Analytical modeling of longitudinal beam dynamics in an RF-gun: From almost zero to relativistic velocities

We develop and test a model for the longitudinal beam dynamics in an RF-gun consisting in a single and fully analytical transfer matrix. This model deals with the main difficulty of beam dynamics in an RF-gun, which is the velocity variation from almost zero to relativistic one along the beam path, by splitting the gun into two zones. A first one, close to the photocathode, where the accelerating field is assumed to be electrostatic. A second one, farther away from the photocathode, where the electron beam is assumed to be ultra-relativistic. We investigate the capability of the model through comparisons with ASTRA simulations, and measurements performed on the PITZ and PHIL facilities. These comparisons show that the agreement with the analytical model is globally good for the cases where the electron bunch has a low density, and is deteriorated when this density increases due to the growing effect of space-charge forces. The agreement with the analytical model is also found to be dependent on the type of RF-gun considered. The comparisons we made also reveal some limitations of the model, for most of which we propose simple practical solutions.