Hydrodynamic Model of Plasma Jet of Cathode Spot of Vacuum Arc in the Presence of External Axial Magnetic Field

Abstract

This paper concerns the paraxial structure of a plasma jet, escaping a cathode spot of a vacuum arc in the presence of an external axial magnetic field. The jet is described in the stationary single-temperature single-fluid approximation with viscosity, thermal conductivity, and radiation disregarded. To take account of the ion composition of the plasma, the average-charge approach is used. Allowance is made for the transonic nature of the flow and the presence of a free boundary. The problem is solved by the method of paraxial expansions and is reduced to a closed system of ordinary differential equations, corresponding to the principal order of the expansion. System singularities relating to the critical section are isolated explicitly and processed. The equation set is integrated in the hydrodynamic region to either side of the critical section. The number of free parameters in the critical section is reduced to two, which are the average charge and temperature. The values of all other parameters of a jet in a wide range of their variation are constructed on the plane of free parameters. The same is performed for jet parameters in the plane, considerably away from the critical section. Axial distributions of the parameters are built. The obtained results generalize those of an earlier paper in the case of the presence of the external axial magnetic field. The results describe the contraction of a jet by the external axial field and the corresponding changes in the behavior of the jet parameters along the axis. It turns out here that, because of the jet contraction, the region of validity of the hydrodynamic description of a jet extends rather far toward the anode.