Space-charge field of sheet electron beam

The space-charge field characteristics of a uniform sheet electron beam in a rectangular waveguide have been investigated theoretically and numerically. The expressions of the space-charge field components are derived, and numerically calculated for different dimensions and current densities. Results show that, for a constant current density of the sheet beam, the sheet beam could propagate with a larger current when the beam cross-section is wider. In addition, the space-charge field of the sheet electron beam with a constant current density will not be enhanced while increasing the width of the beam, but will be enhanced while increasing the thickness of the beam. However, only the electric field component along the direction of the long side of the beam cross-section is weakened by incr