Shock discontinuity in high-current vacuum arcs

The deceleration of a cathode plasma jet caused by interaction with a secondary ion cushion at the anode is analyzed. Copper electrodes are considered. The secondary ions are assumed to be sputtered and/or reflected from the anode. The sputtering coefficient was found by integrating the energy distribution of the cathode spot plasma jet, weighed by the copper-copper self-sputtering yield. The system of equations of motion and continuity for the primary plasma jet and the secondary ions was solved numerically for arc current densities in the range of (3×10⁴-5×10⁵) A/m². It was found that for an interelectrode gap of 2 cm, and a secondary ion velocity of 10³ m/s, there is no upper limit for the current density for continuous jet motion. For secondary ion velocities <0.25×10³ m/s, the upper limit is 10 ⁵ A/m², above which a shock front forms between the primary and secondary plasma