The Arc Cathode Spot and Its Relation to the Diffusion of Ions within the Cathode Metal
Authors: Kingdon Kenneth H. 
Published: April 2005

Kesaev's recent data on the stability of vacuum arcs for a wide variety of solid and liquid cathodes furnish a greatly expanded range of criteria for determining the mechanism of the cathode spot. The large effects of phase and crystalline texture of the cathode suggest that an essential process occurs within the cathode metal itself. This is thought to be secondary electron emission produced by positive ions through a diffusion-controlled neutralization process. Each secondary initiates a short burst of thermal ionization in front of the cathode, which supplies practically all of the arc current. Survival of the arc depends on the emission of at least one new secondary within the period of the burst, and this depends on the current and on the rate of diffusion of ions into the cathode, the secondary emission being greater the larger the current and the slower the diffusion. Relative diffusion rates are estimated for most of the cathode metals used by Kesaev and it is found that the current required for a given arc lifetime increases regularly with the rate of diffusion of ions into the cathode metal. The analysis yields five new heats of diffusion—polycrystalline mercury and bismuth 16.2 and 18.3 kcal/mole, respectively; and liquid bismuth, thallium, and aluminum, 8.8, 3.2, and 3.4 kcal/mole, respectively.
The diffusion rate is correlated with cathode temperature, dislocations, and vacancies, and the moving spot probes in all directions for areas of low diffusion rate. The arc is extinguished when all parts of the cathode line lie on micro-areas of high diffusion. The arc lifetime data furnish estimates of the concentrations of dislocations in all the solid and liquid (transient existence) metals as prepared by Kesaev. The concentration of edge dislocations is found to be approximately inversely proportional to the fourth power of the heat of vaporization.
The statistics of arc lifetime as a function of current may be correlated by the Poisson formula, with each burst of ionization counting as a single Poisson trial, which is successful if it produces one or more secondary electrons. The analysis for liquid indium indicates that the bursts have a lifetime of about 5×10−7 sec.
The random motion of the free spot on mercury is thought to be determined by random radial temperature-fluctuation gradients at the edge of the spot. The velocity of the free spot on mercury is limited to about 104 cm/sec because the spot must not outrun its secondary emission, which lags behind positive ion incidence on the cathode by about the 10−7 sec required for the diffusion secondary emission process in mercury. Retrograde motion of the spot in a magnetic field is found, qualitatively and semiquantitatively, to be due to the temperature gradient set up across the spot by the Righi—Leduc thermomagnetic effect. The retrograde velocity on bulk liquid mercury is subject to the same velocity limit of about 104 cm/sec as is the random velocity in zero field. A spot at a mercury—molybdenum boundary can jump to a substantially higher velocity when the Righi—Leduc gradient is high enough, and when, also, the increased velocity is great enough to permit the spot to operate on a mercury layer so thin that the diffusing ions have access to the molybdenum surface, where the more abundant supply of electrons accelerates the neutralization process, and thus decreases the time-lag of secondary emission.
It is suggested that more sophisticated observation and analysis of cathode-spot statistics should furnish a valuable metallurgical tool for studying the texture and dislocation properties of metal surfaces. From the analysis of Kesaev's data some speculations are made about the origin and behavior of edge dislocations.