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BELL SYSTEM TECHNICAL JOURNAL 



s and / arc plotted as a function of d in V\g. A6.3. Tlie value of Yen using 

 these values of i- and / is compared in Fig. A6.2 with Ye in the vicinity of 

 where I\. is almost tangent to Ye for two typical sets of operating conditions. 



1000 

 800 



600 

 400 



100 

 80 



60 

 40 





f?Ic!?; 6 



1.0 

 0.8 



0.6 



0.4 



7oa 



Fig. A6.4 — Passive mode parameter Qs for a solid beam of electrons of radius h inside 

 a helix of radius a and natural propagation constant 70 , obtained from the equivalent 

 hollow beam parameters of Fig. 3 taken at 7^ = 70 . All the normal mode solutions which 

 have been found*-^' *^' for a hollow beam will be approximately valid for a solitl beam if Q 

 is replaced l)y Q, and A' is replaced by ATj (Fig. 5). 



It is of course |)()ssible to ])ick other criteria for determining an "equiva- 

 lent" hollow beam. In Chapter XI\', in essence, I',, and I',// were e.xpanded 

 in terms of (1 — »-) and the coelTicients of the first two terms were equated. 

 This has been done for the cylindrical beams, and the values of 5 and / found 

 by this method determine values of Y,n shown in Fig. A6.2. The greater 



