854 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 1 



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slowing down and falling further back in phase. At 9 db above satura- > 

 tion, Fig. 7(o), the pattern is quite complex, and at still higher levels it 

 is utterly indescribable. ■ 



It is interesting that the ^'elocity gives a line pattern, even though a ' 

 multi^'alued one. It is reasonable to suppose that the development of 

 the spur is really a folding of the \'elocity line so that the spur is really a 

 double line. Thus, at the 9 db level, and at 0° phase, for instance, there 

 must be electrons originating from five different parts of the initial dis- ; 

 tribution. In an attempt to verify this the resolution of the velocity an-il 

 alyzer was adjusted so that a difference in velocity of 2 per cent of the- 

 overall spread could be observed, but there was no positive indication of r- 

 more than one velocity associated with any line shown. : 



There has been a long-standing debate as to whether or not electrons j 

 are trapped in the circuit field, or continue to override the w^ave at large 

 amplitudes. The observations indicate that with low values of space 

 charge and near synchronous voltage the electrons are effectively trapped: 

 in the wave until well above saturation amplitude. In other circum- 

 stances this is not the case, as we shall see. 



SPACE CHARGE EFFECTS 



The data of Fig. 7 were taken with a very small value of the space 

 charge parameter QC, so small in fact as to be almost negligible as far 

 as low level operation is concerned. Yet the space charge forces evidently 

 played a very strong role in the development of the velocity and currenti' 

 patterns. It is doubtful that space charge would ever be negligible in thisii 

 respect, because if the space charge parameter were smaller, the bunch-i 

 ing would be more complete, the electron density in the bunch would be 

 greater limited only by the balance of space charge field and circuit field 

 in the bunch. The effect of decreaising QC further therefore is a greater 

 localization of the space charge forces, rather than a reduction of their 

 magnitude, at least until the bunch becomes short compared to the 

 beam radius. 



Increasing the value of the space charge parameter has quite the op-' 

 posite effect. In Fig. 8 are shown three velocity-cm-rent distributions ati 

 the saturation level, for different A-alues of QC. It can be seen that a re-' 

 suit of increased space charge is a greater spread of velocities, and a wider 

 phase distribution of current. 



With the introduction of space charge, the velocity difference between 

 the electrons and the circuit wave at low levels is increased. Consequently 

 electrons spend a longer time in the decelerating field before beingj 

 thrown back in the low velocity spur, and thus lose more energy. Thel 



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