1328 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



The observed gain compares well with that calculated from low-level 

 TWT theory provided that we properly consider the effect of the helix 

 attenuator and provided that we assume a hi a of one-half. The method 

 we have used in calculating the Ml 789 gain is discussed further in 

 Appendix I. Fig. 32 compares the measured and calculated gain as a 

 function of beam current and Fig. 33 compares them as a function of 

 frequency. Fig. 34 shows measured and calculated ratios of voltage for 

 maximum gain to synchronous voltage as a function of beam current. 

 In all these figures calculations are shown for several values of the ratio 

 of effective beam diameter to mean helix diameter (6/a). We see that 

 the effective value of 6/a appears to be about one-half. On the basis of 

 measurements made by probing the beam of a scaled up version of a 



1.26 



1.24 



1.22 



1.20 



1.18 



1.16 



1.14 



V/Vs 



1.12 



1.10 



1.08 



1.06 



1.04 



1.02 



1.00 



10 15 20 25 30 35 40 45 50 



BEAM CURRENT IN MILLIAMPERES 



55 



60 



65 



70 



Fig. 34 — Measured and calculated ratio of voltage for maximum gain to syn- 

 chronous voltage as a function of beam current. The calculated curves are shown 

 for several values of the ratio of effective beam radius to mean helix radius (b/a). 

 The location of the measured curve among the calculated ones is taken as an 

 indication of the effective value of b/a in the M1789. At 40 ma it is about 0.5. 



