Model of the short vacuum arc at collision free motion of ions

The 2D mathematical model of the short vacuum-arc discharge is developed that considers a hydrodynamic mode of electron motion and collision-free mode for motion of fast cathode ions in a 2D electric field. The model takes into consideration an angle distribution of ions on the cathode plasma boundary. A method of calculation of plasma density distribution in the gap is proposed. Two-dimensional distributions of discharge current density, plasma density and electric field in an external longitudinal magnetic field are calculated. It is shown that intersections of ion trajectories take place and a part of ion trajectories returns to the cathode. As the value of the external magnetic field decreases, the number of ion trajectories returning to the cathode increases and the number of ion trajectories reaching the anode decreases.