Abstract
The harmonics field effect of a planar undulator on free-electron laser (FEL) harmonic generation has been analyzed. For both the linear case and the nonlinear case, the harmonic fraction of the radiation can be characterized by the coupling coefficients. The modification of the coupling coefficients is given when the third harmonics magnetic field component exists, thus the enhancement of the harmonic radiation can be predicted. The numerical results show that with the third harmonics magnetic field component that has the opposite sign to the fundamental, the intensity of third-harmonic radiation can be increased distinctly for both the small signal gain and the nonlinear harmonic generation. The increase is larger for the smaller undulator deflecting parameter.
Highlights
Using the higher harmonic is a way of free-electron laser (FEL) developing towards the shorter wavelength ranges [1,2,3,4]
The results reveal that the harmonic coupling coefficients and, the harmonic emission are enhanced when Bu3 has an opposite sign to Bu1, and are suppressed when the magnetic fields have the same sign (Fig. 1)
We have analyzed the effects of the undulator harmonics field on the coupling coefficients and FEL harmonic generation
Summary
Using the higher harmonic is a way of free-electron laser (FEL) developing towards the shorter wavelength ranges [1,2,3,4]. For a planar undulator with an ideal sinusoidal periodic magnetic field, the electrons radiate at odd harmonics on axis due to their nonuniform axial motion. The magnetic field is nonsinusoidal and with harmonics field components, that has effects on the harmonic radiation. In the hybrid permanent magnet undulator of the Shanghai deep ultraviolet freeelectron laser source [5], the third-harmonic field is less than 1% of the fundamental field. For a standard Halbachtype pure permanent magnet undulator, which has four magnetic blocks per period, the third-harmonic field may be even weaker. Ratios of the third harmonics magnetic field to the fundamental magnetic field approaching 30% have been measured experimentally by Halbach [9]. We analyze the effect of undulator harmonics field on FEL harmonic generation, the case of third harmonics magnetic field is considered specially
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