GUIDED WAVE PKOPACATIOX THROUGH GYROMAGNETIC MEDIA. II 949 



at which matching will be necessary are surfaces parallel to the 7/-axis 

 and here we need an expression for Hx^nJEy where i/tane is a tangential 

 magnetic field at the surface. For the moment we will consider the 

 admittance looking into the ferrite and take tangential components in 

 the counterclock^^^se sense. From equation (4), then, 



■^tang _ Ey dv _ Ey da (7) 



where d/(dv) is a normal derivative (outward) and 8/ (da), a tangential 

 derivative. It is possible, although by no means essential, to interpret 

 the terms of (7) in the following fashion: the first term is just the admit- 

 tance of a normal TE mode propagating in the interior of the ferrite 

 (which is to have the permeability, ii^s) ; the second term is to be ascribed 

 to an independent surface current, 



da 



)(m- — K-) 



Using this picture one may see how non-reciprocity arises in a simple 

 case. If the ferrite be bounded by the planes x = Xi and a; = X2 , and the 

 2-variation is of the form e~^^^, the admittances due to the surface cur- 

 rents are -\-JK(3/<j:(iJi' — k ). If jS reverses its sign the surface currents are 

 interchanged. If now the external admittances on the two sides of the 

 slab are unequal (and, of course, themselves reciprocal) for given values 

 of w and \ \, there is no reason why jS and — /3 should simultaneously 

 solve the matching problem. 



Almost all the above considerations may be taken over to the case of 

 the plasma. Here the TE fields ^^^ll be undisturbed by the magnetic field 

 (but the dielectric constant is altered by the presence of the charge 

 from its free space value). Equations (4) and (5) are now replaced by 



Me'-r,'~)E.= -^~' + JV^-§, (8a) 



Me' - r,')E. = jrj ^^ -f e ^\ (8b) 



dz ax 



^ Hy d Hy 2 e — ri „ _ . . 



for the TM fields. Here e and rj are the diagonal and off-diagonal terms 

 of the dielectric matrix which is of the same form 



