A study of spot evolution in hot refractory cathodes of high-pressure arcs

Abstract

In this paper the behavior of the cathode spot in atmospheric pressure arc is studied from a dynamic point of view and later applied to a specific case of a tungsten refractory cathode. For this, a model of the cathode region was developed. In this model the tungsten atoms proceeding from the cathode evaporation, which were all supposed to be ionized in the presheath, returned to the cathode surface as ions, provoking a heating of this surface. Therefore, the model allowed us to evaluate the importance of those atoms. Furthermore, different mechanisms of the electron emission from the cathode surface were considered as function of the spot temperature and the electric-field strength. This model of the cathode region allowed getting important parameters in the study of the dynamics of the cathode spot such as total current density, which is necessary for the calculation of Joule heating effect, and the total-energy flux density, which was incorporated as a boundary condition for the solution of the heat conduction equation in the cathode. The dependence of these parameters on the temperature of the cathode surface in contact with the plasma introduced nonlinearities in the equations. The model takes into account the different phase changes that take place in the cathode as well as the thermal ablation of the melted cathode and the dependence on the temperature of the physical magnitudes that characterize the cathode material. In this way, it is possible to get the time evolution of the temperature distribution in the cathode and to study the spot dynamics on the cathode surface. Three different values of the initial cathode voltage drop were used, U0=15, 20, and 25V, which cover a wide range of working conditions. The cathode spot was assumed to be placed on a crater. For U0=15V, the crater radius increases in time until it reaches a critical value when the energy balance principle is broken. This leads to spot death and its jump to another position on the cathode surface. Nevertheless for higher-voltage drops, U0=20 and 25V, the spot reaches a stationary regime before arriving at that critical state and the spot remains fixed. This way, the maximum spot radius and the possibility of the spot moving or not appear naturally during the numerical development of the model. The results of this model show that the contribution of the evaporated and later ionized cathode atoms is not significant in comparison with the electrons and plasmagen ions contributions. In this sense these atoms need not be taken into account in the cathode region models for hot refractory cathodes in atmospheric pressure arcs.