GUIDED WAVE PROPAGATION TIIHorOH G VHOMAGNETIC MEDIA. II 081 



First Ave consider a waveguide, radius /n , into which is fitted a hollow 

 cylinder of ferrite, outer radius /o , inner radius ri . In that cylinder, the 

 magnetic field //; maj^ be taken to be a superposition /l*S'xo(2Q:2r) + 

 BR^o(2air) where, as before. 



a2 = /3" - co-€i/x(l - Ph); S{x) = --^ ; R{x) = — /^ 



0Ph 



0:2 may be either real or positive imaginary. [In choosing this combination 

 we depart from the usual practice of taking a superposition of Jo and 

 Nq in the isotropic case. Were we to follow this practice, it would be 

 necessary to define a new function R^f.CIjx^e^'''"'''^ + Ry^^{ — 2jx)e~^'''^ 

 to correspond to N^(x). Our choice corresponds to taking a combination 

 of Joix) and one of the Hankel functions Ho(x) in the isotropic case. 

 Since the functions H, J, N are linearly dependent, this will not affect 

 the results.] 



In view of the difference relations, equation (39) in Appendix I, 

 and of equation (29) we obtain for the impedance in the ferrite 



E^ ^ >M«2 U(i^ - x')S^ii:2a-2r) + B{2x - l)i?,i(2ct2r)] 



H, (J3'' - coVei) [AS^o{2a2r) + BRA2a2r)] 



A and B must be adjusted so that this quantity vanishes at ro , the guide 

 wall. This gives 



= -(2x - mi - xO 



]r,.i(2«2ro).¥,,i(2«2r) - J/,.i(2a2ro)Tf,,i(2c.2r) 

 (2,_i)TF,,i(2«2ro)ilf„o(2a2r) - (i^ - x')M^A2a,ro)WM^a.^) ' 



In the vacuum, between r = and r = ri , //j is /o(ao?') and the im- 

 pedance is EJH^ = —j(u:ixo/ao)Ii(aor)/Io(aor) where ao" = jS^ — coVeo • 

 At r = ri , the ferrite-vacuum interface, the two impedances must be 

 equal. Thus we obtain the characteristic equation 



Mo /i(ao'*i) A-, iN/i/ 2n a-M 



= (2x - l)(M - X ) 



ao loiaoTi) (3- — w-yuci 



ir,.i(2a2ro)Mx.i(2a2ri) - M ^ A2cc2ro)W ^ A'^a^n) 



(2x - m\A2a,r,)M^,o(2a,n) - (M - x')^1/.,i(2a2rn)Tr,,n(2a2/-i) ' 



(It is understood that for "normal" waveguide propagation a^ will be 

 imaginary, and the / will be replaced by ./). As a simple illustration we 



