IMPEDANCE PROPERTIES OF ELECTRON STREAMS 469 



where 



Jn — T — -^0 

 kme 



e = coT ■ 



Co = -J is the cold capacitance 



T is transit time, seconds 



e is electronic charge, coulombs 



m is electronic mass, grams 



— = 1.77 X 10^ coulomb/gm. 



e is permittivity of vacuum = 8.85 X 10~^^ Farads/cm.^ 

 k = 10-7. 



Present interest lies mainly in the range where the transit angle d is 

 small. Expanding (1) and assuming 6 small, we have: 



r = 



1 (2) 



C ^ Co ^3 • 



6d 



These formulas are also found in Miiller's paper.^ 



With regard to the resistance r it is immediately seen that it is 

 always positive and has the same equation as for complete space 

 charge with current /o and transit time T. 



From the capacitance equation it is immediately evident that an 

 increase is caused by the presence of electrons. The dielectric constant 

 of space charge under the stipulated conditions is seen to be dependent 

 upon the d-c. conduction current Iq. As the injected current is 

 increased the capacitance increases initially at a fairly slow rate, but 



as Jo -7-j becomes comparable with unity the capacitance rises rapidly. 



It becomes infinite for 



and if the left member of (3) were to become greater than unity the 

 capacitance would be negative. The possibility of such a condition 

 deserves careful consideration. 



2 Loc. cit. 



