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 io is 



V=0 V| ^V| 



SPACE CHARGE ^ 

 LIMITED current) 



I 



CATHODE FIRST SECOND 



PLANE, PLANE 



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



y 3/2 y^sn 



i^ — a^ — — - = 2.33 X 10~^ —j^r- (amperes per sq. cm.) (12) 

 d" d- 



The current in units of ia is denoted by 7 so that the injected current / 

 in amperes per sq. cm. is given by 



/ = 7«o. •• (13) 



Similarly, the transmitted current under conditions corresponding to 

 type B potential distributions will be 



ZI = Zyio. ^ (14) 



Specifying 7 and (p is equivalent to specifying a and (p.^^ 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 

 different types of potential distributions may exist are shown in Fig. 7 

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

 (f and the transmitted current Zj. The boundaries of the C and D 



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

 pendix. 



