Maximal charge injection of consecutive electron pulses with uniform temporal pulse separation

A charge sheet model is proposed for the study of the space-charge limited density of consecutive electron pulses injected to in a diode with uniform temporal pulse separation. Based on the model, an analytical formula is derived for expressing the dependency of the charge density limit on the gap spacing, gap voltage, and pulse separation. The theoretical results are verified by numerical solutions up to electron energy of a few MeV, including relativistic effects. The model can be applied to the design of multiple-pulse electron beams for time resolved electron microscopy and free electron lasers.