PHYSICAL LIMITATIONS IN ELECTRON BALLISTICS 315 



electron gun. They are plots of a factor called the perveance, which is 

 deiined as 



P = //F''' (18) 



(that is, current divided by voltage to the 3/2 power) as a function of 9, the 

 half angle of the cone of flow, and d/ro, the ratio of cathode-anode spacing 

 to cathode radius. In getting an idea of the meaning of the curves, we may 

 note that a perveance of 10~^ means a current of 1 milliampere at 100 volts. 

 It is obvious from the curves that to get very high values of perveance, that 

 is, high current at a given voltage, 6 must be large and the cathode-anode 

 spacing must be small. Making d large means that electrons approach the 

 axis at steep angles; aberrations are bad and the beam tends to diverge 

 rapidly beyond crossover. Moving the anode near to the cathode means 

 that the hole which must be cut in the anode to allow the beam to pass 

 through must be large, and cutting such a large hole in the anode defeats 

 our aim of getting higher perveance; we can't pull electrons away from the 

 cathode with an electrode which isn't there. Further, for ratios of spacing 

 to cathode radius less than about .29, the lens action of the hole in the 

 anode causes the emerging beam to diverge, which would make the gun 

 unsuitable for many applications. 



When we build guns for small currents at high voltages, such as cathode 

 ray tube guns, space charge causes little trouble; when we try to obtain 

 large currents at lower voltages, we find ourselves seriously embarrassed. 



Suppose we now turn our attention to the effect of space charge in beams 

 when the beam travels a distance many times its owm width. Consider, 

 for instance, the case of a circular disk forming a space charge limited 

 cathode. Suppose we place opposite this a fine grid, and shoot an electron 

 stream out into a conducting box, as illustrated in Fig. 9a. We immediately 

 realize that there will be a potential gradient away from the charge forming 

 the beam. In this case, the gradient will be toward the nearest conductor; 

 that is outwards, and the electron beam will diverge. 



How can we overcome such divergence? One way would be to arrange 

 the boundary conditions in such a fashion that all the field would be di- 

 rected along the beam instead of outwards; this might be done by sur- 

 rounding the beam by a series of conducting rings and applying to them 

 successively higher voltages as in 9b, the voltages which would occur in 

 electron flow between infinite parallel planes with the same current density. 

 Another way in which the same effect may be achieved is through use of 

 specially shaped electrodes outside of the beam, as shown in Fig. 9c." In 

 maintaining parallel flow by these means, the electric field due to the elec- 

 trons acts along the beam, and increases continually in magnitude with 



