Influence of the photoinjector exit aperture on the wakefield driven by an intense electron beam pulse: a theoretical approach

The wakefield generated in the cylindrical cavity of an RF photoinjector, by the strongly accelerated electron beam, has been analytically calculated under the assumption that the perturbation of the field map by the exit hole is negligible as long as the ratio: exit hole radius/cavity radius is lower than approximately 1/3. Shown experimentally in the different context of a long accelerating structure formed by a sequence of bared pill-box cavities, this often quoted result must be checked for the wakefield map excited in a photoinjector cavity. Further, in the latter case, the empirical rule in question can be broken more easily because, due to the causality, the cavity radius to be considered is not the physical radius but that of the part of the anode wall around the exit hole reached by the beam electromagnetic influence. We present an analytical treatment of the wakefield driven in a photoinjector by the accelerated electron beam which takes this hole effect into account, whatever the hole radius may be