Acceleration of a multicomponent plasma in the cathode region of a vacuum arc

A general solution to the problem of the steady-state spherical expansion of a current-carrying multicomponent plasma into a vacuum is derived. It is shown that, in vacuum arc discharges, the main force accelerating the cathode material, which becomes a plasma at distances of 1 to 300 μm from the cathode surface, is the electron pressure gradient force maintained by Joule heating. It is established that ions of different charges move with the same hydrodynamic velocity, which is uniquely determined by the mass and mean charge of the ions and the maximum electron temperature in the cathode region.