Quasi-linear dynamics of Weibel instability

The quasi-linear dynamics of resonant Weibel mode is discussed. It is found that nonlinear saturation of Weibel mode is accompanied by substantial modification of the distribution function in resonant region. With the growth of the wave amplitude the parabolic bell-like form of the electron distribution function in this region converts into flatter shape, such as parabola of the fourth order. This results in significant weakening of the resonant interaction of the wave with particles. The latter becomes weaker and then becomes adiabatic interaction with the bulk of the plasma. This is similar to the case of Bernstein-Greene-Kruskal (Bernstein et al., 1957) electrostatic waves. The mathematical similarity of the Weibel and magnetic mirror instabilities is discussed.