magnetic field, while the 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 timescale approximately equal to 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. Generation of the long-lived magnetic field in relativistic collisionless shocks with injection-modified upstream explains how they can efficiently produce the synchrotron radiation in Gamma-Ray Bursts.

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The emergence of a density bump at the front of a collisionless electrostatic shock wave have been observed experimentally during the ablation of an aluminium foil by a femtosecond laser pulse. We have performed numerical simulations of the dynamics of this phenomena developing alongside the generation of a package of ion-acoustic waves, exposed to a continual flow of energetic electrons, in a collisionless plasma. We present the physical interpretation of the observed effects and show that the bump consists of transit particles, namely, the accelerated ions from the dense plasma layer, and the ions from the diluted background plasma, formed by a nanosecond laser prepulse during the ablation.