A simple technique for the accurate determination of electron trajectories

Abstract

This paper describes a simple two-step method for the calculation of electron trajectories. First, the potential distribution within the electrode system is determined by means of a resistance network analog which provides, at each network point, the relative potential within the electrode system. A digital voltmeter displays the potentials to four-digit accuracy. The present resistance network simulates systems of cylindrical symmetry. Although space charge can be included by a method of successive approximations, the analogy has not been extended to magnetic fields. After the potential data are obtained, the electron trajectories can be calculated. The general ray equation is used to determine the change in slope caused by the electric field. The field components are first measured at an assumed initial position and slope. The above calculation is then performed on a printing desk calculator to determine the new position and slope, This process is repeated step-by-step throughout the trajectory. The measurements on the resistance network are made in less than a minute, and the calculations in about a minute; therefore, each step requires approximately two minutes. Thus, a typical 20-step trajectory can be determined in less than an hour, Position and slope are calculated to four decimal places.