Circular Electric Wave Propagation in Periodic Structures

Abstract

TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> propagation in helix waveguide and spaced-ring guide is analyzed for frequencies where the wavelength is comparable to the period of the structures. By conformal mapping the boundary value problem is reduced to that of a waveguide with smooth walls but inhomogeneous dielectric lining. The lining modifies the magnetic field near the wall and changes the distribution of eddy currents and heat losses in the wires. As frequency increases, the field penetrates more into the space between wires, the eddy currents are more evenly distributed and the heat loss decreases from its quasistatic value of, for example, 10 per cent more than in plain waveguide to only 5 per cent more. Any substantial increase in heat loss occurs only when the wavelength is shorter than the period of the structure. Due to the periodicity, there are stop-bands when any number of half wavelengths just fit into the period. The relative width of the stop-band and its maximum attenuation per period are independent of waveguide diameter and period length and are only functions of the relative geometry of the section. Because of the stop-bands being so narrow and their attenuation being quite modest, one may well accept them within the range of operating frequencies.