Particle Motion in Longitudinal Waves. I Subluminal Waves

Abstract

The classical equations of motion for a particle moving in a parallel longitudinal wave of arbitrary phase speed are discussed and the case of subluminal waves is considered in detail. Motion of both trapped and untrapped particles is explored with particular reference to the ability of a wave to accelerate particles to relativistic energy. The particle orbit is found in both closed and expanded forms, taking the electric field into account exactly. Expressions are also found for the 'drift velocity' of a particle, which is an important quantity because it is a constant of the particle motion that describes the motion of the centre of oscillation.