The Langmuir limit, defined by B. D. Langmuir, was derived from Lambert’s law. For convex cathode or curved trajectories, beams with brightness higher than the Langmuir limit are obtainable. Measured brightness varies dramatically when we vary the excitation in the first lens of a system consisting of an electron gun and two magnetic lenses. The ratios of maximum to minimum brightness were measured as 717, 403, and 310 for beam energies of 10, 20, and 30 keV, respectively. These results indicate that the brightness was not conserved when lens excitation was varied. The maximum brightness for beam energies of 10, 20, and 30 keV were observed to be, respectively, 143, 208, and 92.1 times higher than the Langmuir limit.

中文翻译：

---

亮度与镜片激发的关系

BD Langmuir定义的Langmuir极限是根据朗伯定律得出的。对于凸形阴极或弯曲轨迹，可以获得亮度高于Langmuir极限的光束。当我们改变由电子枪和两个磁性透镜组成的系统的第一个透镜的激励时，测得的亮度会发生巨大变化。光束能量分别为10、20和30 keV时，最大亮度与最小亮度之比分别为717、403和310。这些结果表明，当改变透镜激励时，亮度不是守恒的。观察到光束能量的最大亮度分别为10、20和30 keV，比Langmuir极限高143、208和92.1倍。