and we may assume 



APPENDIX VII 459 



,+i|)y'^i (12) 



Thus, we may take Ks as the ordinate of Fig. 5 multiphed by c/u^) , from 

 (3), for instance. 



The true impedance may be somewhat less than the impedance for a 

 helically conducting sheet. If the ratio of the circuit impedance to that of a 

 helically conducting sheet is known (see Sections 3 and 4.1 of Chapter III, 

 and Fig. 3.13, for instance), the value of Ks from Fig. 5 can be multiplied 

 by this ratio. 



A7.5 The Space-Charge Parameter Q 

 The ordinate of Fig. 4 of Appendix VI shows <3s — ( 1 + ( — ) I vs. 



I^e \ VTo/ / 



ya for several values of b/a. Here <2,, is the effective value of Q for a solid 

 beam of radius b. As before, for beam voltages of a few thousand or lower, 

 we may take 



The quantity j8e is just 



ft ='^ (13) 



and from (8) we see that for low beam voltages we can take 



I3e = y = 70 

 so that the ordinate in Fig. 4 can usually be taken as simply Qs. 



A7.6 The Increasing Wave Parameter B 



In Fig. 8.10, B is plotted vs. QC. C can be obtained by means of Sections 

 3 and 4, and Q by means of Section 5. Hence we can obtain B. 



A7.7 The Gain Reduction Parameter a 



From (2) we see that we should subtract from the gain of the increasing 

 wave in db a times the cold loss L in db. In Fig. 8.13 a quantity dxi/dd, 

 which we can identity as a, is plotted vs. QC. 



A7.8 The Loss Parameter d 



The loss parameter d can be expressed in terms of the cold loss, L in db. 



