Abstract
Space-charge and axial-field effects are discussed for a free-electron laser with an axial-guide magnetic field. It is found that the maximum gain increases with the beam density and gain saturation occurs for high beam density. The laser frequency is upshifted and downshifted in the low and high density cases respectively. The regimes which permit the amplifying effect of the guide field and the stabilities of both the electron trajectories and the electrostatic mode are found. The maximum amplifying coefficient of the guide field is also obtained by using the stability conditions.
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