The nonlinear interaction between two resonant waves in a waveguide free-electron laser

We extend numerical analysis investigating the waveguide parameter dependency of the two resonant frequencies at the small-signal gain regime in a waveguide free-electron laser to the case that there exists a nonlinear coupling. The properties of the nonlinear interaction between the two resonant waves, one with higher frequency and positive slippage and the another one with lower frequency and negative slippage, are numerically investigated in the high gain regime. The results of numerical work with a set of partial differential equations describing the space and time interaction of the two resonant waves are analyzed.