Modeling the Voltage Drop Across the Cathode Sheath in HPS

An electrical cathode model (ECM) of a high-pressure sodium (HPS) lamp based on physical laws has been developed. The proposed ECM calculates the instantaneous voltage drop in a cathode sheath and the temperature distribution inside the cathode using as input parameter the cathode geometry and the positive column current. The model is based on the electrode heat transport equation, which is solved using the finite-element method. So, since it stems from the physics describing the cathode behavior, it is found that the ECM predicts in a satisfactory way the cathode voltage drop over a wide range of work conditions. The obtained results were compared with those reported in the current literature. It can be concluded that the ECM is a useful tool in understanding the interaction between the positive column and the cathode in order to improve, for instance, HPS lamp ballast designs, as measuring the potential drop across the cathode sheath using a commercial lamp is particularly difficult. The model takes into account the temperature dependence of the thermal conductivity, the electrical cathode resistivity, and the total emissivity.