THE NATURE OF THE WAVES 



409 



tube, 70 = 2.8 and C is about .025. Thus, if we take the effective beam 

 radius as .5 times the helix radius, Q = 5.6 and QC = .14. 



We note from (7.14) that Q is the ratio of a capacitive impedance to 

 {E-/0-P). In obtaining the curves of Fig. 8.12, the value of {E'/^-P) for a 

 helically conducting sheet was assumed. This is given by (3.8) and (3.9). 

 If {E^/l3^P) is different for the circuit actually used, and it is somewhat 

 different, even for an actual helix, Q from Fig. 8.12 should be multiplied 

 by (E^/lS^P) for the helically conducting sheet, from (3.8) and (3.9), and 

 divided by the value of {E-/l3~P) for the circuit used. 



600 

 400 



200 



100 

 80 

 60 



1 



1.0 

 0.8 

 0.6 



7a 

 Fig. 8.12 — Curves for obtaining Q for a helically conducting sheet and a hollow beam. 

 The radius of the helically conducting sheet is a and that of the beam is a\. . 



8.4 Differential Relations 



It would be onerous to construct curves giving 5 as a function of h for 

 many values of attenuation and space charge. In some cases, however, 

 useful information may be obtained by considering the effect of adding a 

 small amount of attenuation when QC is large, or of seeing the effect of 

 space charge when QC is small but the attenuation is large. We start with 

 (7.13) 



