Self-Consistent Analysis Of 3D Undulator Radiation And Relativistic Electron Beam Dynamics Using Lienard-Wiechert Fields

Lienard-Wiechert (LW) fields, which are exact solutions of the wave equation for a point charge in free space, and the Lorentz force equations are employed to formulate a self-consistent treatment of electron beam dynamics and radiation field evolution in magnetic 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 motion enables us to obtain three dimensional undulator radiation by summing up the field contribution of each electron in the beam. The approach used is particularly well suited to the investigation of self amplified spontaneous emission (SASE) without introducing a seed wave at start-up. In this paper, we present studies of non-periodic multi-bucket electron phase dynamics as well as temporal and angular characteristics of the electromagnetic fields radiated by a relativistic short filamentary electron beam interacting with a circularly polarized magnetic undulator