Particle Motion in Longitudinal Waves. II Superluminal and Luminal Waves

Abstract

The motion of charged particles in superluminal and luminal longitudinal waves of arbitrary amplitude is considered in detail, including relativistic effects. In particular we discuss the ability of these waves to accelerate particles. Solutions for the particle orbits are given in both closed form and in terms of relevant expansions. The drift velocity of the particles, which describes the motion of the guiding centre, is identified. Two interesting effects are discovered: (i) the ability of large amplitude superluminal waves to drag particles along at a velocity conjugate to the wave phase speed and (ii) the existence of 'phase locking' particle orbits in the luminal case, in which particles can be accelerated to arbitrary energy.