548 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



20.0 

 O 17.5 



UJ 

 01 



a. 15.0 



UJ 

 Q. 



5 12.5 

 o 



? 10.0 



J 7.5 



in 



II 5.0 



I 



o 

 ^ 2.5 







^0.8 



'0.7 



0.6 



0.5 



0.4 



10 20 30 40 50 60 70 80 

 Xl0"° 

 TIME,!, IN SECONDS 



10 20 30 40 50 60 70 80 

 XlO"6 



Fig. 10 — Lowering of arc initiation voltage under dynamic conditions. 



Defining a charging velocity s/tch = Uch and a deionization velocity 

 s/tdeio = Udeio and substituting in equation 4 gives 



Udeio — 



bm 



(4a) 



Following an arc, the contact voltage increases until a new breakdown 

 occiu's at Vai . At this instant residual ions from the previous arc could 

 be present in the gap only if Uch > Uddo , or if 



Uch > 



6m j 



i'^y 



This is a convenient expression to apply to our measurements, Fig. 

 9. For any breakdown point on the transient Vai is measured and Uch is 

 calculated from the corresponding circuit current, capacity C and con- 

 tact separation. For illustration, for Pd contacts and Vai = 300 volts, 

 equation 5 shows that for the presence of residual ions, the charging 

 velocity Uch must be greater than 10 cms/ sec. For / = 0.3 amp. and C = 10^ 

 farad, tch = VaiC / 1 = 10~ sec and for the presence of residual ions the 

 separation between the contacts must be greater than 1.0 cm. This sep- 

 aration is much greater than most separations involved in our field of 

 study. In Fig. 10(b) are plotted the values of Uch during the transient. Uch 

 reaches a maximum of about 1.8 X 10* cms/sec. This maximum occurs 

 because Uch is proportional to si which is a product of two monotonic 

 functions one increasing and the other decreasing. It is of interest to note 

 that the decrease in Uch caused an increase in the ratio {Vai)dyn/{Vai)stat ■ 



* Deionization by recombination and lateral diffusion were neglected. 



