GUIDED-WAVK riU)l'A(iA TION TllKorCII GYKOMAGNETIC MEDIA (ill) 



-VSa 



dG 



TIui perturbed (^(^2 ,o") which (since 6'(A2o , co) = 0) is 5X> + 0(6(t) 



5X20 



equals the preceeding expression and gives 



dXo = -\/5 



Aio TT r 0*0 

 oA] 



According]}', 6/3" 



dGV' 



axTo, 



+ 0(5a-), a result which shows that /?" 

 tends to its terminal value along the vertical. It is clear analytically and 

 graphically that this mode persists as p ^ 0, and must be identified with 

 the only isotropic mode for this radius, namely TEu . No other branches 

 exist below cr = o-q , since G{Xi , o-) and G(T(\i), a) have opposite signs 

 except in the region just considered. 



The two solution curves considered so far are not the only ones; in 

 fact the infinity of sheets of the surface G(Ai , a) in the region bounded 

 by 7i , Oc and {Ia')t , Fig. 9(a), intersect the transformed sheets G(T{\i)cr) 

 in infinitel}^ many more curves. In the blank areas of that region the 

 G'-functions have equal sign, and all these areas must be carriers of solu- 

 tion curves, since in every one of them every single contour G(\i , a) = g 



0.02 



-1.0 -0.6 -0.6 -0-4 -02 0.2 0.4 0.6 0.8 1.0 



P 



Fig. 10(c) — (3^ versus p for small values of <r — the TEi2-limit mode. 



