370 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



given by (18) is proportional to the ac displacement of electron per unit 

 of ij. (In small-C theorj^ it is proportional to the ac velocity of the elec- 

 tron.) Concentration of curves is obviously proportional to the charge- 

 density distribution of the beam. In the shaded regions, the axially di- 

 rected electric field of the circuit is negative and thus accelerates elec- 

 trons in the positive z direction. Electrons are decelerated in the un- 

 shaded regions where the circuit field is positive. The boundaries of these 

 regions are constant phase contours of the circuit wave. (They are con- 

 stant $ contours in Nordsieck's notation.) 



These figures are actuallj' the "space-time" diagrams which unfold 

 the historj^ of every electron from the input to the output ends. The 

 effect of C can be clearly seen by comparing Figs. 8(a), (b) and (c). 

 These diagrams are plotted for QC = 0.2, A; = 2.5, h for jui = 0.67 

 jui(max) and for Fig. 8(a), C = small, for Fig. 8(b), C = 0.1, and for 

 Fig. 8(c), C = .15. It may be seen that because of the velocity spread of 

 the electrons, the saturation level in Fig. 8(a) is 9.3 whereas in Figs. 8(b) 

 and (c), it is 7.2 and 7.0, respectively. It is therefore not surprising that 

 Eff./C decreases as C increases. 



The effects of h and QC may be observed by comparing Figs. 8(d) and 

 (b), and Figs. 8(b) and (e), respectively. The details will not be de- 

 scribed here. It is however suggested to study these diagrams with those 

 given in the small-C theory. 



-10 -9 



-8 -7 



-4 -3 



1 



10 



Fig. 8(c) — y versus <p — by for QC = 0.2, k — 2.5, b for^i = 0.67^1 (max) and , 

 C = 0.15 (Case 16). 



