COUPLED HELICES 177 



Now J at is equal to the discontinuity in the tangential component of 

 magnetic field which can be written at r = a 



J at = {H,z cos ^i — //^5 sin \pi) — (H,i cos i/'i - H^o sin \f/i) 



\^'hich can be written as 



Ja( = - (H,i - H,3)a((cot i/'i + tau xj/i) slu \Pi (38) 



and similarily at r = h 



Jb( = — (H^7 — H,s)b({cot \p2 + tan 4^2) sin i/'2 (39) 



Equations (38) and (39) can be combined with (37) to give as the condi- 

 tion for complete power transfer 



At = -At (40) 



where 



^ = V (yay / ni) 



(T J^ _i- r V \( T? (/3oa cot <Ai)'^ cot 1^2 „ \ 

 \ {yo,y cot i/'i / 



In (40) At is obtained by substituting jt into (41) and At is obtained by 

 substituting 7 < into (41). 



The value of cot i/'o/cot i/'i necessary to satisfy (40) is plotted in Fig. 

 2.8. 



In addition to cot i/'o/cot i/'i it is necessary to determine the interference 

 wavelength on the helices and this can be readily evaluated by consider- 

 ing (36) which can now be written 



or 



/, = /,,.-«^'+^''-''^> cos ^ilJZ^ , (48) 



and 



J, = J.ce-'''^'^'^''"' cos M/3i^ (49) 



where we have defined 



iSfcO = {yta — jta) (50) 



This value of /S^ is plotted versus /3oa cot i/'i in Fig. 2.4. 



