Nonlinear pulse evolution in seeded free-electron laser amplifiers and in free-electron laser cascades

The advances in laser technology have made available very short and intense laser pulses which can be used to seed a high-gain single-pass free-electron laser (FEL) amplifier. With these seed pulses, a regime of the FEL interaction where the radiation evolution is simultaneously dominated by nonlinear effects (saturation) and time-dependent effects (slippage) can be explored. This regime is characterized by the propagation of a solitary wavelike pulse where the power of the optical wave grows quadratically with time, its pulse length decreases and the spectral bandwidth increases. We analyze the interplay between the field and particle dynamics of this propagation regime which was studied before and termed super-radiance. Furthermore we analyze the properties of the strong higher-order harmonic emission from this wave and its behavior when propagating in a cascade FEL. The super-radiant pulse is indeed capable of passing through the stages of a cascade FEL and to regenerate itself at the wavelength of the higher-order harmonic. The optical pulse obtained is shorter than a cooperation length and is strongly chirped in frequency, thus allowing further longitudinal compression down to the attosecond time scale