Evolution of Copper Vapor from the Cathode of a Diffuse Vacuum Arc

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Abstract
The metal-vapor evolution from the cathode of a diffuse vacuum arc is described by a model that starts from the expression for the collisionless expansion into vacuum of atoms originating from an instantaneous point source. The velocity distribution is assumed to be Maxwellian at the moment the atoms are released from the source. By convolution with the vapor generation rate, which is given by an effective erosion rate and the waveform of the arc current, this expression is generalized to yield the atomic density at an arbitrary distance from a point source which emits atoms for a finite period. The result is integrated over the cathode surface which is treated as an extended homogeneous source of vapor. The copper-vapor density was calculated for a vacuum arc driven by a sinusoidal 50-Hz current half-cycle of 500 A rms, for the center of the contact gap. With a vapor temperature of 2000 K and an effective copper-vapor erosion rate of 3 μ/C, the model well describes the measured decay of the copper-vapor density from about 5 × 1017 m-3 at 300 μs before current-zero to 5 × 1014 m-3 at 400 μs after current-zero. Comparison with calculations based on the assumption that metal vapor is generated predominantly by molten droplets evaporating in flight indicates that before current-zero the contribution of the droplets to the vapor density is negligibly small, while after current-zero both vapor generation mechanisms produce vapor at the same order of magnitude.