. The Bell System technical journal . + 2/3 - /32 2/3/ (1 +i8)(/32- 2) (3) (4) The beam then passes through the aperture in the third plate intofield-free space, and the lens equation for this aperture is (5) 1 1 1 0 - V2 — Vi dp do 4i2 I J Substitution for do now gives 1 1 +/3 r /32- 2 ,1-/3] dp 2/3/ [4 + 2/3- P + 2 ^ J (6) which is the reciprocal of the final focal distance measured from thelast plate. ELECTROSTATIC ELECTRON-OPTICS 25 In complete lens systems, where the symbolic calculations arecomplicated, it is frequently simpler to introduce specific numericalvalues and carry the successi
. The Bell System technical journal . + 2/3 - /32 2/3/ (1 +i8)(/32- 2) (3) (4) The beam then passes through the aperture in the third plate intofield-free space, and the lens equation for this aperture is (5) 1 1 1 0 - V2 — Vi dp do 4i2 I J Substitution for do now gives 1 1 +/3 r /32- 2 ,1-/3] dp 2/3/ [4 + 2/3- P + 2 ^ J (6) which is the reciprocal of the final focal distance measured from thelast plate. ELECTROSTATIC ELECTRON-OPTICS 25 In complete lens systems, where the symbolic calculations arecomplicated, it is frequently simpler to introduce specific numericalvalues and carry the successive steps of the calculation through in anumerical manner. By doing this for a few suitably chosen numericalvalues one can obtain the particular information that is desired. Appendix II—Concentric TubesTwo concentric tubes at different potentials form an electron lensthat is well adapted to practical tube construction. When the twotubes are of the same diameter, the approximate constants of thelens may be determined as follows.^^. Fig. 16—Concentric tubes. In this type of lens, the electric intensity is symmetrical withrespect to an imaginary plane drawn between the two tubes—asillustrated in Fig. 16—and the plane is therefore an equipotentialsurface. Its potential Vq is the mean potential of the two plane is regarded as a division plane separating the lens into twocomponent electric fields. We first consider the component to the right of the plane. Thesolution for the potential inside of the tube may be obtained in theform of a Bessel Function series, and it follows from this series thatthe potential on the axis is 2 V ^ V2 — (V2 — Vo)H fxJiifJ.) exp. ^JLZR (1) where R is the radius of the tubes, and lu. takes on discrete valuesequal to the successive roots of 0. (2) We find that an approximation to the exponential series is given by E ■;: fiJi(n) exp. -^1=1R tanh co2. (3) ^^ We assume that the separation between their ends is negligibly small compare
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