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随着真空电子器件及所用电子注尺寸的减小,发射度效应成为器件设计过程中需要考虑的重要因素之一。圆孔膜片透镜是组成真空电子器件的一种基本元件,本文通过理论推导获得了考虑电子注发射度效应的圆孔膜片透镜焦距公式。首先基于圆孔膜片透镜电位分布,对透镜厚度进行了界定。随后利用透镜区电子注边缘电子的径向动力学方程推导了电子的傍轴轨迹方程,通过对该方程的数学变换获得了考虑电子注发射度效应的圆孔膜片透镜焦距公式。最后以平行圆柱流Pierce枪阳孔为例,分析了典型强流细束电子注不同导流系数、发射度和半径下透镜焦距的变化,与经验修正结果符合较好。
With the decrease of vacuum electron devices and the size of electron injection used, the emissivity effect becomes one of the important factors to be considered in the device design process. Aperture diaphragm lens is a basic component of the vacuum electron device. In this paper, the focal length formula of the circular diaphragm diaphragm considering the effect of electron injection is deduced theoretically. First of all, the thickness of the lens is defined based on the distribution of the aperture of the diaphragm diaphragm. Then, the electron paraxial trajectory equation was deduced by using the radial kinetic equation of electron injection edge electron in the lens region. The formula of the focal length of the circular aperture diaphragm lens was obtained by mathematical transformation of the equation. Finally, taking the pierce hole of parallel cylinder flow as an example, the variation of focal length of lens under different flow conductivity, emissivity and radius is analyzed, which is in good agreement with the empirical results.