Noise in free-electron laser amplifier

The equations of the free-electron laser amplifier are generalized to include higher order modes. The density and velocity fluctuations in the entering electron beam cause noise excitation in the amplifier. The electron beam fluctuations have been studied extensively, both theoretically and experimentally, in traveling wave tubes, and hence the well-tested formalism developed for this purpose is conveniently applied to the present problem. It is found that the fluctuations put a severe constraint on the achievable exponential gain in a proposed Raman-type free-electron laser operating at optical frequencies. A1/\lambda^{3}scaling law is derived.