Energy balance in coherent electromagnetic radiation

Abstract

Bunched charges, as in the 'free electron laser', radiate more energy than unbunched ones. For a better understanding of how the forces between particles determine the conservation of energy, we take the simple model of two charges within a wavelength of a sinusodoidal wave, and show that the relative phase of the particle's motion with respect to the wave is modified by the force between the two particles, and this explains the extra work done by the wave. The phase shift is proportional to the emitted field and depends on the retardation (particle distance divided by speed of light), and turns out to be independent of distance.