Abstract
A new concept of metal spiral coaxial cable is introduced. The solution to Maxwell’s equations for the fundamental propagating TEM eigenmode, using a generalization of the Schwarz-Christoffel conformal mapping of the spiral transverse section, is provided together with the analysis of the impedances and the Poynting vector of the line. The new cable may find application as a medium for telecommunication and networking or in the sector of the Microwave Photonics. A spiral plasmonic coaxial cable could be used to propagate subwavelength surface plasmon polaritons at optical frequencies. Furthermore, according to the present model, the myelinated nerves can be considered natural examples of spiral coaxial cables. This study suggests that a malformation of the Peters angle, which determines the power of the neural signal in the TEM mode, causes higher/lower power to be transmitted in the neural networks with respect to the natural level. The formulas of the myelin sheaths thickness, the diameter of the axon, and the spiral g factor of the lipid bilayers, which are mathematically related to the impedances of the spiral coaxial line, can make it easier to analyze the neural line impedance mismatches and the signal disconnections typical of the neurodegenerative diseases.
Highlights
The coaxial cable invented by Heaviside [1] is a transmission line composed of an inner conductor surrounded by an insulating layer and an outer conducting shield
This study suggests that a malformation of the Peters angle, which determines the power of the neural signal in the transverse electric magnetic (TEM) mode, causes higher/lower power to be transmitted in the neural networks with respect to the natural level
The two-wire transmission line used in conventional circuits is inefficient for transferring electromagnetic energy at microwave frequencies because the fields are not confined in all directions, the energy escapes by radiation, and it has large copper losses due to its relatively small surface area
Summary
The coaxial cable invented by Heaviside [1] is a transmission line composed of an inner conductor surrounded by an insulating layer and an outer conducting shield. The spiral coaxial cable (SCC) discussed in this paper has many advantages with respect to the other types of transmission lines; first of all the elm energy can be distributed efficiently over a larger area, reducing all the undesired aforementioned effects. In view of the nature of the boundary surface, it is convenient to separate these field equations into components parallel and transverse to the waveguide z-axis. This is achieved by scalar and vector multiplication of (1) with êz, a unit vector in the z direction, obtaining. Because of the relationship between E⊥⃗ and H⃗⊥, the Poynting vector Sz will be
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