GUIDKD-W AVE PROPAGATION THROUGH GYROMAGNIOTIC MIODIA ()25 



to an infinite imaginary value and the associated fields are confined 

 very closely to the guide walls. The wall currents are very large and 

 essentially longitudinal. Type III cut-off points [1 ,i — (/,i)r] at Avhich 

 n = — ^:have|CJ' = 0, but the fields are not of a purely TE- or TM- 

 type. They consist essentially of a rotating, transverse, //, which is 

 uniform ovvv the guide. The components 11^ , Ee and Er are smaller 

 by one order of a — <rcut-off and E, , tAvo orders smaller. 



It should l)e stressed again that, in general, the modes are never of 

 pure TI'j or T^I type. Nevertheless, for the sake of brevity, we shall 

 refer to them as such; calling them TE-modes or TM-modes according 

 to their limit as the magnetization is removed. 



4.13. We now consider the behavior of the modes as a function of 

 radius. The reader will be aided by Figs. 8(a) to (e) and 9(a) to (g). In 

 preparation for this it is necessary to examine the movement of the 

 /„ , /,/ and 0„ , 0,/ curves w^hen Va is varied. It will be recalled that the 

 equation for the /„ curves and their reflections, /„', in the origin, is 



1 - X ^ Jn_ 



1 - (rX ro^' 



The contours xO^, o") = ^, where x^ = (1 — X )/(l — <x\) have already 

 been plotted in Fig. 4. The /„ , /„' curves are among these, and, clearly, 

 for a fixed n, the associated x" decreases as Vo increases. The course of a 

 given pair (/„ , /„') maj^ then be seen directly from Fig. 4. The cjualita- 

 tive behavior of the pair changes radically only when ro passes through 

 the^•alue j„ . Before it does so, /„ lies, for X between and 1, above o- = X 

 and tends to o- = ac as X tends to zero. At ro = j„ , the /„ and /„' curves 

 merge into the lines o- = X and X = 0. Beyond j„ , /„ lies below o- = X 

 for X between and 1 and goes to — ^c as X approaches zero. The /„'- 

 curve remains, throughout the reflection of /„ m the origin. As ro — > x^ , 

 In tends to the line X = 1, /„' to X = —1. No /„ curves ever enter the 

 region X > 1, a < 0; no /„' curves enter X < —1, cr > 0. It is also im- 

 portant to relate the /„ , /„' curves to the boundaries of the Polder 

 regions. /„ curves cut the Polder boundary o- = X — p, of the first quad- 

 rant in at most one point. As ro increases from to j„ , this point moves 

 from (T = (To to (T = 00 . Thereafter, no intersection occurs at fixed p until 

 ro equals j„/\^l — p^; it here reappears at cr = and moves steadily to 

 0- = 1 — p as ro increases indefinitely. The only intersection with the 

 other Polder boundary cr = 1/X, is at X = 1, cr = 1, regardless of ro . 

 The 0„ , 0,/ curves are gi\'en by 



;d 



2 



ro 



1 -X^ 



