Magnetic Field Saturation of the Ion Weibel Instability in Interpenetrating Relativistic Plasmas

The time evolution and saturation of the Weibel instability at the ion Alfven current are presented by ab initio particle-in-cell (PIC) simulations. We found that the ion Weibel current in three-dimensional (3D) simulations could evolve into the Alfven current where the magnetic field energy is sustained at 1.5% of the initial beam kinetic energy. The current filaments are no longer isolated at saturation, but rather connected to each other to form a network structure. Electrons are continuously heated during the coalescence of the filaments, which is crucial for obtaining sustained magnetic fields with much stronger levels than with two-dimensional (2D) simulations. The results highlight again the importance of the Weibel instability in generating magnetic fields in laboratory, astrophysical, and cosmological situations.