Reignitions in short vacuum gaps after interruption of high-frequency currents caused by ion bombardment

The internal energy increase of the cathode material during the post arc period as a result of the high electrical field at the cathode surface and the highly energetic ions existing in the vacuum gap is studied in this paper by solving the conservation equations of mass, momentum, and energy together, with the equation of state of electrode material in the cathode region. Solving the heat conduction equation in the cathode region, the temperature distribution of the cathode material is determined. The results for copper indicate that a breakdown can occur at the cathode surface some 100 ns after current zero depending on the form of the cathode surface inhomogeneities, the steepness of the transient recovery voltage, and the initial plasma distribution in the vacuum gap. These results are in accordance with experimental measurements.