Intensity of Electron Beams

The theories of D. Langmuir and J. R. Pierce on the thermal limitations of electron beam current density have a simple interpretation through geometrical optics and the law of photometric brightness. The brightness law together with Abbe's sine law are sufficient for the design of most electron beams for laboratory experiments. Application of the theory is illustrated for the design of low voltage, high-intensity beams as used in low-energy electron-diffraction experiments.