A simplified unified theory of arcs and their electrodes

A recently developed unified theory of arcs and their electrodes, with cathodes which are thermionic emitters, has been simplified so that there is a reduction in computation times by approximately a factor of 100. Electrode and arc regions are treated together and points at the surface of the electrodes are treated in a special way to account for electrode effects; no assumptions are made concerning the current density at the cathode surface. The theory is used to make predictions of arc and electrode temperatures and arc voltages for arcs in argon as a function of current in the range 50 - 400 A. The maximum temperatures of the arc and the cathode and also the current - voltage characteristics are in reasonable agreement with experimental results for cathodes with a included angle. For a cathode with a included angle, we predict a maximum in the temperature several millimetres from the tip of the electrode, in approximate agreement with experiment. Temperatures of the cathode tip are predicted to be much higher for tungsten cathodes than for thoriated tungsten cathodes and are in reasonable agreement with experimental results. Tungsten electrodes are hotter than thoriated tungsten electrodes, partly due to increased ion heating, but largely due to greater heat conduction from the arc to the electrode due to the arc plasma covering a greater area of the electrode surface for tungsten.