Matrix Representation for Calculation of the Second-Order Aberration in Ion Optics

Abstract

The matrix representation for calculating the ion trajectory is extended to include the secondorder aberration terms. Properties of the matrix and relations between its elements are discussed. As an example of the application of the matrix method, the second-order coefficients of a homogeneous magnetic field of arbitrary shape are derived and the relations between the matrix elements and Hinterberger's notations are shown.