Theory of Anode Region of Short High-Current Vacuum Arc

Abstract

A model of the anode region of a high-current vacuum arc is developed, which explicitly takes into consideration the ratio of the drift velocity of the electrons in plasma <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}$ </tex></formula> to their thermal velocity <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{T}$</tex></formula> 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 (AD) as a function of ratio <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}/v_{T}$</tex> </formula> is obtained. It is shown that, in contrast to the well-known Langmuir formula in a 1-D model of a collisionless sheath, the AD remains negative for any value of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}/v_{T}$</tex> </formula> relation. For small values of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$v_{0}/v_{T} \ll 1$</tex></formula> , the expression obtained asymptotically passes into the Langmuir formula. The dependence of the AD value on the current density is used as a boundary condition at the anode in solving the 2-D problems in the theory of short vacuum arc. In accordance with the Langmuir formula, a region with a positive AD is formed at the anode when the current density increases. The results of this paper show that the region with a positive AD is absent.