The matrizant method for an optimal synthesis of electrostatic multiple cylinder lenses

The matrizant method for the synthesis of electrostatic systems with axial symmetry, consisting of multiple cylinder lenses and producing an optimal beam quality, is presented. This method includes: the matrix method for the description of motion of a charged particle beam in the nonlinear approximation; the mathematical analytical model of the axial potential distribution; the method of the moments of the particle distribution function over the whole totality of the phase coordinates for finding the averaged radius of the beam; and the integral equation method to solve Laplaceʹs equation for obtaining the parameters of the physical model which has the same axial potential distribution as the mathematical model. veloped matrizant method is applied to minimize the beam spot size for a given beam current in a focusing system consisting of multi-cylinder lenses with equal diameter. The desired object and image plane positions are satisfied before evaluating the merit function, but are not a part of the set of constraints for the optimization.