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Analysis of Three‐Dimensional Motion of Relativistic Electrons in Ion‐Focused Electrostatic System

Three‐dimensional motion of relativistic electrons in ion‐focused electrostatic system, which is the basis of investigating the ion‐channel electron cyclotron maser (ICECM) or circular polarized ion‐channel laser (CPICL), is analyzed through nonlinear numerical simulation. The results show that the projection of electron orbit in cross‐section is, in general, a precessing ellipse with a center on the axis of the ion‐channel in a cylindrical ion‐focuse electrostatic system. When injection electrons satisfy a specific condition, the electrons can have a steady circular orbit. The effect of relativistic factor on electrons' motion is discussed. Using the perturbation method, the eigenfrequency of this system is derived as Equation \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {4 - \beta _ \bot ^2 } \omega _0 $\end{document} where wo is the cyclotron frequency of the electrons. This implies that there may exist a new kind of instability in ICECM or CPICL.