  The saturation mechanism of the Weibel instability is investigated
theoretically by considering the evolution of currents in numerous cylindrical
beams that are generated in the initial stage of the instability. Based on a
physical model of the beams, it is shown that the magnetic field strength
attains a maximum value when the currents in the beams evolve into the Alfven
current and that there exist two saturation regimes. The theoretical prediction
of the magnetic field strength at saturation is in good agreement with the
results of two-dimensional particle-in-cell simulations for a wide range of
initial anisotropy.
