PHYSICAL LIMITATIONS I IV ELECTRON BALLISTICS 311 



Thus if for a given spot size we want to increase the spot current, and if we 

 are limited to a given cathode current density because of cathode Hfe, 

 we must make 1' larger, W larger or L smaller. 



Making W larger increases both lens and deflection aberrations. Making 

 L smaller means that for a given linear deflection we must increase the 

 angular deflection, and this too tends to defocus the spot. Because of these 

 limitations, it is necessary to avail ourselves of the remaining variable and 

 raise the operating voltage V'. 



Another illustration, perhaps a little more subtle, of the efTect of thermal 

 velocities, lies in the analysis of the properties of a type of vacuum tube 

 amplitier known as the "deflection tube". In such a device, illustrated in 

 Fig. 4, an electron stream from a cathode is accelerated and focused by a 

 lens and deiiected by a pair of deflecting electrodes so as to hit or miss an out- 

 put electrode. Such a device may be used as an amplifier. 



Now it is obvious that as the output electrode on which the beam is 

 focused is moved farther away from the deflecting plates, a given deflecting 

 voltage will produce a greater linear deflection of the beam at the output. 



CATHODE 



/^ "t:, U output ' 



electron' ^-^ -ELECTRODE 



LENS DEFLECTING 

 PLATES 



Fig. 4 — Amplifying tube making use of electron deflection. 



As this at first sight seems desirable; it has been seriously suggested not 

 only that this be done, but that an elaborate electron optical system be 

 interposed between the deflecting plates and the output electrode to amplify 

 the deflection. 



The merit of a deflection tube is roughly measured by the deflecting 

 voltage required to move the beam from entirely missing the output elec- 

 trode to entirely hitting the output electrode, and, of course, moving the 

 output electrode farther away or putting lenses between the deflecting 

 plates and the output electrode doesn't reduce this voltage at all. As we 

 improve the deflection sensitivity by these means, we simply increase the 

 spot size at the same time. Focusing our attention on the beam between 

 the deflecting plates, we appreciate at once that the electron paths through 

 each point will be spread over some cone of half angle 9, and that to change 

 from a clean miss to a clean hit we must deflect the electrons through an 

 angle of at least 26, regardless of what we do to the beam afterwards. 



Returning for a moment to equation (15), we see that it says the current 

 density can be less than a certain limiting value depending on 9. Yet 



