  In this paper, we report our recent findings on the relativistic Weibel
instability and its nonlinear saturation by performing numerical simulations of
collisionless plasmas. Analysis of the obtained numerical results revealed that
the nonlinear phase of the Weibel instability can be described by
characteristic phases based on the Weibel filaments' current density in terms
of particle and Alfv\'en limit currents. We also analyzed the relativistic kink
instability based on the energy principle in the magnetohydrodynamic (MHD)
regime, and found that the Weibel filaments do not suffer from the kink-type
instability in the MHD regime up to 1000 $\omega_{p,i}^{-1}$. This finding
allowed a magnetic field to be sustained by relativistic Weibel instability
that was stable enough to be a seed for MHD dynamos.
