Matrix model for collective phenomena in electron beam’s longitudinal phase space

The possibility to predict, characterize and minimize the presence of spurious harmonic content in the longitudinal profile of high brightness electron beams, namely the microbunching instability, has become vital to ensure accurate modeling and reliable operation of radiofrequency and plasma-based linear accelerators such as those driving free-electron lasers. Recently, the impact of intrabeam scattering (IBS) on the instability has been experimentally demonstrated by the authors. This work complements that experimental study by extending existing theories in a self-consistent, piece-wise calculation of IBS in single pass linacs and multi-bend transfer lines. New expressions for the IBS are introduced in two different semi-analytical models of microbunching. The accuracy of the proposed models and the range of beam parameters to which they apply is discussed. The overall modeling turns out to be a fast comprehensive tool for the optimization of linac-driven free-electron lasers.