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Calculation of the maximum temperature of the arc illuminating lamp electrode at different locations of the discharge cathode spot on its surface

Keywords:

V.I. Kristya – Dr. Sc. (Phys.-Mat.), Professor, Bauman Moscow State Technical University, Kaluga Branch


Currently, in mercury arc lighting lamps the electrodes are used, consisting of the tungsten rod, on which the sintered mass (a mixture of tungsten powder and oxides of alkali-earth metals) is pressed in the form of a cylinder. At the cathode half-period, when the electrode is bombarded by the ion flow, the discharge is localized usually on its surface in the spot with the radius of several tens of microns, which is located on the edge between the side surface and the base of the cylindrical sintered mass (because at such spot position the heat removal from the area of the spot is more difficult, which is energetically advantageous for the discharge). In this case, the temperature increase in the center of the spot relative to its values in the main part of the sintered mass surface should exceed its corresponding increase in the case of the location of the spot on the base or the lateral surface of the cylinder, which can lead to the reduction of the electrode service time due to more rapid evaporation of emission material. However, the dependence of the temperature distribution in the electrode volume on the position of the cathode spot is not been studied so far. In this work, an influence of the discharge spot position at the electrode on its surface temperature in the spot is theoretically investigated. As usually the discharge cathode spot size is much smaller than the radius of the electrode sintered mass, under calculation of the heat transfer in the area near the spot we can neglect the curvature of the electrode boundary and consider the problem as a two-dimensional. Taking this into account, an analytical solution of the stationary heat conduction equation in a rectangular area is obtained for the cases when the section of its boundary, through which the heat flows from the discharge into the area, is located on its edge and on its side center. It is shown that under the location of the spot on the edge of the electrode, the temperature rise in the center of the spot twice exceeds its corresponding rise in the case of the spot location at the lateral surface of the cylinder. The intensity of emission material evaporation increases exponentially with rising of the temperature, therefore, the location of the discharge cathode spot on the surface of the sintered mass can significantly influence the speed of its departure from the electrode. Under parameter values, characteristic for high pressure mercury arc lamps, the difference of the temperature increases is about 300 K, which corresponds to a much higher velocity of emission material evaporation for the spot location on the edge. Estimates show that an increase of the heat flow from the area of the electrode surface near the edge and a reduction of the emission material evaporation velocity from it to the value, corresponding to the spot location on the electrode centre, can be achieved by a small edge rounding.
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June 24, 2020
May 29, 2020

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