Finite-difference method in a nonorthogonal curvilinear coordinate system used for electron gun design

Abstract

ABSTRACT A Finite-Difference Method in Non-Orthogonal Curvilinear Coordinate System (FDM-NOCCS) is the combinationof the domain transformation technique and the Finite-Difference Method (FDM). It has the visualization andsimplification of the traditional FDM. On the other hand, it overcomes the weakness of FDM in dealing withcomplicated boundary shapes, averts the interpolation between the grid points in the vicinities of boundaries. andalso avoids the abnormalism in the transformation from the physical domain to the computational domain. TheFDM-NOCCS is used in the computer aided design of electron gun for color cathode ray tube. Compared with theformal FDM, the FDM-NOCCS can save quite a lot of CPU time and computer memory. FDM-NOCCS workswell with the complicated e-gun systems design.Key words: electron gun, computer aided design, finite difference method, curvilinear coordinate system 1. INTRODUCTION In the study and design for an electron-gun system of color Cathode Ray Tube (CRT). Computer AidedDesign (CAD) is commonly used to make the work feasible. The Finite Difference Method (FDM) is the moststraightforward and extensively one within the algorithms used for the electrostatic field simulation. While thisalgorithm matches the smooth boundaries with ladder-shaped surfaces, and needs some interpolation between gridpoints for the boundary with strong curvature or slope discontinuities. All these may introduce significantnumerical errors.In recent years, a coordinate transformation technique provides the key to the development of finitedifference solutions of partial differential equations on regions with arbitrarily shaped boundaries. It is equally