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BELL SYSTEM TECHNICAL JOURNAL 



attains its maximum value and starts to fall, power can still be transferred 

 to the circuit, though the increase of field with distance will no longer be 

 exponential. This makes it possible that the value of k given by (12.10) will 

 be exceeded. Actually, the true k calculated by Nordsieck is a little higher 

 than that given by (12.10). 



Let us now consider the efifect of loss. Figure 12.4 shows k from (12.10) 

 vs. diox b = QC = 0. We see that, as might be expected, the efficiency falls 

 as the loss is increased. C. C. Cutler has shown experimentally through un- 

 published work that the power actually falls off much more rapidly with d. 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



d 

 Fig. 12.4 — The efficiency parameter k calculated as in Fig. 12.3 but for 6 = (an elec- 

 tron velocity equal to the circuit phase velocity) and for various values of the attenuation 

 parameter d. Experimentally, the efficiency falls off more rapidly as d is increased. 



Finally, Fig. 12.5 shows k from (12.10) vs. QC, with J = and b chosen to 

 make Xi a maximum. We see that there is a pronounced rise in efficiency as 

 the space-charge parameter QC is increased. 



J. C. Slater has suggested in Microwave Electronics a way of looking at 

 energy production essentially based on observing the motions of electrons 

 while traveling along with the speed of the wave. He suggests that the elec- 

 trons might eventually be trapped and oscillate in the troughs of the sinu- 

 soidal field. If so, and if they initially have an average velocity Av greater 

 than that of the wave, they cannot emerge with a velocity lower than the 

 velocity of the wave less Av. Such considerations are complicated by the 

 fact that the phase velocity of the wave in the large-signal region will not 



