本文应用Nadey定理对两维摇摆场自由电子激光的谐波特性进行了研究。导出了这种新型摇摆场结构自由电子激光高次谐波的自发辐射功率密度和小信号增益公式。以及电子与辐射场的耦合系数的表达式。计算结果表明,采用两维摇摆场可以增强电子与辐射场之间的耦合,提高谐波的辐射强度和增益。而且在某些条件下,在轴上既可获得奇次谐波又可获得偶次谐波。

We analyzed the harmonic property of the two-dimensional undulator FEL by using Madey' s theorem. We have derived the formulas of harmonic spontaneous emission power density, small signal gain of this undulator FEL and the coupling coefficients between the electrons and the radiation field. From the numerical calculation results we came to the conclusions that by utilizing the two-dimensional undulator, we can enhance the coupling between the electrons and the radiation field, and hence increase the harmonic spontaneous emission power density and gain. Furthermore, under certain conditions we can not only obtain odd but also even harmonic radiations on the axis.