SPACE CHARGE BETWEEN PARALLEL PLANE ELECTRODES 73 



T = Electron transit time expressed in units of to, 



to = 7.72 X 10-11 ^'(seconds), 



c = 7.72 X 10-" = 3a{mc/2ey'no-\'"' 



7 = Injected current expressed in units of io, 



id = 2.33 X 10-*^ J3 — — -^ — (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.) 



/3 = An integration constant similar to a but associated with an 

 opposite sign. 



Relationship between y and a 

 By definition 



^0 -~Jm~ -- ^^) 



and 



Solving (1) for a 

 Solving (3) for y 



^0 = -^=-- (2) 



cn/2 

 a = 4i^. (3) 





(4) 



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^^ 



^— = — 7F-1/2 (6) 



dx" 9a^ ' ^^ 



^^ 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 = (107c) e.s.u., 1 ampere 

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



^1 See, for example, Dow, "Fundamentals of Engineering Electronics," John 

 Wiley, 1937, pg. 100. 



