BEAM FOKMATION WITH ELECTRON GUNS 



387 



800 805 810 815 820 825 830 835 840 845 850 855 860 



Fig. 4 — Curves for finding the value of Fx to be used in equation (10) for the 

 set of gun parameters of Fig. 3. 



l)oth the direction and magnitude of the total electric field near the 

 beam axis were (with much labor) determined. Once these data had 

 been obtained, a trial value was selected for Vx , and the corresponding 

 local length was calculated by (10). This enabled the electron's path 

 through the associated thin lens to be specified so that, at this point in 

 the procedure, both r and V were known functions of ^, and the quan- 

 tities 8 and f were then obtained as functions of € from (7). Finally the 

 second integral in (9) was evaluated for the particular Vx chosen, and 

 then the process was repeated for other values of Vx . Fig. 4 shows curves 

 whose ordinates are proportional to this second integral and whose 

 abscissae are trial values for Vx . As noted above, the appropriate value 

 for Vx is that value which makes the ordinate vanish, so that we obtain 

 T'c = 813 and 839 for methods A and B, respectively. The percentage 

 difference in the focal lengths obtained by the two methods is thus only 

 1 .6 per cent, and the reasonableness of making calculations as outlined 

 in Part B is thus put on a more quantitative basis. 



Even calculations based on the method of Part B are tedious, and we 

 naturally look for simpler methods of estimating the lens effect. In this 

 fonnection we have found that Vx is usually well approximated by the 

 \alue of the potential at the point of intersection between the beam axis 

 and the ideal anode sphere. The specific values of the potential at this 

 point as obtained by the methods of Parts A and B were 814 and 827, 

 respectively. It will be noted that these values agree remarkably well 

 with the values obtained above. Furthermore, very little extra effort is 

 required to obtain the potential at this intersection in the false cathode 

 case: 



