HELIX WAVEGUIDE 1349 



cumferential current flow at the boundary wall. All other modes in round 

 guide have a longitudinal current present at the wall. Thus the desired 

 attenuation properties can be obtained by providing a highly conducting 

 circumferential path and a resistive longitudinal path for the wall cur- 

 rents. This is done in the spaced-disk line by sandwiching lossy layers 

 between coaxially arranged annular copper disks. ^ Another possibility 

 which has been suggested is a helix having a small pitch. 



Helix waveguide, formed by winding insulated wire on a removable 

 mandrel and coating the helix with lossy material, has been made at the 

 Holmdel Radio Research Laboratory. Wires of various cross sections 

 and sizes have been used to wind helices varying from 3^ to 5 inches in 

 diameter, which have been tested at frequencies from 9 to 60 kmc/s. 

 Pitch angles of from nearly 0° (wire in a plane perpendicular to the axis 

 of propagation) to 90° (wire parallel to the axis of propagation) have 

 been used. The helices having the highest attenuation for the unwanted 

 modes while maintaining low loss for the TEoi mode are those wound 

 with the smallest pitch from insulated wire of diameter 10 to 3 mils 

 (American Wire Gauge Nos. 30 to 40). The high attenuation properties 

 for unwanted modes also depend markedly on the electrical properties 

 of the jacket surrounding the helix. 



In this paper the normal modes of helix waveguide are determined 

 using the sheath helix approximation, a mathematical model in which 

 the helical winding is replaced by an anisotropic conducting sheath. A 

 brief formulation of the boundary value problem leads to an equation 

 which determines the propagation constants of modes in the helix guide. 

 Since the equation is not easy to solve numerically, approximations are 

 presented which show the effects of the pitch angle, the diameter, the 

 conductivity and dielectric constant of the jacket, and the wavelength, 

 when the conductivity of the jacket is sufficiently high. 



By proper choice of the pitch angle and, in some instances, of the 

 polarization, a helix waveguide can be made to propagate any mode of 

 ordinary round guide, with an attenuation constant which should be 

 essentially the same as in solid copper pipe. The pitch is chosen so that 

 the wall currents associated with the desired mode follow the direction 

 of the conducting wires. The losses to the other modes are in general 

 much higher, and are determined by both the pitch angle and the jacket 

 material. 



Special attention is given in the present work to the limiting case of a 

 helix of zero pitch, since the attenuation constant of the TEoi mode will 

 be smallest when the pitch angle is as small as possible. To explore the 



^ Reference 3, p. 1111. 



