Current density limitations in a fast-pulsed high-voltage vacuum diode

Abstract

An investigation into the limitations on the enhanced field-emitted current density in a fast-pulsed (rise-time = ns), high voltage (> 106 V), 1-inch vacuum diode was conducted using a computer simulation based on the Fowler-Nordheim equation. Oscillations in the emitted current density (due to the change in the amount of space charge within the gap) were found to quickly decay into a final steady-state for the voltages applied. Steady-state values for a wide variety of work functions, electric field enhancement factors (based on the theory that "whiskers" on the cathode surface experience varying degrees of enhancement), and applied potentials were compared to two benchmarks: the amount of current density required to explode a whisker in < 10 ns by joule heating (J E = 109 A/cm2 ); and the Child-Langmuir (C-L) spacecharge- limited current density. Steady-state values were found to be less than J E . One model of the formation process of a plasma at the cathode surface requires that J E be met or exceeded by the steady-state value. Thus, such a model is not supported by this project's findings. The C-L limit is based on a thermionic-type emission process. As only pure field emission (i.e., no thermionic emission included) was considered, the steady-state values were, in all conclusive cases, less than the corresponding C-L limited values.