Microbunching-instability-induced sidebands in a seeded free-electron laser

Measurements of the multishot-averaged, soft x-ray, self-seeding spectrum at the LCLS free-electron laser often have a pedestal-like distribution around the seeded wavelength, which limits the spectral purity and can negatively affect some user applications not employing a post-undulator monochromator. In this paper, we study the origins of such pedestals, focusing on longitudinal phase space modulations produced by the microbunching instability upstream of the free-electron laser (FEL) undulator. We show from theory and numerical simulation that both energy and density modulations can induce sidebands in a high-gain, seeded FEL whose fractional strength typically grows as the square of the undulator length. The results place a tight constraint on the longitudinal phase space uniformity of the electron beam for a seeded FEL, possibly requiring the amplitude of long-wavelength modulations to be much smaller than the typical incoherent energy spread if the output sideband power is to remain only a couple percent or less of the amplified seed power.