(;riDKD-wAVE PROi'AGATiox TJiKorcu <;yi{()ma(;n"kth' .mi;i)I.\ (117 



-0.4 -0.2 



0.2 0.4 



P"ig. 10(a) ■ — /S^ versus p for small values of a — the TEu-limit mode. 



clearly equal to the finite (negative) G(Xi , a) somewhere between. This 

 situation persists up to a- = o-q — and a solution curve therefore exists 

 between o- = and a — o-q . It meets a- = for Xi satisfying 



1 



Xi- 





1 



X.^ 



^ F(ro \/r^^-) - 1 



LA2 



and 



Xi + X2 = p. 



im 



These equations have been solved numerically; the corresponding (3"^ 

 = — X1X2 is shown in Fig. 10(a). For ro between Ui and^i a value derived 

 for (3^ from the first three terms of an expansion of jS" in powers of p, 

 equation (01), turns out to be in very good agreement with the numerical 

 calculation up to p = 1, for a = and presumably is good for small a. 

 At (To (the point at which /x becomes negative), the solution curve is 

 "cutoff". However, the corresponding jS^ is not zero. As o-q is approached 

 from below G(Xi , a) -^0 and so G'(X2 , a) tends to zero. Thus, X2 tends to 



