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 ${n}_{b}\ensuremath{\ll}{n}_{p}$, 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 $O(\frac{\ensuremath{\nu}}{\ensuremath{\gamma})}$, and significant plasma heating occurs.