PHYSICAL LIMITATIONS IN ELECTRON BALLISTICS 317 



Then 



V = 5,700 volts 



Thus to maintain parallel motion of the modest current of 10 milliamperes 

 spread over an area of one square centimeter requires 5,700 volts. More- 

 over, the requirement of distributing this voltage smoothly along the beam 

 would make it very difficult to put the beam to any use. 



One means for mitigating the situation is to use an electron lens and 

 direct the beam inward. Of course, the beam will eventually become par- 

 allel and then diverge again, but by this means a fairly large current can be 

 made to travel a considerable distance. Some calculations made by Thomp- 

 son and Headrick^- cover this type of motion, with an especial emphasis on 

 the problem in cathode ray tubes, in which the currents are moderate. 



In order to confine large currents into beams, an axial magnetic field is 



sometimes used, as shown in Fig. 10 Here a cathode-grid combination 



shoots a beam of electrons into a long conducting tube. A long coil around 



the tube produces an axial magnetic field intended to confine the electron 



CONDUCTING 

 TUBE 

 COI L 



cathodeI i ^ > iz=: 



I'I'hr 



i^k^nvyxv V v v y x x v v y x yyv y 



Fig. 10 — Avoiding beam divergence by means of a longitudinal magnetic field. 



paths in a roughly parallel beam. The radial electric field due to space 

 charge will cause the beam to expand somewhat and to rotate about the 

 axis. As the magnetic field is made stronger and stronger, the electrons 

 will follow paths more and more nearly straight and parallel to the axis. 

 For a given current and voltage, there is one sort of physical limitation in 

 the strength of magnetic field we need to get a satisfactory beam. It is 

 another effect that I wish to discuss. 



Suppose we have a very strong magnetic field, in which the electrons 

 travel almost in straight lines. We know, of course, that the radial electric 

 field is still present, and this means that the potential toward the center of 

 the beam is depressed; this in turn means that the center electrons are 

 slowed down. This slowing down of course increases the density of electrons 

 in the center of the beam. The result is that if for some critical voltage or 

 speed of injection we increase current beyond a certain value, the process 

 runs away, the potential at the center of the beam drops to zero, and another 

 type of electron flow with a "virtual cathode" of zero electron velocity at 

 the center of the beam is estabhshed. Thus, although the magnetic field 



