Self-consistent analysis of radiation and relativistic electron beam dynamics in a helical wiggler using Lienard-Wiechert fields

Lienard-Wiechert (LW) fields, which are exact solutions of the Wave Equation for a point charge in free space, are employed to formulate a self-consistent treatment of the electron beam dynamics and the evolution of the generated radiation in long undulators. In a relativistic electron beam the internal forces leading to the interaction of the electrons with each other can be computed by means of retarded LW fields. The resulting electron beam dynamics enables us to obtain three dimensional radiation fields starting from an initial incoherent spontaneous emission, without introducing a seed wave at start-up. In this paper, we present electromagnetic radiation studies, including multi-bucket electron phase dynamics and angular distribution of radiation in the time and frequency domain produced by a relativistic short electron beam bunch interacting with a circularly polarized magnetic undulator.