Cathode Spot Development on a Bulk Cathode in a Vacuum Arc

Abstract

A transient model of spot on a bulk cathode is developed, considering the initial adjacent plasma generated during arc triggering. A self-consistent approach is described and a closed mathematical solution is presented to understand the transient cathode phenomena and the time-dependent cathode potential drop (CPD), considering the kinetics and gas dynamics of the cathode plasma flow. The time-dependent spot development is calculated by considering different existing lifetimes <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\tau$</tex> </formula> of an initial plasma adjacent to the cathode for Cu, Cr, and W and 10-A spot current. The lifetime <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\tau$</tex></formula> is in the range of 2–100 ns. The solution shows that for Cu, the cathode temperature increased from 3500 to 4300 K with spot time. The CPD decreased with spot time from initial values 100–45 V (depending on <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\tau$</tex></formula> ) to 14–15 V at steady state. The solution for a refractory W cathode is obtained using a previously developed virtual cathode model. Calculation shows that a spot current density of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim}{\rm 10}^{7}~{\rm A}/{\rm cm}^{2}$</tex></formula> can support the spot initiation in a time of 2 ns considering W cathode vaporization with plasma generation by atom ionization. When <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\tau$</tex></formula> increased from 2 ns to the 2 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu{\rm s}$</tex></formula> range, the W cathode temperature decreased from <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim}{\rm 10000}~{\rm K}$</tex></formula> to a relatively low level of 7500 K.