Theoretical study of plasma expansion in a magnetic field in a disk anode vacuum arc

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Abstract
The low-density plasma flow in an axial magnetic field to a disk-shaped anode in a vacuum arc was studied theoretically using a two-dimensional model. 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 anode was modeled as a current and plasma collector, which does not influence the plasma flow field. Magnetic forces from both the azimuthal self-magnetic field, and the imposed axial magnetic field were taken into account. It was found that the self-magnetic field does not substantially influence either the plasma jet shape, density, velocity, or the current density distribution for arc currents I⩽200 A. On the other hand, the plasma jet angle (α0) at the starting plane and the radial plasma density gradient force in the expansion region do have a strong influence on the plasma and current flow. The mass and current flow in a 500 A arc are compressed in the near axis region, leading to an increase in the plasma and axial current density by a factor of 1.5 at a distance of about two plasma jet radii from the starting plane. The calculated arc current–voltage characteristics agree qualitatively with experiments on arc behavior in an axial magnetic field.