Impact of radiator length in the emitted power for a high gain harmonic generation free-electron laser

We present a numerical study that characterizes the dependence on the radiator length of the output power produced by a free-electron laser (FEL) operated in the high gain harmonic generation (HGHG) configuration. Using the main parameters of the FERMI@Elettra FEL, numerical simulations of the FEL process have been performed for different lengths of the radiator. Our results show that in the case of HGHG the achievable output power has a dependence on the radiator length that is linear. The impact of the electron beam parameters on the achievable maximum power vs radiator length dependence is also studied. A normalization of the results to the FEL saturation power and to the FEL gain length shows that this dependence can be expressed by a universal linear equation that, in some conditions, is independent on the electron beam current and brightness. The reported results could be useful for the design of future FELs based on the HGHG scheme and could be used for a quick estimate of the best undulator length