SPACE CHARGE BETWEEN PARALLEL PLANE ELECTRODES 73 



T = Electron transit time expressed in units of /o, 



/o = 7.72 X 10-11 -^(seconds), 



c = 7.72 X 10-" = 3a(mc/2g)l/no-^2o 



7 = Injected current expressed in units of ^"o, 



io = 2.33 X 10 ^ ,^ = — -7^ — (amperes per sq. cm.), 



a — Ratio of the potential at a potential minimum when one exists 

 to the potential of the first plane, otherwise merely a con- 

 venient constant of integration. (In the text the symbol 

 <Pmin. is used in the cases where the physical significance can 

 be attached.) 



jS = An integration constant similar to a but associated with an 

 opposite sign. 



Relationship between y and <t 

 By definition 



5.=^ = ^ (1) 



and 



Solving (1) for a 



Solving (3) for 7 



'' = -dr = y' (2) 



en/2 



^ (3) 



aVi"* 



'y (j2 y^zi2 • \v 



But since S = d for the conditions under which 7 is used 



7 = (x^ (5) 



Derivations 



The space charge equation based upon Poisson's equation and the 

 energy equation for an electron is^^ 



^ = A/K-« (6) 



^^ In this work e is the charge on the electron in e.s.u., m its mass in grams, c is 

 the ratio of electrostatic and electromagnetic units, 1 volt = (lOVc) e.s.u., 1 ampere 

 = (c/10) e.s.u. 



^' See, for example, Dow, "Fundamentals of Engineering Electronics," John 

 Wiley, 1937, pg. 100. 



