Potential and current distribution in the interelectrode gap of the vacuum arc in a magnetic field

The plasma jet focusing and voltage distribution in the interelectrode gap of a vacuum arc with a ring anode and subjected to an axial magnetic field were studied theoretically. A 2-dimensional model was developed based on the free plasma jet expansion into vacuum and the steady state solution of the fully ionized plasma in the hydrodynamic approximation was analyzed. It was found that the imposition of an axial magnetic field reduces the radial expansion of the plasma jet. The plasma density on the axis increases by a factor of 2 with imposition of a 20 mT magnetic field. The arc voltage increased with the imposition of a magnetic field, and also increased with the anode length. The arc voltage consists of the cathode drop, the plasma voltage drop and anode sheath drop. The model was compared with experimental measurements of the vacuum arc voltage behavior in an axial magnetic field, and good agreement was found.