Optical Beam Quality in Free-Electron Lasers

The mode quality of the output of free-electron lasers (FELs) is near the diffraction limit. In this paper, we analyze the optical mode quality in FELs using theM2parameter, which is a measure of the size and divergence of the optical beam. We calculateM2in two ways: 1) by a direct integration over the transverse mode structure and 2) by allowing the mode to expand beyond the wiggler and analyzing the divergence. A numerical analysis is conducted using the MEDUSA simulation code that shows thatM2, as expected, is near unity at saturation but increases with the higher order mode content if the interaction proceeds past saturation.