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利用模拟计算机及近似分析两种方法研究了均匀电子束进入周期性磁场形成的轨迹方程,这里的研究主要针对着只对磁场部分屏蔽的理想阴极发出的电子束,并对小幅度和大幅度扇形扩张的两种情形都作了考虑。文中提出了磁场系数α和空间电荷系数β有关的曲线。以前对小幅度扇形扩张下提出的α和β的关系现在表明在大幅度扇形扩张时是不精确的。对没有热速度的电子束的运动在α值小于0.66时得到了稳定的解,同时对α大于0.66的某些值也得到了电子运动的稳定解。
The trajectory equation of uniform electron beam entering the periodic magnetic field is studied by means of simulating computer and approximate analysis. The research here mainly focuses on the electron beam emitted by the ideal cathode which is only partially shielded by the magnetic field. The small and large sector Both cases of expansion have been considered. In this paper, the curve of magnetic field coefficient α and space charge coefficient β is proposed. The previous relationship between α and β proposed for small amplitude fan expansion now shows that in the case of large fan expansion it is inaccurate. For electron beams with no thermal velocity, a stable solution is obtained for alpha values less than 0.66, while some values for alpha greater than 0.66 also give a stable solution to the electron motion.