GriDKD-WAVK PROPAGATION THROUGH GYUOiMAGNETlC MEDIA 645 



where 



^o' = 1 - ' 



n' 



The radius of convergence of these series is not known. It is clear that it 

 will depend on a and Avill become smaller as o- -^1. 



4.2. The Plasma (pr, = 0, vn == I). The characteristic equation (26) 

 may now be written 



— , [XiF„(xiro) - 7i] = i- [X2F„(x2ro) - n], (63) 



xr X2^ 



where (in contrast with the ferrite case) Xi,2 = i8Ai,2 . The X satisfy 



^^j. _ {vE - 1)(1 - ^'M - v.p/ ^^^ _ ^2 = 0, (64) 



Pe 



and the x's are given by 



Xi.2^ = (1 — ^'/vn) — Ph\i.2 (65) 



From the equations for ps and ve in terms of a, q given in Section 2, 

 equation (64) may be written 



Xi/ - f j-^ - -/5^) X,2 - /3^ = 0, (66) 



X1X2 = -^' (67a) 



(67b) 



or 



Xi + Xo = -^ -<r^\ 

 I — q^ 



+ C7X1X2 . 



1 - g2 



Elimination of )3" between equations (64) and (65) enables us to express 

 Xi,2' solely in terms of Xi,2 , ph and vh : 



2 1 ~ Xl,2 



X1.2 = - 



] - 1/ve ^ 



i Ai,2 



PE 



which, from the plasma formulae for pe , ve , can be written 



2 1 ~ Xl,2 



xi/ = ^—^ . (68) 



1 — 0"Ai,2 



