We describe the quantum initiation for free-electron lasers and derive the collective instability threshold starting from the electron position and the momentum quantum fluctuations. We obtain the Glauber distribution P(α) for the field, that is, a displaced Gaussian, which represents the superposition of a coherent field (stimulated emission) and an incoherent one (spontaneous emission). We define and discuss the concept of superradiance for free-electron lasers, both in a classical framework and at a quantum statistical level, stating the conditions under which the effect should be observed.
© 1985 Optical Society of America
Rodolfo Bonifacio and Federico Casagrande, "Classical and quantum treatment of amplifier and superradiant free-electron laser dynamics," J. Opt. Soc. Am. B 2, 250-258 (1985)