On the Mechanism of Retrograde Motion of Cathode Spots of Vacuum Arcs

When a transversal magnetic field is present, current spots on arc cathodes made of volatile metals move predominantly in the anti-Amperian, or “retrograde”, direction; a phenomenon of high theoretical interest and importance for applications. A fresh attempt to find a first-principle explanation of this phenomenon is undertaken in this work. Two 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 ions is not disturbed and the motion of the emitted electrons is disturbed only marginally. Thus, both 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 free parameter appearing in this description is found in two ways, with the use of experimental data and by means of an additional theoretical assumption, and the obtained values are reasonably close.