Computational study of wide electron beam focusing with second order approximation for the electrostatic systems having curvilinear optical axes

The electron trajectory equation of electrostatic wide beam has been researched thoroughly. Equations of curvilinear paraxial trajectories with second order approximation have been derived, and converted into a suitable form for computing. The computational rationality and credibility of curvilinear trajectories are demonstrated by concentric spherical system. There is a difference about the fifth order of magnitude between the first and second-order approximate values of curvilinear trajectories, and about the fourth order of magnitude between these two aberrations. It can be neglected in general engineering applications, but it cannot be neglected in some image tubes requiring high precision.