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BELL SYSTEM TECHNICAL JOURNAL 



from 2 for 6 = up to 5 for larger values of b. It is surprising how well this 

 agrees with corresponding values of 3 and 7 from Nordsieck's work. Moreover 

 (12.13) predicts an increase in efficiency with increasing QC. 



Thus, wc may expect the efficiency to vary with C from several points 

 of view. 



It is interesting to consider what happens if at a given frequency we change 

 the current. By changing the current while holding the voltage constant we 

 increase both the input power and the efficiency, for C varies as l\'^. Thus, 

 in changing the current alone we would expect the power to vary as the 4/3 

 power of /o 



P ^ /o'' (12.14) 



4 



_ 3 



I 2 



1 







Fig. 12.6 — According to a suggestion made by Slater, the velocity by which the elec- 

 trons are slowed down cannot be greater than twice the difference between the electron 

 velocity and the wave velocity. If we use the velocity difference given by the linear theory, 

 for zero loss {d = 0) this would make the efficiency parameter k equal to — 4vi. Here 

 — 4yi is plotted vs h for QC = 0. 



Here space charge has been neglected, and actually power may increase 

 more rapidly with current than (12.14) indicates. 



A variety of other cases can be considered. At a given voltage and cur- 

 rent, C and the efficiency rise as the helix diameter is made smaller. How- 

 ever, as the helix diameter is made smaller it may be necessary to decrease 

 the current, and the optimum gain will come at higher frequencies. For a 

 given beam diameter, the magnetic focusing field required to overcome 

 space-charge repulsion is constant if /o/Fo is held constant, and hence we 

 might consider increasing the current as the 1/2 power of the voltage, and 

 thus increasing the power input as the ?>/2 power of the voltage. On the other 

 hand, the magnetic focusing field required to correct initial angular deflec- 

 tions of electrons increases as the voltage is raised. 



There is no theoretical reason why electrons should strike the circuit. 

 Thus, it is theoretically possible to use a very high beam power in connec- 

 tion with a very fragile helix. Practically, an appreciable fraction of the 

 beam current is intercepted by the helix, and this seems unavoidable for wave 



