Effects of Energy Chirp on Echo-enabled Harmonic Generation Free-electron Lasers∗

Due to the lack of coherent seed at the x-ray wavelengths, a SASE FEL is the most straightforward method to build an x-ray FEL. However, the temporal coherence of a SASE FEL is limited because the process starts from electron shot noise. To overcome this limitation, an ultraviolet seed laser may be used to interact with the electron beam in order to create density modulations at higher harmonics of the laser frequency. The traditional approach for frequency multiplication is the so-called high-gain harmonic generation (HGHG) [1]. Recently, a novel method of harmonic generation using the beam echo effect is proposed in [2] and is studied in details in [3]. The echo-enabled harmonic generation (EEHG) has a remarkable up-frequency conversion efficiency and may drastically simplify the design of seeded, short-wavelength free-electron lasers (FELs). It is largely anticipated that a seeded FEL will be used for the production of relatively long temporally coherent radiation pulses with a narrow bandwidth. This typically requires a very uniform electron bunch with constant current and energy, and specific designs are proposed to generate such a bunch in the accelerator [4]. Nevertheless, residual energy variations due to nonlinearity of the machine or energy modulations due to microbunching instability will be unavoidable and may broaden the bandwidth of such a seeded FEL. In addition, an electron beam with a large energy chirp may be also useful to overcome the sensitivity of the seeded FEL power to electron energy jitters or to control the FEL pulse length. In this paper, we study the dependence of the echo microbunching on the initial energy chirp of the electron beam. We also discuss the EEHG FEL performance in presence of a chirped electron beam or any residual energy modulation created from the upstream accelerator.