MATRIX-THEORY OF THE MOTION OF A CHARGED-PARTICLE BEAM IN CURVILINEARSPACE-TIME .1. GENERAL-THEORY

A general relativistic theory of charged particle beam motion along a curved optical axis, including the gravitational field, is important f or designers of optimal beam control systems. In this paper, which is the first of two, a new matrix approach is presented. This allows the development of a relativistic matrix theory for charged particle beam motion in the most general case of a curved reference trajectory, incl uding the gravitational force. This approach is based on three basic m atrices: the reference frame matrix, the curvature matrix and the elec tromagnetic matrix. The equations of the particle beam motion and of t he electromagnetic field, including the space charge, are given. The n otations used is independent of the units of the measured fields and e nergies. In a second paper, also published in this issue, the matrix a nd recursive methods for solving the nonlinear equations of motion wil l be presented.