Spectral behavior of high-power Compton free-electron lasers. I. Broadening and asymptotic equilibrium

We investigate the nonlinear spectral behavior of high-current Compton free-electron lasers. For that purpose, a multifrequency model is developed in the continuous-beam limit. Both numerical simulations and perturbation expansions allow us to point out a mechanism leading to a broadening of the spectrum. Then, we analyze the saturation and the asymptotic behavior of the spectrum corresponding to a large number of round-trips in the oscillator configuration. The existence of a stable asymptotic regime presenting strong chaotic features is predicted. In this regime, efficiency is provided by a diffusionlike behavior of the electrons rather than a standard synchrotron motion. Consequently, we show that the efficiency and the spectral width can be evaluated simply and in closed form: they behave like the square roots of the electron density, of the wiggler length, and of the cavity quality factor.