A model of the electric arc attachment on nonrefractory (cold) cathodes

In this work, a physical model describing the electric arc attachment on electron emitting non-refractory (cold) cathodes is developed and applied to Cu, Fe and Ti cathodes. The model considers the possibility of a pressure build up in the cathode region due to the strong vaporization of the cathode, the formation of a cathode sheath according to the Bohm's model, and the ion-enhanced thermo-field emission of electrons by the cathode surface. The self-sustaining operating conditions of the discharge are defined by two simple criteria based on particle and energy balance considerations. Results clearly show the necessity of having high local metallic vapor pressures in the cathode region of non-refractory cathodes in order to have a self-sustaining arc attachment. A minimum pressure of at least 19 atm is needed for a Cu cathode. This minimum pressure is shown to decrease as the cathode material boiling temperature increases according to an exponential decay law. Current densities of the order of 1010 A m--2 are maintained at the surface of a Cu cathode mainly by the emitted electrons. A comparison of the three different models for the electron emission current found in the literature allowed to define the limits of validity of each model for two typical arc-cathode interaction systems, and to evaluate the underestimation made on the emission current density when a less appropriate model is used. This underestimation is shown to cause an overestimation of important parameters such as the cathode surface temperature and metallic vapor pressure in the cathode region. An analysis of the mechanisms of heat transfer to the cathode surface allowed to show that the confinement of the cathode spot plasma forming the arc attachment could favor the production of vapors to the detriment of liquids. Such a phenomenon is of importance in Arc Ion Plating for instance. Heat losses by conduction in the cathode bulk larger than 1010 W m--2 are shown to favor the formation of liquid volumes in a mus time scale. This liquid volume formation is shown to increase with the initial cathode temperature and current carried at the arc attachment point.