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

The time evolution and saturation of the Weibel instability at the ion Alfv\'en current are presented by ab initio particle-in-cell simulations. We found that the ion Weibel current in 3D could evolve into the Alfv\'en 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 2D simulations. The results highlight again the importance of the Weibel instability in generating magnetic fields in laboratory, astrophysical, and cosmological situations.