GLIDKI) WAVK TROPAGATION TIIKOUGII GYEOMAGNETIC MEDIA. II 967 



familiar from the planar case; it depends on the magnetic; field and on 

 the propagation direction in a pin-ely reciprocal wny. The term pn^/r, 

 however, reverses sign when either magnetizing field or propagation 

 constant changes sign. The solntions of e({iiation (24) are therefore 

 different for opposite propagation directions (or opposite magnetiza- 

 tions). Thus, in contrast to the planar case, where non-reciprocity arose 

 only through the ])0undary conditions, the cylindi'ical case is inherently 

 non-reciprocal. 



In the absence of the last term in the bracket, equation (24) would 

 be solved by zero order Bessel fimctions, just like equation (21). In the 

 presence of this term, the solutions become confluent hypergeometric 

 functions. Different changes of ^'ariable bring these functions into forms 

 known by different names and notations. One such change leads to 

 Laguerre functions, another to AVhittaker functions. We shall choose 

 the latter representation, since it is closely related to Bessel functions, 

 and numerical tables seem about equally scarce for all representations. 

 In equation (24), let 13" — /3/ = a2 , and let a2r = y. Then it becomes 



l^/"'-U^^Ji)H. = 0, (25) 



ydydy \ y / 



where x = — /Spi//2a;2 . Further, let y = x/2, and H^(y) = h(x)/\/x; 

 then equation (25) becomes 



which is the standard form of the equation for zero order Whittaker 

 functions. It is a special case of the equation for ju order Whittaker 

 functions : 



/I 2 \ 



(27) 



The solution of equation (27) which is regular near zero is denoted in 

 the literature by MxA^)', it is proportional, in the limit x = 0, to the 

 Bessel function I^(x/2). The solution of equation (27) regular at infinity 

 is denoted by W^.^ix), and in the limit x = 0, is proportional to K^{x/2). 

 The factors of proportionality are found in Appendix I, 

 In this notation, the solutions for Hz are thus 



M^fiCIaiv) Wxfi{2a2r) 



* If /3 < /32 , ])oth argument and suffix x are imaginary. These functions are 

 then related to ./o and //o respectivelj'. 



