The free electron laser: A single-particle classical model

Quantum regime of a free-electron laser: relativistic approach

“…However, even for a magnetostatic wiggler we find results [20] analogous to the optical ones, because in its rest frame the electron experiences the wiggler as a counterpropagating wave at approximately the speed of light [13,14].…”

“…(6), and in the phase, Eq. (15), of the Hamiltonian, Eq (13). Classically it can be understood by identifying p µ as an effective longitudinal momentum which contains the effects of the transverse motion of the electron in the wiggler due to the Lorentz force [33].…”

“…To achieve this goal, we have used a nonrelativistic approach in the co-moving Bambini-Renieri frame [13,14]. In contrast, we develop in the present article a fully relativistic model in the laboratory frame and derive within this framework the conditions to enter the quantum regime.…”

The controlling parameters and the laser expression for a wiggler-free free-electron laser

“…Finally, the expression for the radiation field is presented in the small-signal limit. The discussions will be given in the Bambini-Renieri frame 6 in which a nonrelativistic treatment can be used. The space-charge effect is neglected and every physical quantity refers to the Bambini-Renieri frame, except for a particular explanation.…”

On the Quantum Theory of the Free Electron Laser

“…In this Letter we carry out a quantum mechanical calculation starting from the Bambini-Renieri hamiltonian [1] in the Weizsaker-Williams approximation, where the moving frame is such that the frequencies of the wiggler and laser coincide . Recent quantum-mechanical calculations have been performed by Becker et al .…”