Formation Condition of Virtual Cathode in the Relativistic Electron Beam-Plasma System

The formation condition of the virtual cathode (VC) formed by a self-focusing relativistic electron beam in plasma is studied theoretically and numerically. Together with the threshold function of the VC formation and the self-focusing condition, the parametric regions of forming the VC are found. Then the theoretical result is verified by the particle-in-cell (PIC) simulation, which further shows the phase-space characteristics of the VC formation. This study not only provides a theoretical basis for creating VC with a self-focusing relativistic electron beam in plasma but also helps in parameter selections for the related beam-plasma experiments and simulations.