Influence of space charge effect on Nottingham effect in thermal field emission

Abstract

High current electron beam emitting from a thermal field emission cathode has an intense space charge effect. In order to investigate the mechanism for the influence of space charge effect on Nottingham effect in thermal field emission, the results of Nottingham effect with and without space charge effect at different work functions and various applied electric fields are obtained numerically on the basis of the theoretical analyses of space charge effect and Nottingham effect. The results demonstrate that the space charge effect has a significant influence on the steady electric field at the cathode surface, and thus the effect of space charge on Nottingham effect is not ignorable. When the work function is in a range of 3.0–4.52 eV and the applied electric field is in a scope of 3×109–9×109 V/m, the average energy delivered per electron in thermal field emission is in a span of 0–2.5 eV larger than that in the case without space charge effect, and the higher the cathode temperature or applied electric field, the larger the difference between them is. The average energy delivered by per electron emitting from cathode is observed to nonlinearly decrease with the increasing of applied electric field when the space charge effect is included. When the cathode temperature is high, the cooling effect in Nottingham effect can be intensified as the gap distance of diode increases.