A physical model of anode spot formation in a high-current vacuum arc

Physical and mathematical models are suggested for the description of anode heating and anode spot formation. An increase in the vacuum discharge current is accompanied by the crisis of cathode ion flow which leads, at a certain (critical) value of current, to the impossibility for the ions to reach the anode. It is known that, in this case, a layer of negative space charge with positive anode drop is formed, as well as an electron beam. The magnitude of anode drop depends on the thickness of the space charge layer and on the form of the electric circuit. A nonlinear dependence of the space charge layer thickness on the discharge current density is obtained. The presence of such a dependence makes it possible to solve the electric circuit in view of nonlinear unsteady-state resistance and capacitance of the layer and to calculate the voltage across the layer, the current density and the power density on the anode, as well as to calculate the anode surface temperature. The results of calculations of the time required for anode spot formation and of the time dependence of voltage across the space charge layer agree with the experimental data.