The interaction of high- and low-frequency waves in a free electronlaser

When a free electron laser (FEL) interaction occurs inside a waveguide, there are two possible operating frequencies at the two intersections of the beam line with the waveguide dispersion curve. Using a one-dimensional model valid for a low-gain oscillator, the mode competition between the high- and low-frequency waves is studied. It is found that the low-frequency wave can be nonlinearly suppressed, even when its linear growth rate is positive. When the frequency ratio is two, phase locking occurs and the nonlinear gain of the low-frequency wave can exceed its linear growth rate