Coaxial Line with Helical Inner Conductor

Abstract

To obtain an approximate solution for the fields in a coaxial line with a helical inner conductor, the helix is replaced by a fictitious surface that is conducting only in the helix direction, an approximation used in the early work on traveling-wave tubes. Maxwell's equations are solved for the lowest mode (all fields independent of angle) when the medium inside the helix has permittivity and permeability different from that of the medium surrounding the helix. Equations for the velocity along the axis, characteristic impedance, attenuation constant, and Q are given. The significant parameter is (2?Na) (2?a/?). N=number of turns per unit length, a = helix radius, and ? = wavelength. When this parameter is considerably less than 1, the velocity and characteristic impedance depend only on the dimensions. The dielectric inside the helix has only a second-order effect, while the dielectric outside the helix has a first-order effect. The wave appears to propagate along the helix wire with the velocity of light only when the outer conductor is very close to the helix; as the outer-conductor diameter is increased, the apparent velocity along the wire gradually increases and reaches a limiting value when the outer conductor is infinitely large. For the shapes generally used, the apparent velocity along the wire is rarely more than 30 per cent greater than the velocity of light, but with an infinitely large outer conductor this velocity can be 2 or 3 times the velocity of light.