Amplification of Weibel instability in the relativistic beam-plasma interactions due to ion streaming

On the basis of a three-dimensional relativistic electromagnetic particle-in-cell (PIC) code, we have analyzed the Weibel instability driven by a relativistic electron-ion beam propagating into an unmagnetized ambient electron-ion plasma. The analysis is focused on the ion contribution in the instability, considering the earliest evolution in shock formation. Simulation results demonstrate that the Weibel instability is responsible for generating and amplifying the small-scale, fluctuating, and dominantly transversal magnetic fields. These magnetic fields deflect particles behind the beam front both perpendicular and parallel to the beam propagation direction. Initially, the incoming electrons respond to field fluctuations growing as the result of the Weibel instability. Therefore, the electron current filaments are generated and the total magnetic energy grows linearly due to the mutual attraction between the filaments, and downstream advection of the magnetic field perturbations. When the magnetic fields become strong enough to deflect the much heavier ions, the ions begin to get involved in the instability. Subsequently, the linear growth of total magnetic energy decreases because of opposite electron-ion currents and topological change in the structure of magnetic fields. The ion current filaments are then merged and magnetic field energy grows more slowly at the expense of the energy stored in ion stream. It has been clearly illustrated that the ion current filaments extend through a larger scale in the longitudinal direction, while extension of the electron filaments is limited. Hence, the ions form current filaments that are the sources of deeply penetrating magnetic fields. The results also reveal that the Weibel instability is further amplified due to the ions streaming, but on a longer time scale. Our simulation predictions are in valid agreement with those reported in the literature.