Improved method for studying the propagation dynamics of ultrafast electron pulses based on mean-field models

We have studied the propagation dynamics of ultrafast electron pulses by using an improved mean-field model, in which the propagation of the electron pulses across the boundary of the acceleration region is explicitly considered. A large decrease in the speed spread of the electron pulses (we called “boundary kick”) is observed and properly treated leading to a significant improvement in the simulation accuracy, particularly when the density of electrons is very large. We show that our method is consistent with the simulation by the N-particle method, while others can introduce factorial error.