The first extensive study of the electric arc voltage relationships, for moderate levels of current and voltage, was made by Hertha Ayrton [I>, who developed a formula defining the arc voltage on the basis of empirical experimental results. The relationship is still considered to be valid and is still widely used, although within a limited range of current and voltage. The classical Ayrton equation is given as:
The values of the constants A, B, C, and D are empirical values for copper electrodes in air.
The current density at the cathode is practically independent of the arc current, but it is strongly dependent upon the electrode material. In refractory materials that have a high boiling point, such as carbon, tungsten, or molybdenum the cathode spot is observed to be relatively fixed. The cathode operates by thermionic emission and its current density is in the order of l03
amps per cm2. The "cold cathode arc" is characteristic of low boiling point materials such as copper and mercury. The cathode spot in these materials is highly mobile, it operates in some form of field emission, and its current density is in the order of 106
amps per cm2. In those materials that have a low boiling point, a considerable amount of material is melted away from the electrodes. The material losses of refractory materials is only due to vaporization. Under identical arcing conditions the refractory material losses are considerably less than the losses of low boiling point materials, and consequently this constitutes an important factor that must be kept in mind when selecting materials for circuit breaker contacts.
The low-pressure or vacuum arc, like those arcs that occur at or above atrnospheric pressure, share most of the same basic characteristics just described for the electric arc. But the most significant differences are (a) an average arc voltage of only about 40 volts, which is significantly lower than the arc voltages observed in high pressure arcs; (b) the positive column of the vacuum arc is solely influenced by the electrode material because the positive column is composed of metal vapors that have been boiled off from the electrodes. The positive column of the high-pressure arc is made up of ionized gases from the arc's surrounding ambient, and perhaps the most significant and fundamental difference, (c) the unique characteristic of a vacuum arc that allows the arc to exist in either a diffuse mode or in a coalescent or constricted mode. The diffuse mode is characterized by a multitude of fast-moving cathode spots, together with what looks like a multiple number of arcs in parallel. It should be pointed out that this is the only time when arcs in parallel can exist without the need of balancing, or stabilizing inductance. The magnitude of the current being carried by each of the cathode spots is a function of the contact material, and in most cases it is only approximately 100 amperes. Higher current densities are observed on refractory materials such as tungsten or graphite, while lower currents correspond to materials that have a low boiling point such as copper.
HIGH VOLTAGE CIRCUIT BREAKER
Design and Applications
Second Edition, Revised and Expanded
RUBEND . GARZON
Square D Co.