MATRIX-THEORY OF THE MOTION OF A CHARGED-PARTICLE BEAM IN CURVILINEARSPACE-TIME .2. NONLINEAR-THEORY - FORMULAS AND ALGORITHMS

A general relativistic theory of the motion of a charged-particle beam motion along a curved optical axis, including the gravitational field , is of great significance in the design of optimal beam control syste ms. In a first paper, a new matrix approach was presented. In this sec ond paper the expansion of the most general equations of motion and el ectromagnetic field equations in the Taylor series in powers of the de rivation from the reference particle is presented. The nonlinear equat ions in phase space are reformulated as linear equations in phase mome nt space. A compact, conservative, recursive method of integrating the equations of motion is proposed. In some cases it is possible to opti mize the control system by choosing a definite symmetry. This symmetry is considered in the paper.