Heating of refractory cathodes by high-pressure arc plasmas: II

Abstract

Solitary spots on infinite planar cathodes and diffuse and axially symmetric spot modes on finite cathodes of high-pressure arc discharges are studied in a wide range of arc currents. General features are analysed and extensive numerical results on planar and cylindrical tungsten cathodes of atmospheric-pressure argon arcs are given for currents of up to 100 kA. It is shown, in particular, that the temperature of cathode surface inside a solitary spot varies relatively weakly and may be estimated, to the accuracy of about 200-300 K, without actually solving the thermal conduction equation in the cathode body. Asymptotic behaviour of solutions for finite cathodes in the limiting case of high currents is found and confirmed by numerical results. A general pattern of current-voltage characteristics of various modes on finite cathodes suggested previously on the basis of bifurcation analysis is confirmed. A transition from the spot modes on a finite cathode in the limit of large cathode dimensions to the solitary spot mode on an infinite planar cathode is studied. It is found that the solitary spot mode represents a limiting form of the high-voltage spot mode on a finite cathode. A question of distinguishing between diffuse and spot modes on finite cathodes is considered.

Stability of direct current transfer to thermionic cathodes: II. Numerical simulation

“…At the lateral surface, the boundary conditions are ∂T 0 /∂n = ∂T 1 /∂n = 0. Results given in this section have been calculated for the (constant) thermal conductivity equal to 100 W m −1 K −1 and the specific heat equal to 200 J kg −1 K −1 ; these values may be assumed as characteristic for tungsten in the range of temperatures between 1000 and 3000 K. The pattern of the CVCs of different steady-state modes of current transfer to the cathode under these conditions is similar to the one shown in figure 1, except that the first axially symmetric spot mode on the cathode with an insulating lateral surface joins the diffuse mode [1,7]. means of equations (18) and (31) of appendix A in accord with table A1 of appendix A.…”

“…Interaction of high-pressure arc plasmas with thermionic cathodes is a challenging issue of high scientific interest and technological importance. In spite of many decades of research, a self-consistent theory and modelling methods have started to emerge only recently; see [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein. Still, some important questions are far from being answered.…”

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

“…A pattern of different modes on a rod cathode is illustrated by figure 8 (data taken from [73,76]). This figure refers to a cylindrical cathode of radius R = 2 mm and height h = 10 mm, a geometry convenient for illustrative purposes.…”

Joule heat generation in thermionic cathodes of high-pressure arc discharges

“…27 The account of Joule heating changes this pattern, as shown by the distributions for I ¼ 200 A: with increasing current, the maxima of the surface temperature and the current density are shifted in the direction to the base of the cathode. The maxima become very well pronounced while the front surface of the cathode becomes rather cold and collects no current.…”

“…The modelling was performed with the use of an asymptotic boundary condition for the temperature distribution inside the cathode at large distances from the spot which was proposed in Ref. 27. A similar boundary condition was used for the electrostatic potential.…”