TILiVEUNG-WAVE TUBES 23 



largest value r can have is the mean helix radius a minus the wire radius. 

 In Fig. 3.14, the ratio of (E-/^-Py'^ for this largest allowable radius to 

 (E'/^'Py^ at the surface of the developed sheet is plotted vs. d/p. We see 

 that, in terms of maximum available field, {E-/(3-Py'^ is no more than 0.83 as 

 high as for the sheet for four turns per wavelength and 0.67 as high as for the 

 sheet for two turns per wavelength. We further see that there is an optimum 

 ratio of wire diameter to pitch; about 0.175 for four turns per wavelength 

 and about 0.125 for two turns per wavelength. Because the maxima are so 

 broad, it is probably better in practice to use larger wire, and in most tubes 

 which have been built, d/p has been around 0.5. 



In designing tubes it is perhaps best to do so in terms of field on the axis 

 (Fig. 3.13), the allowable value of r/a and the curves of Fig. 3.6. 



Figure 3.15 compares the impedance of the developed helix with that of 

 the developed sheet as given by the straight line of Fig. 3.7. 



There are factors other than wire size which can cause the value of E'/jS-F 

 for an actual helix to be less than the value for the helically conducting 

 sheet. An important cause of impedance reduction is the influence of di- 

 electric supporting members. Even small ceramic or glass supporting rods 

 can cause some reduction in helix impedance. In some tubes the helix is 

 supported inside a glass tube, and this can cause a considerable reduction 

 in helix impedance. 



When a field analysis seems too involved, it may be possible to obtain 

 some information by considering the behavior of transmission lines having 

 parameters adjusted to make the phase constant and the characteristic im- 

 pedance equal to those of the helix. For instance, suppose that the presence 

 of dielectric material results in an actual phase constant ^d as opposed to a 

 computed phase constant /S. Equation (3.64) gives an estimate of the con- 

 sequent reduction of {E~/ff-Pyi^ on the axis. 



This method is of use in studying the behavior of coupled helices. For 

 instance, concentric helices may be useful in producing radial fields in tubes 

 in which transverse fields predominate in the region of electron flow (see 

 Chapter XIII). A concentric helix structure might be investigated by means 

 of a field analysis, but some interesting properties can be deduced more 

 ; simply by considering two transmission lines with uniformly distributed self 

 and mutual capacitances and inductances, or susceptance and reactances. 

 iThe modes of propagation on such lines are affected by coupling in a manner 

 similar to that in which the modes of two resonant circuits are afifected by 

 coupling. 



' If two lines are coupled, their two independent modes of propagation are 

 mixed up to form two modes of propagation in which both lines participate. 

 If the original phase velocities differ greatly, or if the coupling between the 

 ines is weak, the fields and velocity of one of these modes will be almost 



