Analytical model for emittance compensation in RF photo-injectors

In this paper we present a new model to represent analytically the transverse beam dynamics in RF photo-injectors. It consists basically of an enhanced Kim´s model, with incorporation of RF ponderomotive focusing effects, external magnetic focusing and a perturbative treatment of space charge along the beam envelope. Applying the resulting formulas it is possible to predict with high accuracy the transverse beam envelope behaviour in a multi-cell RF gun, as well as the operating conditions to achieve space charge emittance compensation according to Carlsten´s scheme. The agreement with sophisticated numerical simulations is really quite satisfactory, as well as the match with experimental measurements of the predicted operating range for emittance compensation