Interaction of the cathode spot with low pressures of ambient gas

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Abstract
This paper presents a calculation of the interaction of the cathode spot in an electric arc with a low pressure of ambient gas. It is assumed throughout that the basic structure of the spot is unaffected by the gas, the relatively large vacuum spot being a loose collection of smaller fundamental spots. Most of the interaction comes from the smaller current (∼8% of the total) of highly energetic positive ions emitted by the spot; these ions exclude the gas from the neighorhood of the spot which, therefore, never sees the surrounding gas. The equations of the motion yield the pressure dependence of the force on the cathode, the total rate of cathode erosion, and the outward flux of the ions; these agree reasonably well with the experiment, but no force that seems able to separate the components of the vacuum spot has been found (the force that holds them together in vacuum is equally unknown).