Self-consistent calculation of spontaneous emission and small-signal gain in high-voltage free-electron lasers

Abstract

Using the Weisskopf–Wigner technique, we develop a self-consistent quantum-electrodynamic (SCQED) theory of spontaneous emission of radiation and single-photon small-signal gain for high-voltage free-electron lasers (FEL’s). For the first time to our knowledge, excellent agreement is obtained between the predictions and the experimental observations simultaneously for line shift, linewidth, and gain. The SCQED theory predicts line shift and broadening caused by quantum-mechanical effects, which are not predicted by the classical or conventional FEL theories but have been observed. Excellent agreement is obtained between the spontaneous-emission spectra predicted by the SCQED theory and the 1980–1981 ACO [ J. Phys. Lett.41, L-549 ( 1980); Free Electron Generators of Coherent Radiation ( Addison–Wesley, Reading, Mass., 1981, 1982), Vols. 7, 8; the Stanford 10.6-μm [ Phys. Rev. Lett.36, 717 ( 1976)]; and the Stanford 3.4-μm [ Phys. Rev. Lett.38, 892 ( 1977)] FEL experimental spectra. This agreement is much better than that of the prediction from the classical or conventional FEL theory, which gives highly noticeable errors. We show that the spontaneous-emission spectrum that is obtained from classical or conventional FEL theories is valid only in the limit of a short undulator that contains a small number of periods. The small-signal gain derived from the SCQED theory is shown to reduce to Colson’s gain formula [ Phys. Lett.64A, 190 ( 1977)] in the classical limit. However, the SCQED theory predicts significant reductions in the small-signal gain that agree well with the ACO gain data [ Opt. Commun.40, 373 ( 1982)] and are not predicted well by Colson’s formula. Because of the nonnegligible finite electron state lifetime, it is discovered that a fundamental physical gain limit exists that is universal to all types of FEL within the limits of the single-photon transition scheme considered (i.e., if multiphoton effects are ignored). Finally, the implications of the theoretically obtained results are discussed for practical conditions of experimental interest. It is shown that under practical experimental conditions quantum effects can be quite important in FEL’s.