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We present numerical simulations of the magnetic field turbulence incollisionless electron-positron plasma with continuous injection of new pairs,which maintains anisotropy in the particle distribution over long time. {Withthese simulations we follow evolution of a small (and therefore uniform) regionin the fluid comoving frame modelling} generation and decay of the magneticfield in shocks, where the upstream is modified by two-photon pair productiondue to self-absorption of the shock's high-energy radiation. We find that theoverall picture of magnetic field build-up is consistent with development ofWeibel instability. However, the long-term injection of anisotropic pairs inthe upstream leads to formation of large-scale structures in the magneticfield, while the small-scale structures are almost absent. We find that beingamplified at the shock front this magnetic field mostly preserves its largespatial scale and then slowly decays in the downstream on a timescaleapproximately equal to duration of the injection phase. The observed decay ofthe magnetic field is in exceptionally good agreement with predictions of theso-called phase mixing model. Generation of the long-lived magnetic field inrelativistic collisionless shocks with injection-modified upstream explains howthey can efficiently produce the synchrotron radiation in Gamma-Ray Bursts.

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