Theory of a free-electron laser with a Gaussian optical undulator

A theoretical study of the possibility of a free-electron laser in the XUV and soft X-ray region of the spectrum, using a counterpropagaing CO/sub 2/ laser beam as an undulator, is presented. A one-dimensional model is used to evaluate the single-pass power gain of such a device. The detrimental effects due to the energy speed, emittance of the electron beam, and the diffraction of the electromagnetic undulator are explicitly incorporated in the formalism. An oscillator experiment is also considered. The solutions of the optical pulse evolution equation in the weak field, low gain, and long-electron-pulse regimes are all derived.<>