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THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



CENTER OF 



~~ CURVATURE 



OF CATHODE 



SURFACE 



Fig. 3 — The gun parameters used in Section SC for comparing two methods of 

 evaluating the effect of the anode lens. 



The first integral can be obtained from (5) ; hence, if we are able to choose 

 Vx so that the second integral vanishes, we may write: 



Au = 



raV'2riVx 



The reciprocal of the thin lens focal length is therefore 



i _ ^ _ ^' 



F ~ ~raUf ^ ~^VWf 



(10) 



where w/ and F/ are the final velocity and voltage of the electron after 

 it leaves the lens region. 



The real task, then, is to use the potential distribution in the gun as 

 obtained by the methods of Part A or Part B above to find the value of 

 V X which causes the last integral in (9) to vanish : To compare the two 

 focal lengths obtained by the methods of Part A and B respectively, a 

 specific tank design of the type indicated in Fig. 1 was carried out. The 

 relevant gun parameters are indicated in Fig. 3. Approximate voltages 

 on and near the beam axis were obtained as indicated in Parts A and B, 

 above, with the exception that in the superposition method, A, special 

 techniques were used to subtract the effect of the space charge lying in 

 the post-anode region (because the effect of this space charge is accounted 

 for separately as a divergent force in the drift region*). From these data, 



* See Section 4B. 



