Higher order harmonic generation in a free-electron laser amplifier operating in the superradiant regime [R.\,H. Dicke, Phys. Rev. 93, 99 (1954).] has been observed. Superradiance has been induced by seeding a single-pass amplifier with the second harmonic of a Ti:sapphire laser, generated in a $\beta${}-Barium borate crystal, at seed intensities comparable to the free-electron laser saturation intensity. Pulse energy and spectral distributions of the harmonics up to the 11th order have been measured and compared with simulations.

This paper investigates the focusing properties of linear magnetic undulators, i.e., devices characterized by weak defocusing properties in the horizontal (wiggling) plane and strongly focusing in the vertical plane. The problem of identifying the conditions that ensure the existence of the electron beam eigenstates in the undulator lattice for a given working point of electron beam energy Eb and resonant wavelength $\lambda${}r is studied. For any given undulator lattice, a bandlike structure is identified defining regions in the (Eb,$\lambda${}r) plane where no periodic matching condition can be found, i.e., it is not possible to transport the electron beam so that optical functions are periodic at lattice boundaries. Some specific cases are discussed for the SPARC FEL undulator.

We present the experimental evidence of the generation of coherent and statistically stable two-color free-electron laser radiation obtained by seeding an electron beam double peaked in energy with a laser pulse single spiked in frequency. The radiation presents two neat spectral lines, with time delay, frequency separation, and relative intensity that can be accurately controlled. The analysis of the emitted radiation shows a temporal coherence and a shot-to-shot regularity in frequency significantly enhanced with respect to the self-amplified spontaneous emission.

We discuss a two-color self-amplified spontaneous emission free-electron laser (FEL) amplifier where the emission is obtained from two orthogonally polarized undulators with different periods and field intensities. Nonaveraged and averaged equations are compared. The two radiations have not only different frequencies, but also different polarizations, while the total length of the device does not change with respect to usual single-color FELs. The wavelengths of two different colors can be changed by choosing different periods, while variation in the magnetic strengths can be used to modify the gain lengths.