372 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



y-by 



Fig. 8(e) — y versus <p — by for QC = 0.4, k = 2.5, b for in = 0.67ui(max) and 

 C = 0.1 (Case 21). 



are decelerated by the circuit field. At the input end of the tube, elec- 

 trons are uniformly distributed both in the accelerating and decelerating 

 field regions. Bunching takes place when the accelerated electrons push 

 forward and the decelerated ones press backward. The center of a bunch 

 of electrons is located well inside the decelerating field region because 

 the circuit wave travels slower than the electrons on the average (6 is 

 positive). The effectiveness of the amplification, or more specifically the ! 

 saturation efficiency, therefore depends on (1), how tight the bunching :' 

 is, and (2), how long a bunch travels inside the decelerating field region 

 before its center crosses the boundary between the accelerating and 

 decelerating fields. 



For small-C, the ac velocities of the electrons are small compared with 

 the dc velocity. The electron bunch stays longer with the decelerating 

 circuit field before reaching the saturation level when h or QC is larger. 

 On the other hand, the space charge force, or large QC or k tends to dis- 

 tort the bunching. As the consequence, the saturation efficiency increases , 

 with h, and decreases as k or QC increases. When C becomes finite how- 



