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A charge sheet model is proposed to study the space charge effect and uniformity of charge separation of an electron pulse train in a drift space. An analytical formula is derived for the charge density limit as a function of gap spacing, injecting energy and pulse separation. To consider the relativistic effects, the theoretical results are verified by numerical solutions up to 80 MeV. This model can be applied to the design of Smith-Purcell radiation, multiple-pulse electron beam for time resolved electron microscopy, and to free electron laser

Maximal charge injection of a uniform separated electron pulse train in a drift space