BEAM FORMATION WITH ELECTRON GUNS 



385 



1 of deriving a completely new expression for F. In accomplishing this piir- 

 f pose, it will be helpful to define a dimensionless function of radius, 6, by 



- = 1 + 5, 

 r 



and a dimensionless function of voltage, f, by 



(7a) 



(7b) 



where Ta is the radius at the anode lens when the lens is considered thin, 

 and T^'x is a constant voltage to be specified later. (Note that the quan- 

 tities 5 and f are not necessarily small compared to 1.) Using u = \/2r]V, 

 and substituting for -y/V from (7b) we obtain 



f En dl 4 r , 



= 7~7tW / ^"^1 + r + 5 + rs) ^z 



(8) 



where use has also been made of (7a) in the form 1 = r(l + d)/ra . Now, 

 as outlined above, we equate this impulse to 771 An, and we obtain 



^» = WW. (/ ''■'' '' + / ''"'■'^ + ' + ^'' 'i 



(9) 



CATHODE 



Fig. 2 — The heavy line represents an electron's path when the effect of the 

 .•mode hole may be represented by a thin lens, and when space charge forces are 

 iihsent in the region following the anode aperture. For paraxial electrons, the 

 (negative) focal length is related to the indicated angles by (y = + Ta/F). 



