Numerical model of thermoelectric phenomena leading to cathode-spot ignition

This paper deals with the results of a numerical model of the predischarge heating process encountered by a microprotrusion on the cathode surface of a vacuum gap, due to the field-effect current density flowing throughout the protrusion. The model is one-dimensional and nonstationary. The protrusion is sketched as a truncated cone and the material considered is tungsten, whose physical and thermal properties have been assumed temperature dependent. Electron current density emitted by the tip and the Nottingham effect have been calculated solving the integral of the energy distribution of the emitted electrons. In all other existing models, these two quantities are approximated by algebraic equations, valid in a limited temperature range. Results seem to confirm the experimental evidence that breakdown starts from the explosion of microprotrusions in a time of the order of 1-10 ns. In order to induce the explosion, current densities could be as high as 10¹³ A/m², while the corresponding electric field at the tip can reach the value of 10¹⁰ V/m, slightly higher than the value found by others. Numerical results confirm that the more slender the protrusion, the more likely its explosion. Investigation of the role of the surface work function shows that decreasing its value at the cathode surface favors the explosion of a larger number of protrusions, inducing the distribution of the arc current among more spots, with a cathode damage reduction, especially on electrodes operating at high current and low temperature.