Electron Trajectories in a Field Emission Microscope

Trajectories of electrons in a field emission microscope have been calculated for the case of a tip and screen taken as confocal hyperboloids of revolution. The calculations were done in prolate spheroidal coordinates by an iterative method utilizing Hamilton's equations. An IBM digital computer has been programmed to accept values for the initial position and momentum of the electron, the tip and screen radii (each measured at the apex), the tip-to-screen distance and the applied voltage. A calculation yields the final values of position and momentum components at the screen as well as the transit time for the electron. The results of the calculation have been used to predict a field emission pattern which is compared with an experimental pattern. Good agreement is obtained without the use of any adjustable parameters.