Matrix theory of the motion of a charged particle beam in curvilinear space-time. Pt. 1

A general relativistic theory of charged particle beam motion along a curved optical axis, including the gravitational field, is important for 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, including the gravitational force. This approach is based on three basic matrices: The reference frame matrix, the curvature matrix and the electromagnetic matrix. The equations of the particle beam motion and of the electromagnetic field, including the space charge, are given. The notations used is independent of the units of the measured fields and energies. In a second paper, also published in this issue, the matrix and recursive methods for solving the nonlinear equations of motion will be presented. (orig.)