Nonlinear evolution of the Weibel instability of relativistic electron beams

Physics of the long-term evolution of the Weibel instability (WI) of an electron beam propagating through the plasma is described. Several phenomena occurring during the WI are identified: (i) the exponential growth stage resulting in beam breakup into small current filaments; (ii) merger of the small filaments and beam particles' trapping inside them; (iii) filaments' compression and expulsion of the ambient plasma from the filaments; (iv) formation of high-current filaments and their merger. It is shown that during the final stage these beam filaments can carry super-Alfvenic currents and form hollow current density profiles similar to the Hammer-Rostoker equilibrium. This explains why the initially increasing magnetic field energy eventually decreases during the late stage of the instability. Different computational approaches to modeling both collisionless and collisional WI are also described.