Theory of anode region of high-current vacuum arc

A model of the anode region of high-current vacuum is developed that explicitly takes into consideration the ratio of the drift velocity of the electrons in plasma v₀ to their thermal velocity v_T as a parameter of the electron velocity distribution function in the anode sheath. A transcendental equation for determining the value of the negative anode drop as a function of the ratio v₀/v_T is obtained. It is shown that in contrast to the well-known Langmuir formula the anode drop remains negative for any value of v₀/v_T relation. For small values of v₀/v_T <;<; 1 the expression obtained passes asymptotically into the Langmuir formula. The dependence of the anode drop value on the current density is used as a boundary condition at the anode in solving the two-dimensional problems in the theory of short vacuum arc. In accordance with the Langmuir formula a region with a positive anode drop is formed at the anode when the current density increases. The results of present work show that the region with a positive anode drop is absent.