Propagation of Electromagnetic Waves Guided by the Anisotropically Conducting Model of a Tape Helix Supported by Dielectric Rods

Abstract

Abstract-The practically important case of a dielectric-loaded tape helix enclosed in a coaxial perfectly conducting cylindrical shell is analysed in this paper. The dielectric-loaded tape helix for guided electromagnetic wave propagation considered here has infinitesimal tape thickness and infinite tape-material conductivity. The homogeneous boundary value problem is solved taking into account the exact boundary conditions similar to the case of anisotropically conducting open tape helix model [1,2]. The boundary value problem is solved to yield the dispersion equation which takes the form of the solvability condition for an infinite system of linear homogeneous algebraic equations viz., the determinant of the infiniteorder coefficient matrix is zero. For the numerical computation of the approximate dispersion characteristic, all the entries of the symmetrically truncated version of the coefficient matrix are estimated by summing an adequate number of the rapidly converging series for them. The tape-current distribution is estimated from the null-space vector of the truncated coefficient matrix corresponding to a specified root of the dispersion equation.

Propagation of electromagnetic waves guided by perfectly conducting model of a tape helix supported by dielectric rods

“…We make use of the dielectric loaded tape helix structure mentioned in [7], except that, the wedge-shaped dielectric support rods are replaced by a rectangular shaped support structure. Accordingly, we consider a tape helix of infinite length, constant pitch, constant tape width, infinitesimal tape thickness and infinite tape material conductivity surrounded by a dielectric of effective permittivity ɛ eff , enclosed in a coaxial metallic outer conductor as in [7]. In the cylindrical coordinate system with coordinates (ρ, j, z), the z-coordinate is chosen as the tape helix axis as shown in Fig.…”

“…The radius of the helix and the inner radius of the outer cylindrical conductor from the axis of the tape helix are a and b, respectively, with the tape pitch p, the tape width in the axial direction w, and the pitch angle c being defined as cot c = 2pa/p. The notation and terminology employed are as in [7] to make the work tractable.…”

“…The work was extended for perfectly conducting model of open tape helix SWSs by Kalyanasundaram and Babu [5,6] in which the perpendicular component of the surface tape current density is considered for the analysis. In [7], the method of determining the dispersion equation for the practically important case of an anisotropically conducting dielectric-loaded tape-helix enclosed in a coaxial perfectly conducting cylindrical shell was proposed. The work done by Kalyanasundaram and Babu [7] on anisotropically conducting dielectric loaded model is extended to the perfectly conducting model wherein the tape is modelled to be infinitesimally thin and perfectly conducting in all directions of the tape surface but without taking the ill-posed nature of the resulting boundary value problem into account.…”

“…In [7], the method of determining the dispersion equation for the practically important case of an anisotropically conducting dielectric-loaded tape-helix enclosed in a coaxial perfectly conducting cylindrical shell was proposed. The work done by Kalyanasundaram and Babu [7] on anisotropically conducting dielectric loaded model is extended to the perfectly conducting model wherein the tape is modelled to be infinitesimally thin and perfectly conducting in all directions of the tape surface but without taking the ill-posed nature of the resulting boundary value problem into account. Failure to regularise the ill-posed problem before seeking a solution invalidates the numerical computation of the dispersion characteristic in [5] and the tape-current distribution in [4].…”

Large-Signal Field Analysis of a Linear Beam Traveling Wave Amplifier for a Sheath-Helix Model of the Slow-Wave Structure Supported by Dielectric Rods. Part 1: Theory

“…Work on a large-signal field theory for a linear beam travelling wave tube amplifier (TWTA) making use of the dielectric-loaded tape-helix model analysed in [20] for the slow-wave structure is in progress and will be reported in due course.…”