58 BELL SYSTEM TECHNICAL JOURNAL 



These equations serve to determine the ratios of the /3's and to determine 

 7 through 



^^^' n — ^^^7 — \ "" (/So a cot St') . (22) 



ii(7Q;)Ai(7a) 



We can easily express the various field components listed in (6) through 

 (17) in terms of a common amplitude factor. As such expressions are useful 

 in understanding the nature of the field, it seems desirable to list them in 

 an orderly fashion. 



Inside the Helix: 



E, = BIoiyr)e'^'''~^'^ (23) 



Er = j^ ^ hMe'^"'-^'^ (24) 



7 



h^ = -B — — - — -^ h{yr)e' (25) 



■'1(70) cot yp 



"■ = -' I «" '¥\ 7^, 'M'""-'-' (26) 



k (80 /i(7«) cot ^p 



^' = 11 r^! 4-, hiyrV'"-'" (27) 



k /3o hiya) cot r^ 



//* = ;• f ^^ I{yr)e'''''-''\ (28) 



^ 7 



Outside the Helix: 



E, = B —-. — - Ko{yr)e' 

 Ko{ya) 



(29) 



Here 



E.= -jB^-^^K,{yr)e^^^^-^'^ (30) 



7 An(7«) 



£* = -^ i?-? — N — ^, Ai(7r)e (31) 



Ki{ya) cot ^ 



k po Ki{ya) cot ^ 



k Ki{ya) cot ^ 



Z/* =-_;-- — - — - Ki{yr)e' (34) 



yfe 7 A 0(70) 



ife = Vm/c = 120 TT ohms (35) 



