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We discuss a harmonic lasing free-electron laser amplifier, in which the fundamental resonance of the second wiggler is the third harmonic of the first wiggler in order to generate
extreme ultraviolet radiation. A set of coupled nonlinear first-order differential equations describing the nonlinear evolution of the system is solved numerically by MEDUSA code and slippage is ignored. In this paper, we compare nonaveraged and averaged equations. Remarkable
agreement is found between averaged and nonaveraged simulation for the evolution of the third
harmonic. Thermal effect in form of the longitudinal velocity spread is also investigated. For efficiency enhancement, the second wiggler field 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 is found that tapering can increase the saturated power of the third harmonic considerably. In order to reduce the length of
the wiggler, prebunched electron beam is considered.
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