To the theory of helical waveguides

TL;DR

This paper extends the theoretical understanding of helical waveguides by deriving new formulas for wave behavior when a dielectric core is present, including the slowing factor and wave impedance.

Contribution

It provides the first calculation formulas for helical waveguides with dielectric cores, filling a gap in existing theory.

Findings

Derived formulas for wave impedance in helical waveguides.

Obtained an equation for the slowing factor with dielectric core.

Proposed a numerical method for solving the slowing factor equation.

Abstract

It makes sense to consider a helical waveguide with a fine pitch approximately, replacing the turns with anisotropic conductivity: infinite along the turns and zero across them. This approach has been known for a long time, but calculation formulas within it have only been obtained for the case where the winding does not contain a dielectric core. This paper addresses this gap in the theory: calculation formulas are obtained for the case where the waveguide contains a dielectric with a certain permittivity and magnetic permeability. An equation determining the slowing factor is found, and a method for its numerical solution is proposed. Explicit formulas are obtained for the wave impedance.