<title>Matrizant method for an optimal synthesis of nonlinear magnetic and electrostatic focusing systems for a given beam current</title>

Abstract

The Matrizant method for the synthesis of magnetic and electrostatic focusing systems, producing an optimal beam quality (a minimum spot size for a given beam current), is proposed. This method includes: the matrix method for the description of motion of a charged particle beam in the nonlinear approximation on the base of a general relativistic theory of charged particle beam motion along a curved optical axis, developed by one of the authors; the analytical model of the axial field or their derivatives; 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 Laplace's equation for obtaining the parameters of the physical model which has the same axial field as the mathematical model. As an example, the developed Matrizant method is applied to minimize the beam spot size for a given beam emittance in a focusing system consisting of multiple cylinder lenses with equal diameter.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.