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BELL SYSTEM TECHNICAL JOURNAL 



9.4. Space Charge 



We will now consider the case in which QC 9^ 0. We will deal with this 

 case only for d = 0, and for h adjusted for maximum gain per wavelength. 



There is a peculiarity about this case in that a certain voltage V is applied 

 to the circuil at 2 = 0, and we want to evaluate the circuit voltage asso- 

 ciated with the increasing wave, Vd , in order to know the gain. 



Atz = 0,i = 0. Now, the term which multiplies i to give the space-charge 

 component of voltage (the second term on the right in (7.11)) is the same 

 for all three waves and hence at 2 = the circuit voltage is the total voltage. 

 Thus, (9.1)-(9.3) hold. However, after Vi has been obtained from (9.4), with 



0.2 



0.8 



1.0 



0.4 0.6 



QC 

 Fig. 9.4 — A vs QC for d = and b chosen for maximum gain of the increasing wave. 



V = Vi , V — i = 0, then the circuit voltage Vd must be obtained through 

 the use of (7.14), and the initial loss parameter is 



A = 20 1ogio| Vd/V\ (9.15) 



By using the apj^ropriate values of 8, the same used in plotting Figs. 8.1 

 and 8.7-8.9, the loss parameter A was obtained from (9.15) and plotted vs 

 QC in Fig. 9.4. 



9.5 Change in Loss 



We might think it undesirable in introducing loss to make the whole 

 length of the heli.x lossy. P'or instance, we might expect the power output 

 to be higher if the last part of the helix had low loss. Also, from Figs. 8.2 



