550 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



opposite electrode. An estimate of their velocity may be obtained by 

 assuming thermal equilibrium to have preceded the arc extinction and 

 by using the Maxwellian velocity distribution. The most probable 

 velocity of the metal atoms at the boiling temperature 2' & is : 



Uat = I (6) 



\ m / 



Due to subsequent collisions of the atoms, the velocities thus obtained 

 are probably too high. For Pd at Tt = 2500°K, Uat = 6.4 X 10* cms/sec. 

 In Fig. 11 is plotted a portion of the velocity distribution at the above 

 conditions. It appears that residual atoms can still be present in the gap 

 at the initiation of the next arc. If it is assumed that the presence of Pd 

 atoms in the gap is alone responsible for the lowering of the arc initiation 

 voltage, one may conclude that the sparking potential in Pd vapor is 

 lower than in air. No evidence, however, is available to support this. 

 On the other hand, at least for contacts with gaps short enough to ex- 

 clude the surrounding atmosphere, or for vacuum contacts in general, 

 it is quite probable that the presence of metal atoms in the gap could 

 enhance arc initiation. This, as pointed out previously, is because the 

 arc cannot be initiated until atoms from the electrode surfaces are 

 evaporated, by electron bombardment or otherwise, to be subsequently 

 ionized. 



c. Cooling Time of The Arc Spot, Maintenance of Thermionic Emission 



At the interruption of the first arc, the arc spot initially at the boiling 

 temperature of the metal, will start coohng mainly by conduction to the 

 bulk of the surrounding metal. For a certain period, however, it will 

 remain at temperatures high enough to furnish enough thermionically 

 emitted electrons that may enhance the initiation of the following arc. 

 Assuming the arc spot to be a hemisphere of radius "a" initially at a 

 temperature Tb while the rest of the metal is at To, the temperature T 

 at the center of the hemisphere is given by : 



{T - To)/{n - To) = ^^ I z'e-' dz (7) 



Numerically, ior T i = 2500°K and To = 300°K, T drops to 2400°K and 

 to 1600°K at a/2 {at)"' - 2.0 and 1.2, respectively. It is evident 

 that the cooling time is proportional to the area of the arc spot. If the 

 current at which the arc is terminated is /„ and the arc current density 

 is ia, the area of the arc spot is ^o = Im/ia and a = (Jm/T^iaf"- For 



