2D expansion of the low-density interelectrode vacuum arc plasma jet in an axial magnetic field

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Abstract
The two-dimensional expansion of a current carrying plasma jet in the interelectrode gap of a vacuum arc with an axial magnetic field is analysed by finding the steady state solution of the fully ionized plasma in the hydrodynamic approximation. Two models are presented: (1) expansion into a duct with known geometry and (2) free jet expansion. The first approach models the plasma jet expansion with a conical shape. In the second model the geometric position of the free boundary was determined by the free hydrodynamic jet expansion into vacuum without and with the influence of a magnetic field. In the case of plasma expanding into a conical guide, it was found that the flow field in the near-axis region does not depend on the cone angle for cone angles . The radial velocity becomes comparable to the axial velocity due to the expansion, depending on the cone angle and the initial axial velocity. A model of the free boundary plasma expansion was developed, based on the jet-like (i.e. axial velocity larger than the radial velocity) plasma flow in the vacuum arc near the cathode spot. The free jet boundary was calculated by solving the equations for the normal and tangential velocity components at the free boundary. It was found that the plasma jet had a conical shape, and for axial distances 3 - 4 times greater than the initial jet radius, the radial velocity becomes comparable with the axial velocity if no magnetic field is imposed. Imposition of a magnetic field reduces the radial component of the plasma velocity. The streamline angle is about for a 0.001 T magnetic field and about for a 0.01 T magnetic field. The plasma remains quasi-neutral in all regions except in the space charge boundary layer, where an outward directed electric field appears for low magnetic fields, and an inward directed field is present for strong magnetic fields.

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