Analysis of space charge fields using Lienard–Wiechert potentials and the method of images in the RF-free electron laser photoinjectors

Based on Lienard–Wiechert retarded potentials and the potential due to a beam-induced image charge on the cathode, a rigorous relativistic description of a beam transport inside an RF-photoinjector is presented. Velocity-dependent effects are explicitly taken into account. Simulations are presented for parameters appropriate to the ELSA photocathode where velocity-dependent effects are particularly important. These simulations reveal that at the center of the cathode (r=0, z=0) the beam's self-field and the field driven by the charges image on the cathode are equal. However, the self-field of the beam is dominated by the field due to the charges image on the cathode as one moves from the tail to the head of the beam. Far from the cathode, the self-field becomes the dominant one.