Study of magnetic field evolution by Weibel instability in counter-streaming electron–positron plasma flows

Collisionless shocks are generated via the magnetic field mediated by Weibel instability in astrophysical systems. In this work, by performing particle-in-cell (PIC) simulations, Weibel instability-mediated magnetic field amplification is investigated for initially unmagnetized, spatially uniform, counter-streaming electron–positron (e⁻/e⁺) plasma flows and compared with the magnetic amplification for nonuniform counter-streaming e⁻/e⁺ plasma flows by considering their drift velocity of \(0.5 c\). Our simulation results show that initially, the magnetic field grows exponentially in the linear regime and then decays further after saturation for homogeneous e⁻/e⁺ plasma flows. However, in the case of inhomogeneous counter-streaming e⁻/e⁺ plasma flow, the magnetic field re-amplifies in the post-saturation region after the first saturation. It is found that the amplification magnitude of magnetic field energy in the post-saturation region is related to the density fluctuations for upstream plasma. Our calculations show that temperature anisotropy is the reason behind the second saturation of the magnetic field energy in the case of inhomogeneous plasma distribution. Such inhomogeneous media in astrophysical systems like Gamma-ray bursts are common. Therefore, this study will be useful for understanding collisionless shocks' formation and their effects.