BEAM FORMATION WITH ELECTRON GUNS 



383 



therefore consider a case where electrons are emitted perpendicularly 

 and with finite velocity from what would be an appropriate spherical 

 equipotential between cathode and anode in a Pierce type gun. So long 

 as (a) there is good agreement between the LaPlace and Langmuir curves 

 at this artificial cathode and (b) the distance from this artificial cathode 

 to the anode hole is somewhat greater than the hole diameter, we will 

 liiid that the divergent effect of the anode hole will be very nearly the 

 same in this concocted space charge free case as in the actual case where 

 space charge is present. (The quantitative support for this last state- 

 ment comes largely from the agreement between calculations based on 

 this method and calculations by method A.) The electrode configura- 

 tion is shown in Fig. 1(b), and the potential distribution in this space 

 charge free anode region can now be easily obtained in the electrolytic 

 j 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 none 

 of the electric field lines which originate on charges in the cathode-anode 

 region leave the beam before reaching the ideal anode plane where the 

 voltage is F, and that all of these field lines leave the beam symmetrically 

 and radially in the immediate neighborhood of the anode. Electrons 

 I 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 A2 

 V = C 



ANODE A, 



v = c 



(b) 



^ FALSE 

 CATHODE 



Fig. 1(b) — The introduction of a false cathode at the appropriate potential 

 lUows the effect of space charge on the potential near the anode hole to be satis- 

 :ictorily approximated as discussed in Section 3i?. 



