Child-Langmuir law for photoinjectors

The space-charge field at the cathode limits the current density extracted from particle sources such as photoinjectors. For a long time, the maximum current has been estimated by using the classical Child-Langmuir law, which is derived with an assumption inconsistent with the conditions of modern laser-driven electron guns. Here, we introduce a theoretical model that accurately accounts for space-charge effects in transversely confined particle beams emerging from photocathodes. The model enables us to (i) determine the maximum current density extractable from the photocathode for an arbitrary cathode radius, (ii) reveal its dependence on the transverse profile of the particle beam, and (iii) predict its upper limit for structured beams such as the ones produced by surface-plasmon resonance-enhanced photocathodes.