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 not too large beam radius, compared to the electron skin depth, the electron beam is shown to evolve into a ring structure. For low enough transverse temperatures, filamentation instability eventually proceeds and saturates when transverse isotropy is reached. The analysis accounts for the variety of very recent experimental beam transverse observations.
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