Merging of Super-Alfvénic Current Filaments during Collisionless Weibel Instability of Relativistic Electron Beams

The theoretical framework predicting the long-term evolution, structure, and coalescence energetics of current filaments during the Weibel instability of an electron beam in a collisionless plasma is developed. We emphasize the nonlinear stage of the instability, during which the beam density of filaments increases to the background ion density, and the ambient plasma electrons are fully expelled from the filaments. Our analytic and numerical results demonstrate that the beam filaments can carry super-Alfvénic currents and develop hollow-current density profiles. This explains why the initially increasing magnetic field energy eventually decreases during the late stage of the instability.