Abstract
The steady-state cold-fluid-Poisson equations are used to investigate the influence of space-charge effects on relativistic non-neutral electron flow in a planar triode with cathode located at z=−LCA, anode located at z=0, and a plane conductor located at z=d. An intense relativistic electron beam with current density −J0 (generated in the diode region) is injected through the anode plane. A one-dimensional theoretical model is employed in which the spatial variations are assumed to be perpendicular to the planar conductors. Relativistic effects on the electron motion are included, but self-magnetic fields are neglected. An exact analytical expression for the relativistic current flow is obtained. The steady-state and time-averaged equilibrium properties are investigated analytically. The results are compared with approximate analytical solutions and numerical simulation results using a multiple-sheet model. Based on this investigation, it is found that the formation of a virtual cathode downstream can be suppressed by an applied positive potential. The forward electron current is substantially enhanced, while the stable operating range of the steady-state triode current is reduced substantially.
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