  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.
