COUPLED HELICES 169 



and between the two helices 



H,, = BMrr) + BJuirr) ' (7) 



E., = BJoiyr) + B^oiyr) (8) 



H,, = ^~ [B,h(yr) - B^^(yr)] (9) 



7 



Hr, = -^ [53/1(7/0 - BJuiyr)] (10) 



7 



E,, = - J ^ [B^hiyr) - BJuiyr)] (11) 



7 



Er, = -^ [BMyr) - BJv,{yr)\ (12) 



7 



and outside the outer hehx 



H.^ = B,Ko(yr) (13) 



E,, = 58/vo(7r) (14) 



^.s = -J- BsK,{yr) (15) 



7 



Hr, = ^^ 5,Ki(7r) (16) 



7 



^,, = i — BJuiyr) (17) 



7 



^r« = ^^ 58Ki(7r) (18) 



7 



With the sheath helix model of current flow only in the direction of wires 

 we can specify the usual boundary conditions that at the inner and outer 

 helix radius the tangential electric field must be continuous and per- 

 pendicular to the wires, whereas the tangential component of magnetic 

 field parallel to the current flow must be continuous. These can be written 

 as 



E, sin t/' + E^ cos ^ = (19) 



' E, , E^ and (H, sin \f/ -f H^ cos \p) be equal on either side of the helix. 

 By applying these conditions to the two helices the following equations 

 are obtained for the various coefficients. 



