Abstract
The dispersion relations of transverse and longitudinal modes in an electromagnetically pumped free-electron laser with an axial guide field are derived exactly, for the one-dimensional case. The modes with positive and negative helicity are distinguished clearly. Analytic expressions for the growth rate, frequency, and wavelength of the modes, in resonance with the beam are obtained in terms of the system parameters. The dependence of the growth rate on these parameters is illustrated for a broad range of values.
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