Self-consistent harmonic generation in storage ring FELs

We explore the self-induced harmonic generation in Storage Ring Optical Klystron (SR OK) FEL devices. We use a numerical code which accounts for the SR OK FEL longitudinal dynamics, includes the laser pulse propagation, and gives an accurate image of the phenomenology of instabilities associated with the laser–electron beam interplay. The coherent harmonic generation evolution is developed using the bunching parameter theory. The analysis we develop yields the turn-by-turn evolution of the harmonics and provides an accurate physical insight into their dependence on the intracavity laser power. The results obtained with this code are considered with mainly a Q-switched configuration evaluated for an Elettra-like facility.