Spatio-temporal dynamics of Free-Electron Lasers

We present a combined experimental/theoretical study of the storage-ring free-electron laser (FEL) spatio-temporal dynamics, and concentrate in particular on the first steps of the destabilisation process occuring when the drift velocity is increased. We show that the first step of the destabilization is associated with the appearance of spectro-temporal defects, recalling the Eckhaus-type phase slips. Finally we show that the main features of the instability are preserved in simple Ginzburg-Landau equations with advection, implying that we can expect this scenario to occur in a large range of systems.