NATUEE OF POWER SATURATION IN TRAVELING WAVE TUBES 865 



3.5 



3.0 



2.5 



2.0 



c 



1.5 



(.0 



0.5 



• ^ 



• \ 



\ 



,j 



.. ^, 



\ 

 \ 

 S 



V 



0.2 



0.4 



0.6 



0.8 



1.0 1.2 



7ro 



1.4 



1.6 



1.8 



2.0 



2.2 



Fig. 16 — Efficiency versus 7ro for small QC. The dashed curve is proportional 

 to the amount of beam current in the circuit field strength having at least 85 per 

 cent of the intensity at the edge of the beam. This illustrates the fact that for 

 large beams only the edge of the beam is effective. 



that with the reasonable vahies of QC = .25 and 7ro = 0.8 {kr = 2.5), 

 the efficiency would be about 3.8C, whereas the measured value is 3.1C. 

 2. The largest discrepancy in the measured and computed value of 

 r]/C is for large values of yro (small kr), where the computations show a 

 steady increase in efficiency instead of a sharp decrease. This arises be- 

 cause the computational model assumed the electric field to be uniform 

 across the beam, whereas in the actual tube it varies as loiyr), and for 

 large values of 77-0 the field is weak near the beam axis. This effect is 

 shown in Fig. 16 where rj/C is plotted versus yro for small values of QC, 

 on the same scale with a curve proportional to the square of the fraction 

 of the beam within a cylindrical shell such that 



1 - 



Io(yn) 

 hiyro) 



= 0.85 



(11) 



where ri is the inside radius, and ro the outside beam radius (i.e., the 

 fraction of the beam in a field greater than 85 per cent of that at the 

 beam edge). 



No serious studies of velocity were made for large beams, but on cur- 

 sory examination it was evident that the beam modulation varied con- 

 siderably over the cross section when the beam was very large, and 

 scarcely at all when it was smaller than around yro < 0.8. 



