COUPLED HELICES . 137 



other and back. We started, arbitrarily, with all the voltage on the outer 

 helix at 2 = 0, and none on the inner; after a distance, z', which makes 

 the argument of the cosine x/2, there is no voltage on the outer helix 

 and all is on the inner. 



To conform with published material let us define what we shall call 

 the "coupling phase-constant" as 



^, = ^{h + x) (2.3.8) 



From (2.3.3) we find that for (Si = ^2 = |S, and x = h, 



Tt - Ti = jl3c 



2.4 Non-Synchronous Helix Solutions 



Let us now go back to the more general case where the propagation 

 velocities of the (uncoupled) helices are not equal. Eciuation (2.2.5) can 

 be written: 



Further, let us define 



(2.4.1) 



r- = -^- [1 + (1/2)A + xb ± 



V(l + xb)A + (1/4)A2 + (6 + xy] 

 where 



L /3 _ 

 In the case where x = h, (2.4.1) has an exact root. 



r,, , = j^ [Vl + A/4 ± 1/2 Va + (a; + by] (2.4.2) 



We shall be interested in the difference between Tt and Tt, 



Tt-Tf = j^ Va + (x + by- (2.4.3) 



Now we substitute for A and find 



Tt- Tc = j V(^i - ^2y + ^M& + 4' (2.4.4) 



Let us define the "beat phase-constant" as: 



Pb = V(/3i - /32)2 + nb + xy 



so that 



r, - r, = jA (2.4.5) 



(3a = \ i5i - iSo 



