Postsaturation dynamics and superluminal propagation of a superradiant spike in a free-electron laser amplifier

We study the dynamics of an isolated spike of radiation in superradiant regime. We show that conditions exist where the pulse moves with a group velocity larger than the velocity of light in vacuum and is followed by a pedestal resulting from a complex postsaturation dynamics. The tail is constituted by a train of subpulses with both transverse and longitudinal coherence and decaying amplitudes. We analyze the dynamical conditions leading to the formation of the main pulse and the tail. We study the correlation of the tail structure with the longitudinal phase space of the electrons, and provide a recipe to partially suppress this tail.