Hydrodynamic model of vacuum arc plasma flow in a positively biased toroidal macroparticle filter

A hydrodynamic model of vacuum arc plasma flow through a toroidal magnetized macroparticle duct has been developed. The case of the duct wall having positive potential with respect to the adjacent plasma is analysed. The quasi-neutral plasma and the sheath appearing near the duct wall were considered. The plasma parameters obtained in the sheath region were used as a boundary condition for the problem of the plasma flow. The plasma flow in the quasi-neutral region was modelled by sourceless steady-state equations. It was found that the plasma density distribution within the filter cross-section has a maximum near the outer wall. In the course of the flow through the duct the plasma velocity generally decreases along the duct and at the filter exit is about half of the initial value in the centre. We find that the plasma loss is mainly in the second half of the filter. The ion throughput at the exit cross-section depends upon the applied voltage drop and increases by a factor of two for the case of a magnetic field of about 0.01 T. The ion throughput has a maximum at a duct bias of about 20 V. These results are in agreement with experiments.