52 BELL SYSTEM TECHNICAL JOURNAL 



The results are shown in Figs. 2, 3 and 4. Figures 6 to 11 refer to 

 current voltage relationships discussed in a later section. 



To find the potential distribution when a second plane at a distance 

 a away from the first plane is held at a potential <p, one enters the 

 figures with the values of ^ and <j. Any member of the family of 

 curves drawn in heavy solid lines passing through this point represents 

 a possible potential distribution. The regions occupied by the heavy 

 curves are bounded by certain limiting curves identified by lower case 

 letters. These curves correspond to certain space charge conditions 

 between the planes and are indicated by the same letter whenever 

 met. The dashed curves refer to transit time and are explained below. 

 Situations corresponding to low potentials and large spacings occur, 

 for the most part, on Fig. 2, while those for high potentials and small 

 spacings occur on Fig. 3. An overlap region exists for which potential 

 distributions may be found on both families of curves. The interpre- 

 tation of this is found by inquiring more closely into the nature of the 

 curves of Figs. 2, 3 and 4. 



There are in all four distinct types of potential distributions. 

 These are : 

 Type A — The second plane is at a negative potential. All the injected 



current is reflected. Potential distributions are the same as 



for the case of temperature limited emission with the current 



2/ from the zero potential plane. 

 Type B — Both planes positive with potential zero between them. 



Injected current partially transmitted and partially reflected. 



Potential distributions corresponding to space charge limited 



emission on both sides of a virtual cathode at the zero of 



potential. 

 Type C — Both planes positive with a potential minimum (at a positive 



potential) between them. Complete transmission of injected 



current. 

 Type D^ — Both planes positive with no minimum between them. 



Complete transmission of injected current. 

 The curves on Fig. 2 are seen to fall into two groups, those which 

 extend to negative values of (p (marked with values of jS) and those 

 which contain the value ip = Q but which remain positive. The first 

 group (Type A) obviously corresponds to conditions under which all 

 of the injected current returns to the first plane. The slopes of these 

 potential curves at the reflection planes are not zero but are related to 

 the parameter /3 (shown on the curves) by the equation 



^=-tV2/3^'*- (5) 



do- 6 



