Space-charge oscillations in a self-modulated electron beam in multi-undulator free-electron lasers

We examine here the oscillation of electron-beam density perturbations (longitudinal plasma oscillations) produced at the exit of a high-gain free-electron laser (FEL) by the action of the FEL instability. These oscillations, which are analyzed in the case of both a free-space drift and a dispersive section, can degrade the bunching of the beam in the drift between undulator sections in multi-stage FELs. The impact of these oscillations on the gain of an FEL in an undulator following such a drift, as well as the case of an optical klystron is studied.