Coupled-wave theory of FEL sidebands in a waveguide

Free electron laser (FEL) sidebands in waveguides are studied using a set of coupled-wave equations. Using a separate wave equation for each frequency to be studied allows one to correctly include the effects of dispersion, since each frequency evolves with a different velocity. Within the coupled-wave description, the particles and fields evolve as a set of coupled pendulums. Since more than one frequency in a waveguide can move at the same phase velocity, it is possible for additional sideband peaks to form in a waveguide. A variety of three-wave and four-wave interactions are possible, and some combinations of waves are unstable and lead to sideband growth. A dispersion analysis is performed and used to predict the sideband growth rate. This analysis agrees well with a computer simulation designed to perform FEL simulations in a dispersive waveguide. It is shown that the upper and lower branches of the sideband spectrum are created by different physical processes and that the coupling between the various possible waves can explain all the features of a complicated sideband spectrum