SPACE CHARGE BETWEEN PARALLEL PLANE ELECTRODES 59 



relations which exist at the second plane are of considerable interest. 

 Since the distance between the planes is now fixed, the parameter o- is 

 not appropriate. However, the spacing d between planes and the 

 voltage Vi serve to define a natural unit of current density io, which 

 is indicated by the hypothetical situation of Fig. 6. The value of U is 



v=o 



V| 



i-o 



SPACE CHARGE 

 LIMITED CURRENT 



CATHODE 



FIRST 

 PLANE, 



fV| 



SECOND 

 PLANE 



Fig. 6 — Hypothetical conditions to illustrate the significance of the unit of current ia 



7q3/2 y^zn 



io = a^ -^- = 2.33 X 10-^ -^ (amperes per sq. cm.) (12) 



The current in units of to is denoted by y so that the injected current I 

 in amperes per sq. cm. is given by 



I = yio. 



(13) 



Similarly, the transmitted current under conditions corresponding to 

 type B potential distributions will be 



ZI = Zyit\ 



(14) 



Specifying 7 and ^ is equivalent to specifying a and cp}^ For this 

 reason many of the limiting curves of the circuit characteristic plots 

 are simply related to those shown in the potential distribution plots 

 and are designated by the same letters. The regions for which the 

 diff'erent types of potential distributions may exist are shown in Fig. 7 

 now in terms of 7 and ip. In Fig. 8 the regions are defined in terms of 

 ip and the transmitted current Zy. The boundaries of the C and D 



1* This is a consequence of the relationship 7 = a"^, which is derived in the ap- 

 pendix. 



