Stochastic electronic motion and high-efficiency free-electron lasers

We consider the asymptotic behavior of high-power Compton free-electron laser oscillators. We observe that the electronic motion along the wiggler presents intrinsic stochasticity. We show that the high efficiency in the broad spectrum regime is due to chaotic diffusion of the electrons toward lower energies, rather than to standard synchrotron motion. We obtain simple estimates of the properties of the system at saturation, which agree with complete numerical simulations. Namely, both efficiency and spectral width are predicted to behave like the square roots of the electronic density, of the cavity quality factor, and of the wiggler length, in such a way that their ratio is a universal brightness of the order of \ensuremath{\surd}3 /2.