Wavelength control in high-gain harmonic generation seeded free-electron lasers

The basic theory of free-electron lasers (FELs) indicates that the output wavelength of a seeded FEL operated in the high-gain harmonic generation (HGHG) configuration is determined by the wavelength of the seed laser and light is emitted when the undulators are tuned to an exact harmonics of the seed laser. In a realistic case, when taking into account the electron beam imperfections and the finite bandwidths of the seed and of the amplification process, the output wavelength is influenced by these factors and can deviate from the exact harmonic resonance. These effects are responsible for the small wavelength fluctuations of the FEL pulses but can also be exploited for an accurate FEL wavelength tuning. In this work, we show how the dispersive section, the curvature of the electron beam longitudinal phase-space and frequency pulling can influence the FEL wavelength and can be, in principle, used to control it. Furthermore, we show how one can reconstruct the electron beam longitudinal phase-space from the analysis of the FEL wavelength sensitivity to the seed laser delay with respect to the beam arrival time.