ABSTRACT
Geometrical optics of charged particle beams begins with relativistic classical mechanics, specifically, the motion of a charged particle in the presence of external electric and magnetic fields. The fields exert an instantaneous resultant force on the particle, which determines the path of motion. Mathematically, the solution consists of finding the three-vectors for position x and velocity v at any time t, given initial values at time zero, taking account of the influence of the fields. This chapter begins with a review of relativistic classical mechanics, focusing only on those specific topics which will lead directly to geometrical optics. It seeks a general condition governing the motion of a particle with charge q and rest mass m in external electric and magnetic fields. Formulation of the dynamical problem in this way has the advantage that it does not rely on time as an explicit parameter, as long as the potentials are time independent.
