Quantum Theory of the Free-Electron Laser.

A fully quantum-mechanical theory of the free -electron laser (FEL) is presented. The theory is developed in the laboratory frame (in contrast with most previous quantum treatments), starting from Quantum Electrodynamics, yet the final result is formally simple. The theory is applied to the study of the start-up and the growth of coherence, the quantum corrections to the gain and saturation, and the photon statistics. To study the start-up problem, a multimode theory is used; equations are derived giving the change in the first-order correlation function for the radiation field after one pass through the cavity in the linear regime, which show how a coherent field evolves from spontaneous emission. The theory is one-dimensional: diffraction and other three-dimensional effects are therefore ignored. As regards the photon statistics, it is shown that, to a very good approximation, the intensity fluctuations of the FEL radiation are those characteristic of thermal (or "chaotic") light, in the linear regime, that is, until saturation becomes important. It is also shown that perturbation theory is not appropriate to the study of the photon statistics at saturation. Throughout, the results presented include quantum corrections to all orders, as well as corrections arising from the discrete nature of the electron current. The possibility of actually operating an FEL in the "quantum regime", where the classical theory no longer holds, is discussed at length in the context of the proposed use of an FEL with an electromagnetic-wave wiggler to generate VUV or soft x-ray radiation. The feasibility of these devices is studied, taking into account electron beam characteristics such as energy spread and emittance. The effect that diffraction of a very high-power wiggler beam would have on the FEL gain is also studied here at length for the first time. The conclusion is that the proposed devices are at the edge of what could be achieved with present day technology.