Minimum voltage principle in the theory of a high-current vacuum-arc discharge

The effect of an inhomogeneous magnetic field with axial and radial components on the structure of a high-current vacuum-arc discharge (VAD) has been theoretically studied. The characteristic features of current passage in a short VAD are considered using analytical expressions for the slope of the total current lines (TCLs) relative to the discharge axis, the axial components of the electric and magnetic fields, and the effective conductivity of discharge plasma. A two-dimensional mathematical model has been used to calculate the TCL shapes and the discharge voltage for various dimensions of the region of cathode spots. Calculations showed that the voltage drop on the discharge gap as a function of the arc discharge radius on the cathode has a minimum. The shape of TCLs and the arc radius on the cathode at this minimum agree with the available experimental data.