860 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



z 



UJ 

 (T 



a. 



O 



UJ 



> 



u 



EC 



o 

 > 



y o 



i-\ 



o u 

 u 

 -J I 



> LJ 



< I- 



erg 



UJ 



-2 



-6 



-180 



120 



-60 60 



RELATIVE PHASE IN DEGREES 



120 



180 



Fig. 11 — AC current and electric field in the beam. The upper curve comes 

 directly from Fig. 8(a). The lower curve is deduced by an approximate method 

 from the velocity curve of Fig. 8(a). The double value below 90° is partly due to 

 inconcistency between the two parts of the velocity curve, and partly due to the 

 nature of the approximation. 



pole, and the range of the space charge force (dependent upon QC and 

 7ro) determines its effect upon the electron dynamics. 



Most of the current is incorporated in the two bunches nearly 180° 

 apart, as we have seen, each bunch having a current density many times 

 the average. 



We might obtain the space charge fields from the current density, but 

 this would require a rather definite knowledge of the characteristic 

 space charge field versus distance as influenced by beam diameter. It 

 would also be pushing the accuracy of charge density measurement, 

 which is crude at best. A better way is to compute the electron accelera- 

 tion from the velocity curves. This may be done by taking two velocity 

 patterns at slightly different signal levels, and tracing electrons from one 

 to the next, using the measured velocity to determine the relative phase 

 shift of any electron. 



In the appendix it is shown that a close approximation to this is 



E^ = 2/3CYo 



[ 



(Fo - FJ + A7 ' 

 2FoC 



(10) 



