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 the
M

²
parameter, which is a measure of the size and divergence of the optical beam. We calculate
M

²
in 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 that
M

²
, as expected, is near unity at saturation but increases with the higher order mode content if the interaction proceeds past saturation.