The computation of electron trajectories in axially symmetric fields

Abstract

Existing methods for calculating electron paths are discussed and some factors limiting their accuracy and general application are pointed out. A new method, which overcomes these difficulties, is proposed. The equations of motion are integrated numerically in a most direct manner, and at each stage the accuracy may be checked by using the energy equation. The method may be used in a combined electric and magnetic field, and it is not limited to paraxial rays or to rays which are initially parallel to the axis. The necessary computations may be carried out rapidly with the aid of a computing machine.