Revisiting Theoretical Description of the Retrograde Motion of Cathode Spots of Vacuum Arcs

A fresh attempt to develop a self-consistent description of the retrograde motion of cathode spots on volatile cathodes is undertaken. Three potential mechanisms of effect of transversal magnetic field on the distribution of parameters in the spot are studied: the effect of magnetic field on hydrodynamics processes in the spot, in particular, on the formation of liquid-metal jet and the droplet detachment, and the effect of transversal magnetic field over the motion of ions and emitted electrons in the near-cathode space-charge sheath. It is found that for typical conditions of cathode spots in vacuum arcs the effect of magnetic field over the formation of liquid-metal jet and the droplet detachment is negligible; the motion of the ions in the near-cathode space-charge sheath is not disturbed; and the motion of the emitted electrons is disturbed only marginally. Thus, the above-mentioned potential mechanisms are hardly relevant and the first-principle understanding is still missing. A phenomenological description of the retrograde motion is developed as an alternative. The description employs general considerations without relying on specific assumptions and the (only) unknown parameter can be determined from comparison with the experiment.