Abstract
The effect of prebunching of the electron beam and tapering of the wiggler amplitude on the harmonic upconversion in free-electron laser amplifier is studied in three dimensions. A set of coupled nonlinear first-order differential equations that describe the three-dimensional simulation of the system is solved numerically. This set of equation describes self-consistently the longitudinal spatial dependence of radiation waists, curvatures, and amplitudes together with the evaluation of the electron beam. The analysis is related to extreme ultraviolet and x-ray emission. In addition to uniform beam, prebunched electron beam has also been studied. The effect of sinusoidal distribution of entry times for the electron beam on the evolution of radiation is compared with uniform distribution. It is shown that prebunching reduces the saturation length substantially. For efficiency enhancement, the wiggler is set to decrease linearly when the radiation of the third harmonic saturates. The optimum starting point and the slope of tapering of the amplitude of the wiggler are found by a successive run of the code. It was found that tapering can increase the saturated power of the third harmonic considerably.
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