Theoretical approach of the photoinjector exit aperture influence on the wake field driven by an electron beam accelerated in an RF gun of free-electron laser “ELSA”

The wake field generated in the cylindrical cavity of an RF photoinjector, by a strongly accelerated electron beam, has been analytically calculated (Salah, Dolique, Nucl. Instr. and Meth. A 437 (1999) 27) 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 bored pill-box cavity (Figuera et al., Phys. Rev. Lett. 60 (1988) 2144; Kim et al., J. Appl. Phys. 68 (1990) 4942), this often-quoted result must be checked for the wake field map excited in a photo injector cavity. Further, in the latter case, the empirical rule in question can be broken more easily because, due to 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 wake field driven in a photoinjector by the accelerated electron beam which takes this hole effect into account, whatever the hole radius may be.