. The Bell System technical journal . focal length is therefore i _ ^ _ ^ F ~ ~raUf ^ ~^VWf (10) where w/ and F/ are the final velocity and voltage of the electron afterit leaves the lens region. The real task, then, is to use the potential distribution in the gun asobtained by the methods of Part A or Part B above to find the value ofVX which causes the last integral in (9) to vanish: To compare the twofocal lengths obtained by the methods of Part A and B respectively, aspecific tank design of the type indicated in Fig. 1 was carried out. Therelevant gun parameters are indicated in Fig. 3. Ap
. The Bell System technical journal . focal length is therefore i _ ^ _ ^ F ~ ~raUf ^ ~^VWf (10) where w/ and F/ are the final velocity and voltage of the electron afterit leaves the lens region. The real task, then, is to use the potential distribution in the gun asobtained by the methods of Part A or Part B above to find the value ofVX which causes the last integral in (9) to vanish: To compare the twofocal lengths obtained by the methods of Part A and B respectively, aspecific tank design of the type indicated in Fig. 1 was carried out. Therelevant gun parameters are indicated in Fig. 3. Approximate voltageson and near the beam axis were obtained as indicated in Parts A and B,above, with the exception that in the superposition method, A, specialtechniques were used to subtract the effect of the space charge lying inthe post-anode region (because the effect of this space charge is accountedfor separately as a divergent force in the drift region*). From these data, * See Section 4B. 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 theset of gun parameters of Fig. 3. l)oth the direction and magnitude of the total electric field near thebeam axis were (with much labor) determined. Once these data hadbeen obtained, a trial value was selected for Vx , and the correspondinglocal length was calculated by (10). This enabled the electrons paththrough the associated thin lens to be specified so that, at this point inthe 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 thesecond integral in (9) was evaluated for the particular Vx chosen, andthen the process was repeated for other values of Vx . Fig. 4 shows curveswhose ordinates are proportional to this second integral and whoseabscissae are trial values for Vx . As noted above, the appropriate valuefor Vx is that value w
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