NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 857 



ridiculously small beam. By comparison with curves taken for larger 

 beams, the tail is diminutive, electrons are much more uniformly dis- 

 tributed over all velocities and phases, and a peculiar splitting of veloci- 

 ties in the main bunch is found. The latter indicates that electrons 

 entering from the higher velocity region move forward in the bunch, and 

 the rest gradually retard. The smaller reduction in velocities, and the 

 spread of electrons into the higher velocity regions is consistent with the 

 lower efficiency measured (Fig. 2). 



To explain the observed difference in high level performance of tubes 

 with different size beams we must consider the character of the ac longi- 

 tudinal space charge field. The coulomb field from an elemental length 

 of an electron beam is inversely proportional to the square of the dis- 

 tance from the element 



E = Const 7-^, (7) 



provided (z — Zi) » ro and {z — Zi) « a. 



For (z — zi) not small compared to a, (i.e., circuit radius not awfully 

 large) the field would drop even faster with (z — zi) due to the shielding 

 effect of the circuit. On the other hand, very near to the beam element 

 {z — zi <K To), the field is approximately that of a disc, which is nearly 

 independent of z, i.e., 



E = Const -^^ (8) 



Trro 



independent of z for z <^ro . 



Thus to a fair approximation the space charge field may be considered 

 to be uniform for an axial distance of the order of a half a beam radius, 

 and to drop rapidly at greater distances. For a given current element, a 

 small diameter beam has an intense field extending only a short dis- 

 tance, while an equal charge element in a larger beam has a weaker longi- 

 tudinal field extending to a greater distance. 



At low amplitudes the extent of the forces makes no difference in 

 operation, for a sinusoidal current gives a sinusoidal space charge field in 

 either case. However, at large amplitudes, a sharp change in current 

 density has a very high short range space charge field if the beam is 

 small, or a much smaller smoothed out long range field if the beam is 

 large. For 7/-o = 0.5 which appears to be an optimum compromise be- 

 tween the effects of space charge and field non-uniformity, the space 

 charge field could scarcely be confined closer than about ±30° in phase. 

 < )n the other hand, a sharp bunching of electrons in a beam having 



