The trajectory analysis algorithm for electrostatic fields providing an angle focusing of given order in the plane of symmetry

摘要

A class of focusing electrostatic fields built as a solution for the inverse corpuscular optics problem has been investigated. An effective algorithm for trajectory analysis of these fields was suggested and tested. The algorithm was based on the special parametric form of potentials representation. The main complexity of the problem is in treating the result of inverse form of potential representation, where coordinates are functions of the potential and the flux, but it is impossible to give the potential by an explicit function of coordinates. To solve the equations of motion in a direct form, it is necessary to find (numerically) coordinates at every integration step. It reduces the precision and increases the time of the calculations. We suggested using a parametric form of the potential and the relationship between coordinates. Direct equations of motion can be replaced with differential equations for parameters, which can be solved without any difficulty. The results obtained can be applied to designing of new energy-analyzing devices with enhanced capabilities.