Evolution of three-dimensional Relativistic Ion Weibel Instability: Competition with Kink Instability

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.