Simulation of the hot core mode of arc attachment at a thoriated tungsten cathode by an emitter spot model

Recently, a constricted attachment of an atmospheric pressure low-current argon arc in the centre of the flat end face of a thoriated tungsten cathode was observed and spectroscopically analysed. Its diameter of 0.6 mm and its length of the free standing part of 10 mm are the typical dimensions of electrodes for high-intensity discharge lamps. This paper gives a physical interpretation of the axially symmetric arc spot by a simulation of its properties with a cathodic sheath model which takes into account a reduction in the work function above a critical temperature of the cathode surface by a thorium ion current. At first the optical observation and spectroscopic investigations are recapitulated. Then, an overview is given on the essential elements which are needed to simulate the cathodic arc attachment on a hot electrode. A simulation of a central cathode spot with these elements gives results which are far away from the experimental findings if a constant work function phi is used. Therefore, a temperature-dependent work function phi(T) is introduced. This phi(T) transitions from 4.55 to 3 eV above temperatures of the order of 3000 K. With this emitter spot model a constricted arc attachment is obtained by simulation in the centre of the flat end face of the cathode in accordance with experiment. For currents below i(arc,max) approximate to 15.5 A, two spot solutions with different cathode falls are found. They form a current-voltage-characteristic consisting of two branches which extend from a turning point at i(arc,max) to lower currents. For i(arc) > i(arc,max), only a diffuse mode of cathodic arc attachment is obtained. It is shown by a comparison with measured data for i(arc) = 7.5, 10, 12.5 and 15 A that the solution with the lower cathode fall is observed experimentally.