Method of Computing First-, Second-, and Third-Order Transfer Coefficients for Arbitrary Fields

Abstract

For given arbitrary electromagnetic fields, an analytical method to obtain transfer coefficients up to the third order in phase-space coordinates is described in this paper. The method is based on numerical tracking of a number of representative particles followed by the least-square minimization. The result is applied to an arbitrary beamline consisting of linear and nonlinear beam-optical elements and favorably compared with the numerical particle tracking. Transfer coefficients obtained with our method are also compared with those obtained from an existing computer code. Index Terms—Beam optics, third-order map, transfer matrix.