168 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



been att-aiiu>(l iiur can it l)c expected. Nevertheless, the kind of physical 

 phenomena occurring with coupled helices are, at least, qualitatively 

 described here and should permit one to develop and construct various 

 types of (lexices with fair chance of success. 



ACKNOWLEDGEMENTS 



As a final note the authors wish to express their appreciation for the 

 patient work of Mrs. C. A. Lambert in computing the curves, and to 

 G. E. Korb for taking the experimental data. 



Appendix i 

 i. solution of field equations 



In this section there is presented the field equations for a transmission 

 system consisting of two helices aligned with a common axis. The propa- 

 gation properties and impedance of such a transmission system are dis- 

 cussed for various ratios of the outer helix radius to the inner helix radius. 

 This system is capable of propagating two modes and as previously 

 pointed out one mode is characterized by a longitudinal field midway 

 between the two helices and the other is characterized by a transverse 

 field midway between the tw^o helices. 



The model which is to be treated and shown in Fig. 2.3 consists of an 

 inner helix of radius a and pitch angle \pi which is coaxial with the outer 

 helix of radius 6 and pitch angle \j/2 . The sheath helix model will be 

 treated, wherein it is assumed that helices consist of infinitely thin sheaths 

 which allow for ciuTent flow- only in the direction of the pitch angle \p. 



The components of the field in the region inside the inner helix, be- 

 tween the two helices and outside the outer helix can be written as 

 follows — inside the inner helix 



H,, = BrIoM (1) 



E., = B^hM (2) 



H,, = j - BMyr) (3) 



7 



Hr, = ^^ BMyr) (4) 



7 



E,, = -j "^ BMyr) (5) 



7 



Er, = -^ BJ,(rr) (()) 



7 



