Plasma expansion and current flow in a vacuum arc with a small anode

A low-density plasma flow in a vacuum arc with a small anode which intercepts only part of the cathodic plasma was studied theoretically using a two-dimensional approximation. The plasma expansion was modeled using the sourceless steady-state hydrodynamic equations, where the free boundary of the plasma was determined by a self-consistent solution of the gas-dynamic and electrical current equations. The influence of the ratio of the anode radius R_a to initial plasma jet radius R_o on the plasma density, velocity, current distribution and anode sheath voltage drop is analyzed. The mass and current flow in a 500 A arc with R_a/R_o = 1 are compressed near the axis, leading to an increase in the plasma density by a factor of 2 and in the axial current density by a factor of 1.5 at a distance of about the plasma jet radius from the starting plane. In this case the radial anode sheath drop distribution is approximately uniform and the anode sheath drop has a value of about 0.4 T_e where T_e is the electron temperature. In the case of a small anode, the anode sheath potential drop becomes non-uniform radially and the centerline anode voltage drop increases to 0.9 T_e.