Combination of high efficiency and high increment in an FEL by profiling the inertial electron-bunching parameter

It is noted that it is advantageous to have a high value of the bunching parameter in the input section of a free-electron-laser amplifier and a low value of this parameter in the output section. As a result, the input section provides for a high linear gain while the output section provides for efficient energy extraction from the electron beam. It is shown that if the increment of the input section is sufficiently high (so that the scatter of beam parameters does not have a significant effect on the linear interaction regime) the further effect of the scatter is not all that significant for the deceleration section either in the case when a well-bunched beam and a wave of relatively high amplitude are inputted to this section.