Influence of upstream ion current on relativistic field-emission-limited diodes

Abstract

Summary form only given. The field emission process is described quantum-mechanically by the Fowler-Nordheim equation. The cathode plasma and surface properties are considered within the framework of the effective work function approximation. Space charge effects are described by Poisson's equation including relativistic effects. The numerical calculations are carried out on a time scale much shorter than the emergence of the gap closure. We found that the quasi-stationary state of the diode exhibits a cutoff voltage. The electric field on the cathode surface is found to be saturated in the high voltage regime and is determined by the effective work function only. In the present work, we consider the anode plasma effects on the relativistic field-emission-limiting current. Thus, the previous theory is extended to the bipolar field-emission-limited flow. The ion current has been included in the relativistic Poisson's equation and has been treated as a tuning parameter. The comparisons of emission characteristics between space-charge-limited and field emission-limited diodes are given. The Je-V and Es-V curves are plotted for variant ion current, where Je is the electron current density, V is the diode voltage, and Es is the electric field on the cathode surface.