Generalization of the paraxial trajectory method for the analysis of non-paraxial rays: simulation program G-optk for...

The paraxial trajectory method has been generalized for the application to the cathode rays inside electron guns. The generalized method can handle rays that initially make a large angle with the optical axis with a satisfactory accuracy. The key to success of the generalization is the adoption of the trigonometric function sine for the trajectory slope specification, instead of the conventional use of the tangent. Formulas have been derived to relate the ray conditions (position and slope of the ray at reference planes) on the cathode to those at the crossover plane using third-order polynomial functions. Some of the polynomial coefficients can be used as the optical parameters in the characterization of electron sources; the electron gun focal length gives a quantitative estimate of both the crossover size and the angular current intensity. An electron gun simulation program G-optk has been developed based on the mathematical formulations presented in the article. The program calculates the principal paraxial trajectories and the relevant optical parameters from axial potentials and fields. It gives the electron-optical-column designers a clear physical picture of the electron gun in a much more faster way than the conventional ray-tracing methods.