28 BELL SYSTEM TECHNICAL JOURNAL 



The principal focal distances for various voltage ratios are given in 

 terms of the tube diameter by the curves of Fig. 18. For rough 

 calculations, these plotted values may be used in the lens equation 



^ + ^=1. (8) 



where focal distances are again measured from the division plane of 

 the tubes. 



The electric field of the concentric tubes has two maxima of \v"\ 

 located symmetrically with respect to the division plane, as illustrated 

 in Fig. 16. Each maximum is located at a distance .SR from the 

 plane. The electron lens may therefore be treated in a somewhat 

 more exact manner by considering it as two thin lenses located at 

 these points. The inverse focal term of the equivalent lens to the 

 left of the plane is 



1 C0V2 



— I'l L 



F vo -• ' ^ 



vo^i^ - Vi^'^ 



(9) 



and the inverse focal term of the equivalent lens to the right of the 

 plane is 



Vo 



(VlJ2 — ^0) — 



v^i-^ - z;o'/2 



(10) 



The final focal distance in any particular case is found by carrying 

 out the calculations for the two lenses in succession, with their separa- 

 tion taken equal to R. 



Appendix III ** 



A Plane Electrode at the End of a Tube. — In addition to their above 

 application, the last two equations may be used for other purposes. 

 In electron devices, one frequently puts a plane electrode at the end 

 of another, tubular electrode. ^^ The approximate lens action of the 

 electric field between the plate and tube is then described by one or 

 the other of these equations. Equation 9 applies when the plane 

 follows the tube in the direction of electron motion ; and equation 10 

 applies when the plane precedes the tube. 



In structures of this type, the plate is usually pierced with an 

 aperture for the passage of electrons. When the aperture is small 

 compared to the tube diameter, the lens system can be treated in the 

 following manner. 



'* We assume the separation between the plate and the end of a tube to be negli- 

 gible compared to the tube diameter. 



