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

The nonlinear surface heating model of plasma-cathode interaction in high-pressure arcs is extended to take into account the Joule effect inside the cathode body. Calculation results are given for different modes of current transfer to tungsten cathodes of different configurations in argon plasmas of atmospheric or higher pressures. Special attention is paid to analysis of energy balances of the cathode and the near-cathode plasma layer. In all the cases, the variation of potential inside the cathode is much smaller than the near-cathode voltage drop. However, this variation can be comparable to the volt equivalent of the energy flux from the plasma to the cathode and then the Joule effect is essential. Such is the case of the diffuse and mixed modes on rod cathodes at high currents, where the Joule heating causes a dramatic change of thermal and electrical regimes of the cathode. The Joule heating has virtually no effect over characteristics of spots on rod and infinite planar cathodes.