Electromagnetic Instabilities, Filamentation, and Focusing of Relativistic Electron Beams

We report nonlinear studies of the Weibel instability of a relativistic electron beam in a plasma. If $n_b\ll n_p$, the beam splits into self-pinched filaments at density $n_p$. These filaments then recombine into a single dense beam, from which the return current is expelled. The ratio of final magnetic to final streaming energy is $O(\frac{\nu }{\gamma )}$, and significant plasma heating occurs.