152 THE BELL SYSTEM TECHXICAL JOURNAL, JANUARY 1956 



2.6 



2.4 



2.2 

 2.0 



i.8 



1.6 





u 



1.4 



i.2 



1.0 



0.8 



0.6 



0.4 



0.2 



o.t 



0.2 0.3 



0.4 0.5 



0.6 



0.7 



0.8 



0.9 



1.0 



1.1 



1.2 



/iofcOT^^ 



Fig. 2.7 — ^ The effect of dielectric material between coupled infinite radius 

 sheath helices on their relative coupling phase-constant shown as a function of 

 fiod/2 cot \pi . The effect of shielding on this relation is also indicated. 



condition for coupling is not necessarily associated with equal \'elocities 

 on the uncoupled helices. 



2.12 Mode Impedance 



Before leaving the general theor_y of coupled helices something should 

 be said regarding the impedance their modes present to an electron beam 

 traveling either along their axis or through the annular space between 

 them. The field solutions for cross woimd, coaxiall}^ coupled helices, 

 which are given in Appendix I, have been used to compute the imped- 

 ances of the transverse and longitudinal modes. The impedance, /v, is 

 defined, as usual, in terms of the longitudinal field on the axis and the 

 power flow along the system. 



