The Vacuum Arc
The Closed Contact
The vacuum interrupter’s contacts are the heart of its performance. When closed they permit the flow of current in an electrical circuit. The current must flow through the contacts without overheating them. In some applications the contacts may stay closed for many years: in others, frequent opening and closing may be normal. When contacts open under load the vacuum arc that forms between them must be stable to the natural current zero of an ac circuit or to the forced current zero in a dc circuit. The region of the contacts where this electric arc attaches is subjected to very high temperatures. Even under these severe conditions, the contacts must resist excessive erosion and maintain their mechanical integrity. The contact surfaces must also maintain a reasonably high electrical conductivity so that, when they again close, current can flow without excessive heating. When the contacts are opened under fault current conditions (such as short-circuit currents), the designer has to consider how to control the resulting high-current vacuum arc. When current zero is reached in an ac or dc circuit and the arc extinguishes, the gap between the electrical contacts has to recover its dielectric properties very rapidly.
In all vacuum interrupters the properties of the electric contacts are vital for a successful dielectric recovery. For example, the contacts must not exhibit severe field distortion or stay hot long enough to liberate large numbers of electrons or too much metal vapor. In some applications the contacts are required to close and latch on very high short-circuit currents. Here they not only have to withstand the mechanical forces involved but also the opening mechanism must be designed to break any contact welds that form. Thus, it is apparent that the electric contact participates in every phase of a vacuum interrupter’s operation. No matter what the voltage range or current level, the choice of the contact material and the correct design of the electrical contact are essential (see Chapter 3, this volume).
In a power system an understanding of electric contacts is not just confined to the design of the vacuum interrupter. It is also required for the proper connection of the vacuum interrupter into its switching mechanism and into the electrical circuit: e.g., how the vacuum interrupter’s fixed terminal is connected to the circuit breaker’s bus, how the connection is made to the moving terminal and how the circuit breaker itself is joined to the electrical circuit. These contacts are usually not affected by arcing, but their design is an integral part of the successful operation of the vacuum interrupter; see Section 6.2.1 will therefore begin this chapter with a brief discussion of electrical contact theory. A more thorough review of this subject is presented in my book Electrical Contacts (CRC Press, 2014)  and in the seminal work by Ragnar and Else Holm . I will then continue with how the vacuum arc forms between two opening contacts. After this I will present the different kinds of vacuum arc. I will conclude with a review of how these different modes of vacuum arc are affected by the imposition of external magnetic fields.
Making Contact, Contact Area, and Contact Resistance
If the two cylinders shown in Figure 2.1 are butted together and the resistance between points a and b is measured, the resistance will be found to be:
Total resistance a <-> b= (bulk resistance of the cylinders) + (contact resistance)
FIGURE 2.1 The electrical contact.
The reason for this is that no matter how carefully the cylinders’ faces are prepared; they will never be perfectly flat. Indeed, they will make contact only at a number of discrete points on these flat surfaces [2-4]. You have already seen in Figure 1.26 that a high-magnification picture taken of a smooth metal surface reveals a number of microscopic peaks and valleys. Thus, when two such surfaces are brought together, they initially touch at the two highest micro-peaks. Even under light loads the pressures at these peaks will be very high [2, 3] so the peaks will deform plastically. As the first tw'o micro-peaks deform, more micro-peaks will come into contact and they in turn will deform plastically. This process will continue until the force on the contacts is fully supported by a small number of microscopic contact spots. This is shown conceptually in Figure 2.2, and the process can be represented by [2, 3].
Contact closing force « [contact material’s hardness] x [£ real microscopic areas of contact] or:
where £ is a constant (It is « 1 for plastic deformation). This state is usual for the forces typically used in the mechanisms that operate vacuum interrupters, i.e., greater than ION) and is the microscopic contact spot. It can be seen that Equation (2.2) implies that the actual area of contact depends only on the contact force and the contact’s material properties; it does not depend upon the total area of the contact face. This is true for contacts carrying very low' currents (e.g., in electronic
FIGURE 2.2 Plastic deformation and the real area of contact.
FIGURE 2.3 Example of the real area of contact vs. contact load for two contact sizes: (a) solid line, 10cm2 nominal area: (b) dashed line, 1cm2 nominal area .
circuits) as well as for contacts carrying the range of currents usually found in vacuum interrupters (e.g., 50A to 80kA). Figure 2.3 illustrates this for a 10-fold change in contact face area .
Calculation of Contact Resistance
The Real Area of Contact a Small Disk of Radius “a”
Consider as a first approximation of Figure 2.4, where a disk-shaped area A,, of radius “a” is achieved after the contacts have been forced together. The flow of current from one conductor to the other would then be constrained to flow through this area. The constriction resistance is given by [2,3,6]:
Where p is the resistivity of the contact material. Substituting from Equation (2.2) and noting that
A,. = ла2:
FIGURE 2.4 The average area of contact, A,, showing how the lines of current flow are constricted to flow through it.
FIGURE 2.5 The change in total impedance of a vacuum interrupter (R, = R„ + Rc) with annealed Cu-Cr contacts as a function of the contact load;(B) experimental data.
If Rf is the resistance of any film, then the total contact resistance Rc is given by (Rc = RK + RF). In a vacuum interrupter RF is usually zero, so:
Thus, the contact resistance results from the current being forced to flow from the bulk of the conductor into a small area radius “a.” Figure 2.5 presents data for fully annealed Cu-Cr (25 wt% Cr) contacts inside a vacuum interrupter showing how (Rr = RB + Rc), where RB is the bulk resistance of the Cu terminals plus the bulk resistance of the contact material (see Figure 1.2) varies with F and how closely Equation (2.4) describes the data. The actual contact spot is usually not just one spot as shown in Figure 2.4. In most practical contact systems and certainly with vacuum interrupter contacts the region of actual contact is made up of a number of microscopic contact spots distributed within an overall contact region. This is illustrated in Figure 2.6 . Fortunately, calculations on randomly arrayed contact spots with a practical distribution of diameters [2-4], show that the microscopic effect of these spots gives a similar relationship to those given in Equations (2.3) and (2.4) with an average microscopic radius of contact like the one shown in Figures 2.4 and 2.6. For practicing engineers Equations (2.3) and (2.4) give values of constriction resistance, which are close enough to the real value (within 20%). Thus no one is really interested in the actual individual contact spots. The reason why these two equations satisfy most practical situations is that the constriction of the current as it travels to the region of contact does not recognize that there are individual microscopic contact spots until the current flow is extremely close to each contact’s surface. While the individual micro contact spots do determine the final current path, most of the current constriction effect, and hence the effect on the contact resistance has already occurred. It is also fortunate that the average contact constriction radius shown in Figures 2.4 and 2.6 gives an equivalent area of plastic deformation of the contact surface that is more or less the same as the sum of areas of all the individual contact spots.
For large area contacts such as those found in power vacuum interrupters (see Section 3.3), it is common to observe that more than one region of contact occurs. If these regions of contact are located a sufficient distance apart, they can be considered independent of each other [7, 8]. These are therefore similar current paths in parallel. Indeed, Dullni et al.  show that for large area, Cu-Cr, vacuum interrupter contacts both before and after high-current interruption testing that three regions of contact are most likely to occur. In this case Equation (2.4) becomes:
FIGURE 2.6 A random distribution of contact spots, giving the equivalent single contact area shown in Figure 2.4 .
where n = 3. They also show the top 100-200 pm of the contact surfaces change their composition: see Figure 3.6, this volume. This surface layer has a higher hardness and a higher resistivity than the original contact material: see Table 2.1. This results in a higher contact resistance after the series of high-current interruption tests. They conclude that the higher hardness contributes to most of the increase in the contact resistance and the increase in the surface resistivity only has a small effect. This observation is consistent with the fact that the contact resistance results from the flow of current from the bulk of the contact into the small areas of contact. Thus, the thin surface later only has a minor effect on its value. Taylor et al.  also observe a similar effect in the contact resistance of Cu-Cr contacts after high-current interruption testing.