Ginzburg-landau model and single-mode operation of a free-electron laser oscillator

It is shown that the radiation field in a long-pulse, low-gain free-electron laser oscillator obeys the complex Ginzburg-Landau equation. The question of single-mode operation is investigated by analysis and simulation, and the results are compared with experiments at the University of California at Santa Barbara, as well as the Dutch fusion free-electron-maser experiment. It is shown that the intervention of a frequency-dependent reflection coefficient can facilitate the realization of single-mode operation.