STOCHASTIC ELECTRONIC MOTION AND HIGH-EFFICIENCY FREE-ELECTRON LASERS

We consider the asymptotic behavior of high-power Compton free-electro n laser oscillators. We observe that the electronic motion along the w iggler presents intrinsic stochasticity. We show that the high efficie ncy in the broad spectrum regime is due to chaotic diffusion of the el ectrons toward lower energies, rather than to standard synchrotron mot ion. We obtain simple estimates of the properties of the system at sat uration, 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 bri ghtness of the order of square-root 3/2.