An Electrical Cathode Model of a High Pressure Sodium Lamp

An electrical cathode model (ECM) of a high pressure sodium lamp (HPS) 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, solved using the finite elements method. 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.