COUPLED HELICES 141 



helix only at the far left side of the sketch. One, perfectly legitimate, 

 view of the situation is that the RF power, initially all on the outer helix, 

 leaks into the inner helix because of the coupling between them, and then 

 leaks back to the outer helix, and so forth. 



Apart from noting the appearance of the stationary spatial beat (or 

 interference) phenomenon these additional facts are of interest: 



1) It is a simple matter to excite such a beat- wave, for instance, by 

 connecting a lead to either one or the other of the helices, and 



2) It should be possible to discontinue either one of the helices, at 

 points where there is no current (voltage) on it, without causing reflec- 

 tions. 



2.6 A Simple Estimate of h and x 



How strong a coupling can one expect from concentric helices in prac- 

 tice? Quantitatively, this is expressed by the values of the coupling fac- 

 tors X and h, which we shall now proceed to estimate. 



A first crude estimate is based on the fact that slow-wave fields are 

 known to fall off in intensity somewhat as c where (3 is the phase con- 

 stant of the wave and r the distance from the surface guiding the slow 

 wave. Thus a unit charge placed, say, on the inner helix, will induce a 

 charge of opposite sign and of magnitude 



-Pib-a) 



on the outer helix. Here h = mean radius of the outer helix and a = 

 mean radius of the inner. We note that the shunt mutual admittance 

 coupling factor is negative, irrespective of the directions in which the 

 helices are wound. Because of the similarity of the magnetic and electric 

 field distributions a current flowing on the inner helix will induce a simi- 

 larly attenuated current, of amplitude 



on the outer helix. The direction of the induced current will depend on 

 whether the helices are woimd in the same sense or not, and it turns out 

 (as one can verify by reference to the low-freciuency case of coaxial 

 coupled coils) that the series mutual impedance coupling factor is nega- 

 tive when the helices are oppositely wound. 



In order to obtain the greatest possible coupling between concentric 

 helices, both coupling factors should have the same sign. This then re- 

 fiuires that the helices should be wound in opposite directions, as has 

 been pointed out by Pierce. 



When the distance between the two helices goes to zero, that is to say, 



