Since the electromagnetic energy gained by the laser wave in a free-electron laser (FEL) is transferred from the kinetic energy loss of a relativistic electron beam, the stability of electron motion is one of the key factors that affect FEL performance. In this paper the stability of electron motion is compared for different focusing regimes. It is demonstrated that the natural focusing regime of a three-dimensional wiggler is easily broken by the self-field of the electron beam. The magnetic focusing regime of an axial guide magnetic field is based on the superposition of a strong Larmor rotation on the transverse quiver motion of the electrons, while the electric focusing regime of an ion-channel guiding field generates an electric force to counteract the divergent effect of the beam self-field. In comparison with the magnetic focusing regime of an external magnetic system, the electric focusing regime of an ion-channel guiding field may yield smaller instantaneous Larmor radius and slighter Larmor-centre deviation from the axis and provide better motion stability.
Based on the conservation of particle number, analytical expressions of the Gaussian-profile density and self-fields of the equilibrium electron beam in a free-electron laser are deduced in terms of the macroscopic design parameters. Compared to the Gaussian-profile model, both the particle distribution and self-fields effect of the equilibrium electrons are overestimated by the uniform-profile model. It is demonstrated by experimental observation that the Gaussianprofile model is more coincident with the actual fact of the equilibrium electron beam than the uniform-profile model.
Yu-Pin(吉驭嫔) a) , Wang Shi-Jian(王时建) a) , Xu Jing-Yue(徐竟跃) a) , Xu Yong-Gen(徐勇根) a) , Liu Xiao-Xu(刘晓旭) a) , Lu Hong(卢 宏) a) , Huang Xiao-Li(黄小莉) b) , and Zhang Shi-Chang(张世昌) a) †
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