Generalization of paraxial trajectory method for the analysis of non-paraxial rays

Abstract

Abstract The paraxial trajectory method has been generalized for application to the cathode rays inside electron guns. The generalized method can handle rays that initially make a large angle with the optical axis. The key to success of the generalization is the adoption of the trigonometric function sine for the trajectory slope specification, instead of the conventionally used tangent. An improved assignment of paraxial trajectory to the actual ray becomes possible by the new slope specification. It is possible to relate the ray emittance condition (the combination of position and slope of rays at reference planes) on the cathode to that at the crossover plane using polynomial functions, whose coefficients can be used as the optical parameters in electron source characterization. The most important among the parameters is the Electron Gun Focal Length, which gives quantitative estimate of both the crossover size and the angular current intensity. Electron gun simulation program G-optk has been developed based on the generalized paraxial trajectory theory. The program calculates the principal paraxial trajectories, optical parameters as well as source emittances solely from the axial potentials and field distributions. It gives a clear physical picture of electron sources and can be used for the gun design optimization.