(color online) (a) Conceptual sketch for the mean-field approach. A bunch of discrete electrons is treated as a smooth charge density profile. (b) A schematic diagram of an ultrafast electron diffraction system. The trajectory of electrons is separated into three regions. (c) An enlarged plot of a cylindrically symmetric electron bunch (in this case with a top-hat charge density distribution). A, B and C are the tail, front and center of the bunch. (d) A highlight of the boundary region.