GUIDED WAVK rii( )1'A(;ATI( )X TllHorciI CVKOMACXKTK' Ml.DI A. II *);>;) 



to l)e treated here, is a sheet of neghgible thickness, lying in the plane 

 X = 0, which conducts only in a single direction making an angle \p 

 with the //-axis. In this direction it will l)e supposed lossless. In addition 

 we assume that the i-egions, x < and < x < .ro are empty, while the 

 space .ri > .ro is hlled with ferrite. As usual the magnetic field is along 

 the 2/-axis and the fields are independent of //. The problem is clearly 

 the limit for very large radius of that of an empty, helically-conducting 

 c^'linder, surrounded by an infinitely thick shell of ferrite, circumfercn- 

 tially magnetized, the whole system carrying fields with no angular 

 \ariation. 



We first consider the boundary conditions for the plane helix, after 

 noting that it is evident that both TE and TM fields ^\'ill be required. 

 The tangential electric field on either side of the sheet must necessarily 

 be at right angles to the direction of conduction since the conductivity 

 is infinite. Further, the tangential electric field must be continuous through 

 the sheet. Hence, if the field normal to the direction of conduction is 

 £"0 (omitting here and elsewhere the factor e~^^^), we have 



^/ = Er = Eo cos lA, 



Ey'^ = Ey" = -Eosin^l/, 



where the symbols -j- and — refer to x > and x < respectively. 

 Again, since current cannot flow normal to the direction of conduction, 

 the tangential magnetic field along the latter must be continuous 

 through the sheet or 



(F,+ - H~) sin rp + (/// - Hy') cos lA = 0. 



The boundary conditions may be combined into a single equation, by 

 introducing admittances, in the form 



Hy _ Hy 



j:.+ E, 



(Hi _Hr\ 



\Ey+ Ey-j ' 



77-T - VT- I sill' "A = 



cos' ^. 



(16) 



The left-hand side refers to the TE fields and the right to TM fields. 

 In the empt}^ regions surrounchng the sheet 



^-, - (^^ - w-eoMo) 



H,. = 



dx' 



Hy = 0, 



E. = 



jweo dx 



and 



