PHYSICAL LIMITATIONS IN ELECTRON BALLISTICS 313 



special cathode ray tube designed by Dr. C. J. Davisson of the Bell Tele- 

 phone Laboratories. 



When we become thoroughly convinced that these equations expressing 

 the effects of thermal velocities very much cramp our style in designing 

 electron-optical devices, as good engineers we wonder if there isn't, after all, 

 some way of getting around them. I don't think there is. The suggestion 

 illustrated in Fig. 6 is a typical example of such an attempt. We know 

 that in a strong magnetic field electrons tend to follow the lines of force. 

 Why not use a very strong magnetic field with lines of force approaching the 

 axis at a gentle angle to drag the electron stream toward the axis? 



An electron off axis traveling parallel to the axis certainly will be dragged 

 inward by such a field. The catch is that the field pulls the electron in 

 because it makes the electron spiral around the axis. As the beam con- 

 verges and the field becomes stronger, the pitch of each spiral decreases and 

 the angular speed of each electron increases. Finally, if the field is strong 

 enough, all the kinetic energy of the electron is converted from forward 



ELECTRON^ V^ .^OT — — — MAGNETIC' 



PATH > ?<~ — >C^O __ LINES OF 



FORCE 



Fig. 6 — Reflection of an electron by a magnetic field with strongly converging lines of 



force. 



motion to revolution about the axis; the electron ceases to move into the 

 field and bounces back out. It may be some small consolation to know 

 that very high-current densities can be achieved by this means, but only 

 because in their flat spiralling the electrons approach a spot at much wider 

 angles with the axis than the small inclination of the lines of force. 



Space Charge Limitations 



In electron beam devices using reasonably large currents, the space 

 charge of the electrons is a very serious source of trouble both in compli- 

 cating design of the devices and in limiting their performance. 



Let us begin our consideration right at the electron gun, the source of 

 electron flow in many devices such as cathode ray tubes and certain high- 

 frequency tubes. Electron guns are sometimes designed on the basis of 

 radial space charge limited electron flow between a cathode in the form of a 

 spherical cap of radius fo and a concentric spherical anode a distance d from 

 the cathode. It can be shown that by use of suitable electrodes external to 

 the beam, radial motion can be maintained between cathode and anode along 



