Modeling the Voltage Drop Across the Cathode Sheath in HPS

• Published in: IEEE transactions on plasma science Vol. 35; no. 4; pp. 1104 - 1110
• Main Authors: Fabela, J.L.T., Pacheco-Sotelo, J.O., Pacheco, M.P., Benitez-Read, J.S., Lopez-Callejas, R., Zissis, G., Bhosle, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cathode temperature distribution; Cathodes; Conductivity; Discharges for spectral sources (including inductively coupled plasmas); Electric discharges; Electric potential; electrical cathode model (ECM); Electrochemical machining; Electrodes; Electronics; Engineering Sciences; Equations; Exact sciences and technology; Finite element methods; finite-element method; Geometry; high-pressure sodium (HPS) lamps; Lamps; Mathematical models; Optics; Photonic; Physics; Physics of gases, plasmas and electric discharges; Physics of plasmas and electric discharges; Plasmas; Positive columns; Sheaths; Sodium; Temperature; Temperature distribution; Thermal conductivity; Voltage; Voltage drop; Temperature distribution; Positive column; Temperature dependence; Transport equation; Electric discharges; Lamps; Theoretical study; finite-element method; Cathode temperature distribution; High pressure; Design; Finite element method; Emissivity; Sodium; Electric resistivity; Thermal conductivity; Modelling; high-pressure sodium (HPS) lamps; electrical cathode model (ECM); Heat transfer
• ISSN: 0093-3813; 1939-9375
• DOI: 10.1109/TPS.2007.902125

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.