A comparison of electron-emission equations used in arc - cathode interaction calculations

Abstract

The predictions of a numerical model of the cathode-sheath region of high-pressure arcs using three different equations for the cathodic electron-emission current density are compared for two typical arc - cathode systems. These equations for cathodic electron emission include: (i) the field-enhanced thermionic emission (FEE) equation representative of the electron emission for high temperatures and moderate electric field strengths ; (ii) the Murphy and Good (MG) equation for thermo-field (T-F) emission valid for high temperatures and high surface electric field strengths in the range about - ; and (iii) the Murphy and Good equation for T-F emission enhanced by the presence of a high density of slowly moving ions in the cathode region (the MG+I equation). Results show that, in the case of a metal vapour arc (representative of vacuum arcs and high-pressure arcs on non-refractory cathodes) the use of the MG+I equation is always prescribed due to the formation of the high-local-pressure cathode-spot plasma. For high-pressure arcs on refractory cathodes the results show that, at atmospheric pressure, the generally used FEE equation introduces an underestimation by at least around 20% of the cathodic electron current density compared with the MG+I equation. The same comparison but for an ambient pressure of 50 atm shows that this underestimation becomes considerable.