. The Bell System technical journal . d onthis method and calculations by method A.) The electrode configura-tion is shown in Fig. 1(b), and the potential distribution in this spacecharge free anode region can now be easily obtained in the electrolyticj tank. This potential distribution will be used in the next section to pro-^•ide a second basis for estimating a correction to the Davisson equation. C. Calculation of Anode Lens Strength by the Two Methods The Davisson equation, (1), may be derived by assuming that noneof the electric field lines which originate on charges in the cathode-anoder
. The Bell System technical journal . d onthis method and calculations by method A.) The electrode configura-tion is shown in Fig. 1(b), and the potential distribution in this spacecharge free anode region can now be easily obtained in the electrolyticj tank. This potential distribution will be used in the next section to pro-^•ide a second basis for estimating a correction to the Davisson equation. C. Calculation of Anode Lens Strength by the Two Methods The Davisson equation, (1), may be derived by assuming that noneof the electric field lines which originate on charges in the cathode-anoderegion leave the beam before reaching the ideal anode plane where thevoltage is F, and that all of these field lines leave the beam symmetricallyand radially in the immediate neighborhood of the anode. ElectronsI are thus considered to travel in a straight line from cathode to anode,and then to receive a sudden radial impulse as they cross radially diverg-ing electric field lines at the anode plane. A discontinuous change in CATHODE. ANODE A2V = C ANODE A, v = c (b) ^ FALSECATHODE Fig. 1(b) — The introduction of a false cathode at the appropriate potentiallUows the effect of space charge on the potential near the anode hole to be satis-:ictorily approximated as discussed in Section 3i?. 384 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 slope is therefore produced as is common to all thin lens diverging effect of electric field lines which originate on chargeswhich have passed the anode plane is then normally accounted for bythe universal beam spread curve/ In our attempt to evaluate the lenseffect more accurately, we will still depend upon using the universalbeam spread curve in the region following the lens and on treating the;equivalent anode lens as thin. Consequently our improved accuracymust come from a mathematical treatment which allows the electricfield lines originating in the cathode-anode region to leave the beam grad-ually, rather than a treatm
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