Evolution of magnetic field in a weakly relativistic counterstreaming inhomogeneouse(-)/e(+)plasmas

The nonlinear evolution of electron Weibel instability in a symmetric, counterstream, unmagnetized electron-positrone(-)/e(+)plasmas is studied by a 2D particle-in-cell (PIC) method. The magnetic field is produced and amplified by the Weibel instability, which extracts energy from the plasma anisotropy. A weakly relativistic drift velocity of 0.5cis considered for two counterstreaminge(-)/e(+)plasma flows. Simulations show that in a homogeneouse(-)/e(+)plasma distribution, the magnetic field amplifies exponentially in the linear regime and rapidly decays after saturation. However, in the case of inhomogeneouse(-)/e(+)plasma distribution, the magnetic field re-amplifies at post-saturation. We also find that the amount of magnetic field amplification at post-saturation depends on the strength of the density inhomogeneity of the upstream plasma distribution. The temperature calculation shows that the finite thermal anisotropy exists in the case of an inhomogeneous plasma distribution which leads to the second-stage magnetic field amplification after the first saturation. Such density inhomogeneities are present in a variety of astrophysical sources: for example, in supernova remnants and gamma-ray bursts. Therefore, the present analysis is very useful in understanding these astrophysical sources, where anisotropic density fluctuations are very common in the downstream region of the relativistic shocks and the widely distributed magnetic field