Field Plotting and Ray Tracing in Electron Optics A Review of Numerical Methods

Abstract

This chapter reviews the numerical methods of field plotting and ray tracing in electron optics. Most methods of trajectory tracing given in this chapter refer to axially symmetrical fields, as employed in electron lenses; the application of similar methods to plane fields, which occurs frequently, follows the same lines, and is not treated separately. The practical value and field of application of the many different methods of field plotting and trajectory tracing are discussed in this chapter. It is generally sufficient for the designer to predict the focal length, or the focusing ratio, of a cathode-ray tube up to, say, 10%. Electrolytic tanks or resistor networks will be very useful for obtaining the required field maps with sufficient accuracy, but numerical relaxation with a fairly coarse mesh, or graphical field mapping if the electrode structure is very irregular, will be equally successful, and will frequently take a comparable time for similar accuracy. Amongst the field plotting methods, the application of the resistor network is very useful. For the ray tracing only the more accurate numerical methods can be used with confidence.