Modification of Child-Langmuir Law for Electrodes of Different Materials and Shapes Using Nitrogen Gas

A dc glow discharge plasma between the planar electrode and planar, conical, and hemispherical electrodes was studied. The electrode materials made of aluminum, graphite, and stainless steel (SS) were used. The experimental results showed a deviation in the traditional Child-Langmuir (CL) law as a result of the use of different shapes and materials of anodes and cathodes. The new parameters of the modified CL law as a function in the surface areas of electrodes, their work function materials, and their contributions to the electrical discharge. The lowest discharge characteristics were for the aluminum planar electrode (anode or cathode) with the aluminum and graphite hemispherical one. The planar aluminum cathode with the conical SS anode gave the highest discharge characteristics. The planar aluminum anode with conical SS cathode had the lowest Paschen curve values. In Paschen curves, the highest values were discovered to be for the planar cathode in a comparison with different cathodes. The hemispherical aluminum anode had the highest Paschen values compared with different anodes. Moreover, the contribution ratio of the anode to the cathode in the discharge for the aluminum planar diode was equal to the ratio between their surface areas and the ratio between their work function materials. In contrast, this contribution ratio for the other discharge cases was equal to the multiplication of the surface areas ratio of the anode to cathode and the ratio of their materials’ work functions. The modified CL law and its coefficient were generalized for the electrodes of different shapes, materials, and used gases.