Simulation of Magnetic Electron Cut-off in a Vacuum Switch with an Anode in the Form of an Inductor

The simulation of the process of magnetic cut-off of electrons in a vacuum switch (VC) with an anode in the form of an inductor was performed. Calculations were performed according to the physico-topological model of physical processes in the vacuum switch, which took into account current distribution along electrodes, the trajectory of electrons emitted by the cathode and the conditions of current interruption in VC. Determination of current distribution along the anode, as well as configurations of electric and magnetic fields were performed according to a mathematical model based on Maxwell's equations for vacuum and conductive medium of the anode and boundary conditions adapted to the shape of the elements of the VC. Material equations were also used for certainty. The initial kinetic energy of electrons emitted from the cathode was set equal to zero. Their direction of departure from the cathode surface was determined by the direction of the lines of force of the electric field near the surface. Electron emission was given by the uniform distribution of emission points on the surface of the cathode tip. The calculation of the structure of the magnetic field was performed taking into account the secondary magnetic fields and the current distribution over the cross section of the anode inductor, which is caused by the skin effect. It is established that a decrease in the step of the inductor turns and an increase in the amplitude of the current pulse in it lead to an increase in the magnetic field strength in the cathode region, which improves the focusing of electrons. At anode-cathode voltage of 10 kV, the step of the inductor of 6 mm and the amplitude of the anode inductor current pulse of 900 A, all the electrons emitted from the cathode are focused outside the anode. The influence of design parameters on the electron cut-off efficiency is determined. For the investigated design, the optimal cathode-anode distance was 12 mm with a step between the turns of the inductor of 6 mm. The results of calculations showed that reducing the distance between the turns of the inductor increases the efficiency of electron cut-off, which confirms the physical adequacy of the mathematical model and the correctness of the calculations. Calculations also showed that at a cathode-anode distance below 12 mm, the focusing of electrons deteriorates. In the proposed design of the VC with the anode inductor in the form of three turns, the complete cut-off of electrons, i.e. the time of flight of electrons through the electrode system, at anode-cathode voltage of 10 kV, occurred by less than 1 ns at an inductor current pulse of 900 A. The inductor current pulse duration was 5 μs had the form of the half-sinusoid arc. The used method of modeling allows to establish in what part of the inductor pulse the full cut-off of electrons is provided. The obtained results can be used in the development of the VC with interruption of the current of vacuum-arc discharge.