Effect of Protrusions on Cathodic-Arc-Attachment Mode in High-Pressure Arc Discharges

Abstract

Abstract-It is shown via computer simulations that a protrusion on a thermionic arc cathode may dramatically change the pattern of steady-state modes of current transfer. This happens through a bifurcation of a special type occurring at certain geometry of the cathode and may play a role in operation of electrodes of compact high-intensity discharge lamps.Index Terms-Arc attachment, arc cathode, bifurcation of current transfer, bifurcation theory, high-pressure arc. CONSIDERABLE advances in theoretical and experimental investigation of the plasma-cathode interaction in high-pressure arc discharges have been achieved during the last decade [1]. Simulation methods, available at present and validated experimentally, allow one to reliably describe many aspects of operation of thermionic cathodes.A challenging task is to simulate operation of cathodes of complex geometries, which are of practical interest, in particular, those with protrusions [2], [3]. Results of such simulations are reported in this paper.Steady-state modes of current transfer have been calculated with the use of the commercial software COMSOL Multiphysics, as described in [4]. Stability of each of the steady-state modes has been investigated, as described in [5].In Fig. 1, current-voltage characteristics U (I) are shown of axially symmetric steady-state modes of current transfer to an axially symmetric tungsten cathode in the form of a rod of radius R = 750 µm and a height of 12 mm (here, U is the near-cathode voltage drop, and I is the arc current). The cathode has a hemispherical tip. A spherical protrusion with a radius of 200 µm is located at the top of the tip. The arc operates in argon under the pressure of 2 bar. Also shown is the dependence of the maximum temperature of the cathode surface on the arc current. Stable and unstable sections of each mode are shown by solid or dotted lines, respectively.There are two separate modes in Fig. 1 Apart from this S-shape, the current-voltage characteristics shown in Fig. 1 are similar to those calculated for a cathode in the form of a cylindrical rod with a flat top [4]. On the basis of this similarity, one would expect that the mode a is the axially symmetric spot mode, and the mode b is diffuse. However, high values of the maximum temperature in mode b and low values of the maximum temperature on both branches of the mode a do not fit this interpretation.An inspection of distributions of the temperature of the cathode, shown for several states in Fig. 1, disproves such interpretation. While high-current states belonging to the mode b are characterized by smooth temperature distributions typical for the diffuse mode, there is a well-defined spot in lowcurrent states belonging to the mode b. The stable branch of the mode a is diffuse, and there seems to be something that can be identified as a poorly pronounced spot on the unstable branch, although this spot can hardly be seen in Fig. 1. In other words, each of the two modes of steady-state current transfer existing in this geometry embraces diffuse ...

Understanding and modelling plasma–electrode interaction in high-pressure arc discharges: a review

“…Presumably, some of these other modes can be described by means of the same model of nonlinear surface heating that has been successfully applied to the diffuse and spot modes. For example, this is presumably the case of the super-spot mode: it has already been mentioned above that this mode may be related to the change in the pattern of steady-state modes of current transfer caused by a protrusion, detected by simulations [109] performed in the framework of the model of nonlinear surface heating. In connection with the blue-core mode, one could think of the above-mentioned solutions with different branches of the function q(T w , U): a branch with low values of T e would describe the diffuse and spot modes and a branch with high T e would describe the blue-core mode.…”

“…A protrusion on a thermionic arc cathode dramatically changes the pattern of steady-state modes of current transfer in certain cases, as shown by simulations [109]: it may happen that there is only one steady-state mode in a wide current range and this mode is spot-like. This finding may be related to the so-called super-spot mode observed in the experiment [110] and to observations [111] indicating that a protrusion on the front surface facilitates stable operation of the cathode in a mode with a spot.…”

Analysing bifurcations encountered in numerical modelling of current transfer to cathodes of dc glow and arc discharges

“…In the following sections, the bifurcations identified above will be discussed in some detail. Also discussed will be transcritical bifurcations {1D, 2D} and {2D, 2D} of second-order contact encountered in the modelling of glow discharge [33] and non-cylindrical arc cathodes [19,20], respectively.…”

“…Numerical modelling of arc cathodes of shapes of industrial interest [19,20] revealed a possibility of dramatic changes in the pattern of steady-state modes of current transfer. As an example, figure 13(b) shows the temperature at the centre of the front surface of a cathode having the shape of a rod (cylinder) with a hemispherical tip.…”

“…One can see that the pseudodiffuse and the first 2D spot modes, representing separate modes at R 1.169 mm, become connected when R has increased up to a certain value around 1.169 mm, then they exchange branches and separate once again. Each of these two new disconnected modes embraces states typical for both diffuse and spot modes [19,20] and cannot be termed (pseudo)diffuse or spot mode. On the other hand, one of these modes exists at all values of the discharge current and may be termed fundamental mode.…”