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Identification of the Amplification Mechanism in the First Free-Electron Laser as Net Stimulated Free-Electron Two-Quantum Stark Emission

We find that the electron phase with respect to the incident laser radiation must be random in the first free-electron laser (FEL) and, hence, the incident laser radiation works as a relaxation force to keep a Maxwellian distribution. We formulate the threshold laser intensity for amplification which agrees with the measured value in the order of magnitude in the first FEL. The magnetic wiggler must produce an electric wiggler whose period is the same as that of the magnetic wiggler. We find that net stimulated free-electron two-quantum Stark (FETQS) emission driven by this electric wiggler is the mechanism responsible for the measured gain and the measured laser intensity at the plateau in the first FEL.