468 



BELL SYSTEM TECHNICAL JOURNAL 



After this survey of the several possible d-c. space charge conditions 

 we may proceed to the a-c. phenomena involved. At the present 

 time the impedance between the two planes of Fig. 1 can be found only 

 if the electrons move in one direction, i.e. if no virtual cathode is 

 present between the planes, and therefore this assumption is made. 

 It will be further assumed that electrode "a" where the injection takes 

 place is at a-c. ground potential. This insures constant conduction 

 current and electron speed at the plane of injection. The impedance 



Fig. 2 — Variations of the magnitude of the potential minimum as 

 function of injected current. 



may then be found by proper application of the general theory de- 

 veloped by MiiUer and Llewellyn. ^ The result is that the impedance 

 may be represented by a series combination of a resistance r and a 

 capacitance C having the values 



r = J, 



T^ 2 - 2 cos - sin 



c = a 



1 



(1) 



0" 



1 - /o 



2 sin g - g - g COS 



2 J. Miiller, Hochfrequenztechnik u. Electroakustik, May 1933; F. B. Llewellyn, 

 Bell Sys. Tech. Jour., October 1935. 



