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BELL SYSTEM TECHNICAL JOURNAL 



Solving for h, we obtain 



" = ±1 2- 



f^-ff 



)/(?F^r- <--> 



The positive sign inside of the brackets always gives a real value of h 

 and hence unattenuated waves. The negative sign inside the brackets gives 

 unattenuated waves for small values of U/b. However, when 



© 



?v > I 



(16.20) 





1 2 4 6 8 10 20 40 60 80 100 200 400 600 1000 



Fig. 16.3 — The abscissa is proportional to d-c current. As the current is increased, the 

 gain in db per wavelength approaches 27.3b, where h is the fractional separation in ve- 

 locity. If the two electron streams are separated physically, the gain is lower and first rises 

 and then falls as the current is increased. 



there are two waves with a phase constant /3« and with equal and opposite 

 attenuation constants. 



Suppose we let U m be the minimum value of U for which there is gain. 

 From (16.20) 



U\ = &V8 (16.21) 



From (16.19) we have, for the increasing wave, 



1112 



(16.22) 



