A numerical model is developed to study the cathode spot initiation of an electric arc. It takes into account the electron emission, the Nottingham effect at the surface, the vaporization of material, the ohmic heating and the thermal conduction in the electrode bulk. The main feature of this work involves considering a two-dimensional thermal structure of the electrode. The Joule effect and the phenomena in the cathode layer are taken into account. In contrast to most proposed models, the electric field and the ion current at the cathode surface are considered as two independent external parameters. This allows us to study the spot initiation under different conditions, namely for an applied electric field with different amounts of external ion flux impinging upon the cathode. As for most theoretical models, there is no direct comparison with experiments, but, under quasi-stationary conditions, our model yields results in agreement with the models found in the literature. The overheating phenomenon below the surface is observed and it can be considered as the origin of the micro-explosion which can be a possible mechanism for the crater formation on the cathode. The conditions for the appearance of the overheating phenomenon are also examined.

No abstract