The interaction between low- and high-frequency waves in a waveguide free-electron laser amplifier

We examine the essential physics of the interaction between the downshifted and upshifted radiation fields during a single pass of a waveguide free-electron laser. It is found that after a sufficient period of interaction has elapsed, generally one frequency will predominate over the other. In the case where the lower frequency begins with an infinitesimal amplitude, the outcome may be predicted with a high degree of confidence through a semiempirical formula, given the initial phase velocities and frequency ratio, as well as the initial amplitude and dimensionless current density for the higher frequency. We also discuss an effect in which energy may be exchanged back and forth between the two branches.