Lethargy of laser oscillations and supermodes in free-electron lasers. II. Quantitative analysis

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Abstract
In this paper we use a recently suggested analytical solution of the pulse propagation equation in free-electron lasers (FEL) to get further information on the lethargy and on the velocity of propagation of the optical packet. We also introduce a refractive index for the FEL interaction. Finally, the supermodes relevant to the regime of long electron bunch are found analytically and a comparison with earlier numerical results is carried out.