Arc Spot on Film Cathode Using Kinetic Approach of Plasma Flow

Abstract

Spot behavior on Cu film cathodes in vacuum arcs was studied theoretically. A kinetic model was developed and a system of equations was derived to understand Kesaev’s measurements of spot parameters on Cu films deposited on glass substrates. The solution showed a cathode potential drop of 12 V, lower than the value for a bulk Cu cathode, 16 V, in accordance with the measured data for film cathode, 11 V. This low value can be understood by the calculated power losses, which were lower than that for bulk cathodes, due to film heat conduction, which was comparable with the power losses by vaporization. Both increased from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 0.1$ </tex-math></inline-formula> up to about 1 W when the thickness was increased from 0.017 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.14~\mu \text{m}$ </tex-math></inline-formula> . The plasma velocity in the Knudsen layer normalized by the plasma sound speed is < 1, indicating impeded plasma flow. The spot velocity was determined using directly calculated erosion rate in the film track left by the spot motion. This velocity decreased from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\times 10^{4}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times 10^{3}$ </tex-math></inline-formula> cm/s, agreeing well with the measurements for film thickness larger than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.06~\mu \text{m}$ </tex-math></inline-formula> . The track width increased with film thickness and the calculated dependence was comparable with that measured.