Dynamics of longitudinal phase-space modulations in an rf compressor for electron beams

Free-electron lasers operating in the UV or x-ray radiation spectrum require peak beam currents that are generally higher than those obtainable by present electron sources, thus making bunch compression necessary. Compression, however, may heighten the effects of collective forces and degrade the beam quality. In this paper we provide a framework for investigating some of these effects in rf compressors by focusing on the longitudinal dynamics of small-amplitude density perturbations, which have the potential to cause the disruptive appearance of the so-called microbunching instability. We develop a linear theory valid for low-to-moderate compression factors under the assumption of a 1D impedance model of longitudinal space charge and provide validation against macroparticle simulations.