One mode nonlinear regime of Weibel instability in a plasma with anisotropic temperature

An analytical solution is found to the vortex electron anisotropic hydrodynamic equations which describe the nonlinear evolution of the long wavelength Weibel instability. The presented analytical approach shows that the long wavelength Weibel instability saturates without a decrease in the temperature anisotropy in the one mode regime due to the rotation of the anisotropy axes. The generated magnetic field is circular polarized and its amplitude varies periodically in time.