Modification of Paschen's Law for Electrodes with Different Shapes and Materials using DC Nitrogen Glow Discharge

Abstract

In this manuscript, d.c. glow discharge of conical, hemispherical, and spherical electrodes made of different materials was measured using nitrogen gas. The electrodes' materials from aluminum, graphite, and stainless steel were used. From the experimental results, the work function of anode and cathode materials with different shapes play an important role in the electrical discharge characteristics and Paschen curves. It was found that the cathode material with a low work function and large surface area became a control factor in the determination of the low breakdown voltage (Vb)minimum values. In addition, the work function of different materials for conical anode or conical cathode with hemispherical and spherical cathode or anode had the minimum values of breakdown voltages. In Paschen curves, the hemispherical anode and cathode with the same and different materials gave a small difference in their values. The conical stainless steel cathode gave the lowest values of Paschen curve in a comparison between different materials of conical cathodes in cases of hemispherical aluminum anode and spherical graphite one. In addition, the conical graphite anode gave the lowest values of Paschen curve in case of the hemispherical aluminum cathodes. The modified Paschen's law indicated that the breakdown voltage was not only as a function in the product of gas pressure and inter-electrode distance but also the ratio of materials' work functions and surface areas of electrodes. It was deduced in a general formalism according to the materials and shapes of cathodes for discharge cases having the same (Vb)min. value.