Restoration of Rectangular Pulse Shape after Edge Erosion for a Space-Charge Dominated Electron Bunch

We present in this Letter a novel experimental method that demonstrates the time reversability of the 1D cold-fluid equations for a space-charge dominated beam. A bunch of charged particles with an initially rectangular line-charge and velocity profile experiences edge erosion during transport through a focusing system due to the nonlinear, longitudinal space-charge forces at the edges. By imposing on the eroded beam pulse a linear velocity gradient at a proper location one can restore the rectangular line-charge profile downstream. This technique could be used to offset edge erosion and assure a rectangular pulse shape for efficient acceleration and uniform power flow in the interaction region for applications of intense, high-power beams.