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

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.

A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations

“…At high (compared to B θ ) values of B z , the system becomes almost uniform, and the problem -one-dimensional. We will emphasize that no data on the pattern of distribution of the potential and of the components of the vector of current density on the starting plane were given in previous studies employing various two-dimensional models [5][6][7][8].…”

A Two-Dimensional Mathematical Model of a Short Vacuum Arc in External Magnetic Field

“…This model was used previously in the VA theory as well [4,5]. In the case of a high-current VA, a large number of cathode spots are located on the cathode (made, for example, of CuCr) and uniformly distributed over its surface [13].…”

“…We follow [4,5] and assume that jets from individual flames intersect during the motion of plasma toward the anode, and that a conventional plane is located at some distance from the cathode, which is referred to as starting plane beginning from which plasma may be treated as a continuum; at the same time, plasma is substantially discrete in the cathode-starting plane gap. We will assume that the starting plane is the cathode boundary of plasma and study the motion of plasma in the starting planeanode gap.…”

“…This model was used to calculate the distributions of densities of current and plasma and determine the shape of the plasma channel boundary for relatively low (~500 A) values of current. The model of [4,5] ignored the anode drop which may affect significantly the current density distribution. In addition, no boundary condition was formulated in [4,5] for the Poisson equation on the cathode boundary of plasma.…”

“…An important step forward in the development of two-dimensional mathematical models was made by the authors of [4,5] who used hydrodynamic equations for electrons and ions (assuming the constancy of temperatures) along with electrodynamic equations. The problem was reduced to a simultaneous solution of the equation of motion for ions and the equation for potential of the type of Poisson equation with a complex right-hand side dependent on unknown functions.…”