134-4 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



gain in the attenuator is a small fraction of the total gain in the tube so 

 that the over-all gain is not particularly sensitive to the means we use 

 for treating the attenuator. Essentially what we have done is to con- 

 sider the high loss part of the attenuator as a severed helix region and 

 the low loss part of the attenuator as a lossy helix region. 



Fig. 48 shows the value of the growing wave parameter as a function 

 of the loss parameter d for various values of QC as calculated from theory. 

 Because of discontinuity losses to the growing wave as it propagates in 

 a region of gradually increasing loss, the actual gain will be less than 

 that calculated from Fig. 48. Some rather crude probe measurements 

 have indicated that the effective x vs. d curve can be approximated by 

 a straight line through the d = and d = 1 points — the dotted line in 

 Fig. 48. 



Since the helix is effectively severed by the high loss portion of the 

 attenuator we must subtract some discontinuity loss from the gain in 

 the attenuator region. The effective drift length in the severed region 

 is unknown so this discontinuity loss cannot be accurately calculated 

 from the low-level theory. The discussion in chapter nine of Pierce^ 

 indicates that an average value of about 6 db is reasonable. 



An alternate method of treating the attenuator was also tried. In this 

 calculation, the x vs. d curves in Fig. 48 were assumed to be correct to 



0.9 

 0.8 

 0.7 

 0.6 

 0.5 

 0.4 



0.3 



0.2 

 0.1 



0.4 



0.8 



1.2 



1.6 



2.0 



d 



2.4 



2.8 



3.2 



3.6 



4.0 



Fig. 48 — Curves of growing wave parameter x as a function of loss parameter 

 d showing approximation (dotted lines) used in gain calculations for the M1789. 



