858 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



7/'o = .05 would have 100 times the space charge field, extending how- 

 ever only one tenth as far from the current discontinuity. 



Returning to Fig. 9 we can see how these considerations enter into the | 

 development of the beam modulation. In the case of the small beam, 

 Fig. 9(c), at the very beginning of the formation of a cusp, the strong 

 highly concentrated space charge force causes a rapid deceleration of 

 nearby electrons, resulting in the relatively early formation of a diminu-i 

 tive tail. The very high localized space charge force also prevents as tight 

 bunching of electrons, forcing some to move forward and continuously ; 

 repopulate the accelerating part of the wave. The relatively early falling; 

 apart of the initial bunch and the greater acceleration of the overriding; 

 electrons evidently give the latter enough velocity to penetrate the main i 

 bunch of electrons and form the second class of electrons in the main 

 bunch, 90°-150° in Fig. 9(c). Thus the net result of reducing the beami 

 size is a severe aggravation of space charge debunching effects, with ai 

 consequent reduction in efficiency. To get high efficiency, we conclude, 

 the beam should not be small. It should not be larger than 77-0 = 0.7 ' 

 however, for then the circuit field is not uniform enough over the beam i 

 cross-section to excite it properly, resulting in a loss in efficiency as is , 

 evident in Figs. 2 and 3. 



EFFECT OF INCREASED BEAM VOLTAGE 



It is common practice in the operation of traveling wave tubes to ele- 

 vate the beam voltage, taking a sacrifice in gain in order to obtain in- 

 creased power output. The effects on the beam modulation are shown in 

 Fig. 10. In Fig. 10(a), the voltage is somewhat below that giving maxi- 

 mum gain. The curve is characteristic of what we have already seen but 

 the bunching is less pronounced and the velocities are less reduced. In 

 Fig. 10(b) the voltage is somewhat above that giving maximum gain and \ 

 the curve is much like that of Fig. 8 except that the decelerated elec- 

 trons are slowed by a greater amount, consistent with the increased 

 separation of electron and wave velocity, and also with the measured 

 increase in power output. 



Increasing the beam voltage still further gives only a slight increase 

 in efficiency. Fig. 10(c) shows that even though electrons are slowed to 

 still lower velocities, and the velocity spread is increased, many more 

 electrons override the circuit Avave and are accelerated, thereby off- 

 setting the greater contribution of the slower electrons. This is much 

 like what was seen with increasing space charge (QC) and indeed the 

 effects are almost ecjuivalent. As one would expect therefore, little is 

 gained by elevating the beam voltage if the space charge is large, the 



