466 BELL SYSTEM TECHNICAL JOURNAL 



referred to. The investigation comprises the calculation of the im- 

 pedance between two parallel planes in vacuum, at known d-c. poten- 

 tials, when an electron stream with normal d-c. velocities corresponding 

 to these potentials is injected at right angles to the planes. As a 

 further step, the effect of a negatively polarized grid interposed be- 

 tween the two planes will be considered. This latter arrangement 

 may be taken to correspond to an idealized space charge grid tube. 



Before these calculations are presented it is well to set forth as 

 concisely as possible those results of the d-c. space charge analysis ^ 

 which will be of most immediate interest. For this purpose we start 

 with a qualitative review of the work of Fay, Samuel and Shockley. 



V02 



Vom 



Fig. 1 — Potential distributions between two planes of positive potential. 



Consider two planes a and b, Fig. 1, of fixed d-c. potentials Foi and 

 T^o2 {Vq2 — Vqi) respectively, separated by a distance d. Let a uni- 

 directional and uniform electron stream of /q amp./cm.^ be injected 

 into the space from the left at right angles to the planes. When the 

 injected current is extremely small the potential distribution does not 

 differ very much from the free space one, represented by curve 1 on 

 Fig. 1. As the injected current is increased slightly, the potential 

 curve starts to sag, curve 2, and a further small increase causes a 

 potential minimum to develop at the electrode of lower potential, 

 curve 3. Still more increase in injected current makes the potential 



^ Loc. cit. 



