FULLY QUANTIZED MANY PARTICLE THEORY OF A FREE-ELECTRON LASER

We investigate the standard free-electron laser in the small signal, cold beam regime using a fully quantized approach which has been employed earlier in the one electron case. The method as presented relies on the many-particle Hamiltonian with a classical wiggler field transformed to a moving frame, but could also be used for more general field configurations in the lab frame. Although we neglect direct electron-electron interactions, many particle effects still show up, because the radiation emitted by one electron interacts with the other ones. We evaluate the time-evolution operator for the electron photon states in the interaction picture in an approximation which takes linear changes in the electron momentum into account. Our main results are : gross features of the amplification like gain and spread are virtually without many-particle effects. These effects are mainly important in the case of spontaneous emission. For a sufficiently high current, the build-up of the laser field from vacuum is enhanced by amplified spontaneous emission, which shifts the center of the spontaneous line shape towards positive gain. Spontaneous radiation from one electron is essentially coherent, apart from slight deviations from Poisson statistics which lead to photon-bunching on the positive and antibunching on the negative gain side. In contrast, spontaneous radiation from several electrons is always incoherent to such a degree that it masks the above-mentioned one-particle effect. Squeezing is obtained for positive gain independent of the number of electrons. However, due to some idealizations used in the model, it is uncertain whether this applies to a physically realizable situation