Early-out of Equilibrium Beam-Plasma Evolution

We solve analytically the out-of equilibrium initial stage that follows the injection of a radially finite electron beam into a plasma at rest and test it against particle-in-cell simulations. For initial large beam edge gradients and moderate beam radius w.r.t skin depth the electron beam is seen to evolve into a ring structure. For low enough transverse temperatures, filamentation instability proceeds and saturates when transverse isotropy is reached. This analysis agrees with very recent experimental beam transverse observations.